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http://www.mathworks.com/help/physmod/sps/ref/asynchronousmachinewoundrotorfundamentalsi.html?requestedDomain=www.mathworks.com&nocookie=true | 1,508,753,114,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825889.47/warc/CC-MAIN-20171023092524-20171023112524-00780.warc.gz | 503,764,783 | 14,889 | Asynchronous Machine Wound Rotor (fundamental, SI)
Wound-rotor asynchronous machine with fundamental parameterization in SI units
Library
Machines / Asynchronous Machine (Wound Rotor)
Description
The Asynchronous Machine Wound Rotor (fundamental, SI) block models a wound-rotor asynchronous machine using fundamental parameters expressed in the International System of Units (SI). A wound-rotor asynchronous machine is a type of induction machine. All stator and rotor connections are accessible on the block. Therefore, you can model soft-start regimes using a switch between wye and delta configurations or by increasing rotor resistance. If you do not need access to the rotor windings, use the Asynchronous Machine Squirrel Cage (fundamental) or Asynchronous Machine Squirrel Cage (fundamental,SI) block instead.
Connect port ~1 to a three-phase circuit. To connect the stator in delta configuration, connect a Phase Permute block between ports ~1 and ~2. To connect the stator in wye configuration, connect port ~2 to a Grounded Neutral or a Floating Neutral block. If you do not need to vary rotor resistance, connect rotor port ~1r to a Floating Neutral block and rotor port ~2r to a Grounded Neutral block.
The rotor circuit is referred to the stator. Therefore, when you use the block in a circuit, refer any additional circuit parameters to the stator.
Electrical Defining Equations
The Asynchronous Machine Wound Rotor (fundamental, SI) converts the SI values that you enter in the dialog box to per-unit values for simulation. For information on the relationship between SI and per-unit machine parameters, see Per-Unit Conversion for Machine Parameters. For information on per-unit parameterization, see Per-Unit System of Units.
The asynchronous machine equations are expressed with respect to a synchronous reference frame, defined by
`${\theta }_{e}\left(t\right)=\underset{0}{\overset{t}{\int }}2\pi {f}_{rated}dt,$`
where frated is the value of the Rated electrical frequency parameter.
Park’s transformation maps stator equations to a reference frame that is stationary with respect to the rated electrical frequency. Park’s transformation is defined by
`${P}_{s}=\frac{2}{3}\left[\begin{array}{ccc}\mathrm{cos}{\theta }_{e}& \text{cos}\left({\theta }_{e}-\frac{2\pi }{3}\right)& \text{cos}\left({\theta }_{e}+\frac{2\pi }{3}\right)\\ -\mathrm{sin}{\theta }_{e}& -\text{sin}\left({\theta }_{e}-\frac{2\pi }{3}\right)& -\text{sin}\left({\theta }_{e}+\frac{2\pi }{3}\right)\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right],$`
where θe is the electrical angle.
The rotor equations are mapped to another reference frame, defined by the difference between the electrical angle and the product of rotor angle θr and number of pole pairs N:
`${P}_{r}=\frac{2}{3}\left[\begin{array}{ccc}\mathrm{cos}\left({\theta }_{e}-N{\theta }_{r}\right)& \text{cos}\left({\theta }_{e}-N{\theta }_{r}-\frac{2\pi }{3}\right)& \text{cos}\left({\theta }_{e}-N{\theta }_{r}+\frac{2\pi }{3}\right)\\ -\mathrm{sin}\left({\theta }_{e}-N{\theta }_{r}\right)& -\text{sin}\left({\theta }_{e}-N{\theta }_{r}-\frac{2\pi }{3}\right)& -\text{sin}\left({\theta }_{e}-N{\theta }_{r}+\frac{2\pi }{3}\right)\\ \frac{1}{2}& \frac{1}{2}& \frac{1}{2}\end{array}\right].$`
Park’s transformation is used to define the per-unit asynchronous machine equations. The stator voltage equations are defined by
`${v}_{ds}=\frac{1}{{\omega }_{base}}\frac{d{\psi }_{ds}}{dt}-\omega {\psi }_{qs}+{R}_{s}{i}_{ds},$`
`${v}_{qs}=\frac{1}{{\omega }_{base}}\frac{d{\psi }_{qs}}{dt}+\omega {\psi }_{ds}+{R}_{s}{i}_{qs},$`
and
`${v}_{0s}=\frac{1}{{\omega }_{base}}\frac{d{\psi }_{0s}}{dt}+{R}_{s}{i}_{0s},$`
where:
• vds, vqs, and v0s are the d-axis, q-axis, and zero-sequence stator voltages, defined by
$\left[\begin{array}{c}{v}_{ds}\\ {v}_{qs}\\ {v}_{0s}\end{array}\right]={P}_{s}\left[\begin{array}{c}{v}_{a}\\ {v}_{b}\\ {v}_{c}\end{array}\right].$
va, vb, and vc are the stator voltages across ports ~1 and ~2.
• ωbase is the per-unit base electrical speed.
• ψds, ψqs, and ψ0s are the d-axis, q-axis, and zero-sequence stator flux linkages.
• Rs is the stator resistance.
• ids, iqs, and i0s are the d-axis, q-axis, and zero-sequence stator currents, defined by
$\left[\begin{array}{c}{i}_{ds}\\ {i}_{qs}\\ {i}_{0s}\end{array}\right]={P}_{s}\left[\begin{array}{c}{i}_{a}\\ {i}_{b}\\ {i}_{c}\end{array}\right].$
ia, ib, and ic are the stator currents flowing from port ~1 to port ~2.
The rotor voltage equations are defined by
`${v}_{dr}=\frac{1}{{\omega }_{base}}\frac{d{\psi }_{dr}}{dt}-\left(\omega -{\omega }_{r}\right){\psi }_{qr}+{R}_{rd}{i}_{dr},$`
`${v}_{qr}=\frac{1}{{\omega }_{base}}\frac{d{\psi }_{qr}}{dt}+\left(\omega -{\omega }_{r}\right){\psi }_{dr}+{R}_{rd}{i}_{qr},$`
and
`${v}_{0r}=\frac{1}{{\omega }_{base}}\frac{d{\psi }_{0r}}{dt}+{R}_{rd}{i}_{0s},$`
where:
• vdr, vqr, and v0r are the d-axis, q-axis, and zero-sequence rotor voltages, defined by
$\left[\begin{array}{c}{v}_{dr}\\ {v}_{qr}\\ {v}_{0r}\end{array}\right]={P}_{r}\left[\begin{array}{c}{v}_{ar}\\ {v}_{br}\\ {v}_{cr}\end{array}\right].$
var, vbr, and vcr are the rotor voltages across ports ~1r and ~2r.
• ψdr, ψqr, and ψ0r are the d-axis, q-axis, and zero-sequence rotor flux linkages.
• ω is the per-unit synchronous speed. For a synchronous reference frame, the value is 1.
• ωr is the per-unit mechanical rotational speed.
• Rrd is the rotor resistance referred to the stator.
• idr, iqr, and i0r are the d-axis, q-axis, and zero-sequence rotor currents, defined by
$\left[\begin{array}{c}{i}_{dr}\\ {i}_{qr}\\ {i}_{0r}\end{array}\right]={P}_{r}\left[\begin{array}{c}{i}_{ar}\\ {i}_{br}\\ {i}_{cr}\end{array}\right].$
iar, ibr, and icr are the rotor currents flowing from port ~1r to port ~2r.
The stator flux linkage equations are defined by
`${\psi }_{ds}={L}_{ss}{i}_{ds}+{L}_{m}{i}_{dr},$`
`${\psi }_{qs}={L}_{ss}{i}_{qs}+{L}_{m}{i}_{qr},$`
and
`${\psi }_{0s}={L}_{ss}{i}_{0s},$`
where Lss is the stator self-inductance and Lm is the magnetizing inductance.
The rotor flux linkage equations are defined by
`${\psi }_{dr}={L}_{rrd}{i}_{dr}+{L}_{m}{i}_{ds}$`
`${\psi }_{qr}={L}_{rrd}{i}_{qr}+{L}_{m}{i}_{qs},$`
and
`${\psi }_{0r}={L}_{rrd}{i}_{0r},$`
where Lrrd is the rotor self-inductance referred to the stator.
The rotor torque is defined by
`$T={\psi }_{ds}{i}_{qs}-{\psi }_{qs}{i}_{ds}.$`
The stator self-inductance Lss, stator leakage inductance Lls, and magnetizing inductance Lm are related by
`${L}_{ss}={L}_{ls}+{L}_{m}.$`
The rotor self-inductance Lrrd, rotor leakage inductance Llrd, and magnetizing inductance Lm are related by
`${L}_{rrd}={L}_{lrd}+{L}_{m}.$`
Plotting and Display Options
You can perform display and plotting actions using the Power Systems menu on the block context menu.
Right-click the block and, from the Power Systems menu, select an option:
• Display Base Values displays the machine per-unit base values in the MATLAB® Command Window.
• Plot Torque Speed (SI) plots torque versus speed (both measured in SI units) in a MATLAB figure window using the current machine parameters.
• Plot Torque Speed (pu) plots torque versus speed, both measured in per-unit, in a MATLAB figure window using the current machine parameters.
Parameters
All default parameter values are based on a machine delta-winding configuration.
Main Tab
Rated apparent power
Rated apparent power of the asynchronous machine. The default value is `15e3` `V*A`.
Rated voltage
RMS line-line voltage. The default value is `220` `V`.
Rated electrical frequency
Nominal electrical frequency corresponding to the rated apparent power. The default value is `60` `Hz`.
Number of pole pairs
Number of machine pole pairs. The default value is `1`.
Impedances Tab
Stator resistance, Rs
Stator resistance. The default value is `0.25` `Ohm`.
Stator leakage reactance, Xls
Stator leakage reactance. The default value is `0.9` `Ohm`.
Referred rotor resistance, Rr'
Rotor resistance referred to the stator. The default value is `0.14` `Ohm`.
Referred rotor leakage reactance, Xlr'
Rotor leakage reactance referred to the stator. The default value is `0.41` `Ohm`.
Magnetizing reactance, Xm
Magnetizing reactance The default value is `17` `Ohm`.
Stator zero-sequence reactance, X0
Stator zero-sequence reactance. The default value is `0.9` `Ohm`.
Initial Conditions Tab
Initial rotor angle
Initial rotor angle. The default value is `0` `deg`.
Initial stator d-axis magnetic flux linkage
Initial stator d-axis flux linkage. The default value is `0` `Wb`.
Initial stator q-axis magnetic flux linkage
Initial stator q-axis flux linkage. The default value is `0` `Wb`.
Initial stator zero-sequence magnetic flux linkage
Initial stator zero-sequence flux linkage. The default value is `0` `Wb`.
Initial rotor d-axis magnetic flux linkage
Initial rotor d-axis flux linkage. The default value is `0` `Wb`.
Initial rotor q-axis magnetic flux linkage
Initial rotor q-axis flux linkage. The default value is `0` `Wb`.
Initial rotor zero-sequence magnetic flux linkage
Initial rotor zero-sequence flux linkage. The default value is `0` `Wb`.
Ports
The block has the following ports:
`R`
Mechanical rotational conserving port associated with the machine rotor.
`C`
Mechanical rotational conserving port associated with the machine case.
`~1`
Expandable three-phase port associated with the stator positive-end connections.
`~2`
Expandable three-phase port associated with the stator negative-end connections.
`~1r`
Expandable three-phase port associated with the rotor positive-end connections.
`~2r`
Expandable three-phase port associated with the rotor negative-end connections.
`pu`
Physical signal vector port associated with the machine per-unit measurements. The vector elements are:
• pu_torque
• pu_velocity
• pu_vds
• pu_vqs
• pu_v0s
• pu_ids
• pu_iqs
• pu_i0s
References
[1] Kundur, P. Power System Stability and Control. New York, NY: McGraw Hill, 1993.
[2] Lyshevski, S. E. Electromechanical Systems, Electric Machines and Applied Mechatronics. Boca Raton, FL: CRC Press, 1999. | 3,012 | 10,159 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 22, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.578125 | 3 | CC-MAIN-2017-43 | latest | en | 0.740605 |
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# Assignment 2 key-2 - Here is the textbook answer key 4 a b...
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Here is the textbook answer key 4. a. Y increases by 1/(1- c 1 ) b. Y decreases by c 1 /(1- c 1 ) c. The answers differ because spending affects demand directly, but taxes affect demand indirectly through consumption, and the propensity to consume is less than one. d. The change in Y equals 1/(1- c 1 ) - c 1 /(1- c 1 )=1. Balanced budget changes in G and T are not macroeconomically neutral. e. The propensity to consume has no effect because the balanced budget tax increase aborts the multiplier process. Y and T both increase by one unit, so disposable income, and hence consumption, do not change. 5. a. Y = c 0 + c 1 Y D + I + G implies Y =[1/(1- c 1 + c 1 t 1 )][ c 0 - c 1 t 0 + I + G ] b. The multiplier=1/(1- c 1 + c 1 t 1 )<1/(1- c 1 ), so the economy responds less to changes in autonomous spending when t 1 is positive. After a positive change in autonomous spending, the increase in total taxes (because of the increase in income) tends to lessen the increase in output. After a negative change in autonomous spending, the fall in total taxes tends to lessen the decrease in output. c. Because of the automatic effect of taxes on the economy, the economy responds less to changes in autonomous spending than in the case where taxes are independent of income. Since output tends to vary less (to be more stable), fiscal policy is called an automatic stabilizer. 6. a. Y =[1/(1- c 1 + c 1 t 1 )][ c 0 - c 1 t 0 + I + G ] b. T = t 0 + t 1 [1/(1- c 1 + c 1 t 1 )][ c 0 - c 1 t 0 + I + G ] c. Both Y and T decrease. d. If G is cut, Y decreases even more. A balanced budget requirement amplifies the effect of the decline in c 0 . Therefore, such a requirement is destabilizing. 8. a. Y = C + I + G Y =[1/(1- c 1 - b 1 )]*[ c 0 - c 1 T + b 0 + G ] b. Including the b 1 Y term in the investment equation increases the multiplier.
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# 400
Mechanics. Electricity & Magnetism. Fluids & Thermal. Potpourri. Waves, Optics Modern Physics. 200. 200. 200. 200. 200. 400. 400. 400. 400. 400. 600. 600. 600. 600. 600. 800. 800. 800. 800. 800. 1000. 1000. 1000. 1000. 1000.
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## 400
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### Presentation Transcript
1. Mechanics Electricity&Magnetism Fluids&Thermal Potpourri Waves, OpticsModern Physics 200 200 200 200 200 400 400 400 400 400 600 600 600 600 600 800 800 800 800 800 1000 1000 1000 1000 1000
2. How does an air mattress protect a stunt person landing on the ground after a stunt? (A) It reduces the kinetic energy loss of the stunt person. (B) It reduces the momentum change of the stunt person. (C) It increases the momentum change of the stunt person (D) It shortens the stopping time of the stunt person and increases the force applied during the landing. (E) It lengthens the stopping time of the stunt person and reduces the force applied during the landing
3. (E) It lengthens the stopping time of the stunt person and reduces the force applied during the landing The change in momentum is the same, but by increasing the time, the force can be reduced.
4. The cart of mass 10 kg shown above moves without frictional loss on a level table. A 10 N force pulls on the cart horizontally to the right. At the same time, a 30 N force at an angle of 60° above the horizontal pulls on the cart to the left. What is the magnitude of the horizontal acceleration of the cart? (A) 0.5 m/s2 (B) 1.6 m/s2 (C) 2.0 m/s2 (D) 2.5 m/s2 (E) 2.6 m/s2
5. (A) 0.5 m/s2 10 - 30 cos 60° = 10a therefore a = -0.5 m/s2
6. A ball is thrown straight up in the air. When the ball reaches its highest point, which of the following is true? (A) It is in equilibrium. (B) It has zero acceleration (C) It has maximum momentum. (D) It has maximum kinetic energy. (E) None of the above
7. (E) None of the above
8. An empty sled of mass M moves without friction across a frozen pond at speed vo. Two objects are dropped vertically into the sled one at a time: first an object of mass m and then an object of mass 2m. Afterward the sled moves with speed vf . What would be the final speed of the sled if the objects were dropped into it in reverse order? (A) vf / 3 (B) vf / 2 (C) vf (D) 2 vf (E) 3 vf
9. (C) vf The order in which the objects are dropped does not change the horizontal component of momentum or the final velocity.
10. A block attached to the lower end of a vertical spring oscillates up and down. If the spring obeys Hooke's law, the period of oscillation depends on which of the following? I. Mass of the block II. Amplitude of the oscillation III. Force constant of the spring (A) I only (B) II only (C) III only (D) I and II (E) I and III
11. (E) I and III The amplitude is not one of the independent variables.
12. A student obtains data on the magnitude of force applied to an object as a function of time and displays the data on the graph. • The increase in the momentum of the object between t = 0 s and t = 4 s is most nearly • 40 N.s (B) 50 N.s • (C) 60 N.s (D) 80 N.s • (E) 100 N.s
13. (C) 60 N.s Find the area under the graph: a rectangle and a triangle give 5(4 ) + 0.5(4 )(25-5 ) = 60N.s
14. Daily Double
15. Two large, flat, parallel conducting plates are 0.04 m apart, as shown above. The lower plate is at a potential of 2 V with respect to ground. The upper plate is at a potential of 10 V with respect to ground. Point P is located 0.01 m above the lower plate The magnitude of the electric field at point P is (A) 800 V/m (B) 600 V/m (C) 400 V/m(D) 200 V/m (E) 100 V/m
16. (D) 200 V/m Uniform field (V = Ed) 10 -2 = E (0.04) so E = 200 V/m.
17. How do the currents I1, I2, and I3 compare? (A) I1 > I2 > I3 (B) I1 > I3 > I2 (C) I2 > I1 > I3 (D) I3 > I1 > I2 (E) I3 > I2 > I1
18. (A) I1 > I2 > I3 Since I1 is the total current it must be the larger of the three. Because R2 and R3 have the same potential drop across them, the smaller resistance, R2 has the larger current.
19. As shown above, a positively charged particle moves to the right without deflection through a pair of charged plates. Between the plates are a uniform electric field E of magnitude 6.0 N/C and a uniform magnetic field B of magnitude 2.0 T, directed as shown in the figure. The speed of the particle is most nearly (A) 0.33 m/s (B) 0.66 m/s (C) 3.0 m/s (D) 12 m/s (E) 18 m/s
20. (C) 3.0 m/s FM = FE qvB=qE v= E/B = 6/2 = 3 m/s
21. The total capacitance of several capacitors in parallel is the sum of the individual capacitances for which of the following reasons? (A) The charge on each capacitor depends on its capacitance, but the potential difference across each is the same. (B) The charge is the same on each capacitor, but the potential difference across each capacitor depends on its capacitance. (C) Equivalent capacitance is always greater than the largest capacitance. (D) Capacitors in a circuit always combine like resistors in series. (E) The parallel combination increases the effective separation of the plates.
22. (A) The charge on each capacitor depends on its capacitance, but the potential difference across each is the same.
23. A wire of length L and radius r has a resistance R. What is the resistance of a second wire made from the same material that has a length L/2 and a radius r/2 ? (A) 4R (B) 2R (C) R (D) R/2 (E) R/4
24. (B) 2R
25. Which of the following will occur if the average speed the gas molecules in a closed rigid container is increased? (A) The density of the gas will decrease. (B) The density of the gas will increase. (C) The pressure of the gas will increase. (D) The pressure of the gas will decrease. (E) The temperature of the gas will decrease
26. (C) The pressure of the gas will increase. If the average speed of the gas molecules increases the temperature, (the KE of the molecules also increases). If the volume is held constant the pressure must increase.
27. Each of the beakers shown above is filled to the same depth h with liquid of density p. The area A of the flat bottom is the same for each beaker. Which of the following ranks the beakers according to the net downward force exerted by the liquid on the flat bottom, from greatest to least force? (A) I, III, II, IV (B) I, IV, III, II (C) II, III, IV, I (D) IV, III, I, II (E) None of the above; the force on each is the same.
28. (E) None of the above; the force on each is the same. Pascal's principle says the pressure is independent of the shape of the vessel. Also, since all of the factors which determine pressure are the same all of the pressures must be the same.
29. A T-shaped tube with a constriction is inserted in a vessel containing a liquid, as shown above. What happens if air is blown through the tube from the left, as shown by the arrow in the diagram? (A) The liquid level in the tube rises to a level above the surface of the liquid surrounding the tube. (B) The liquid level in the tube falls below the level of the surrounding liquid. (C) The liquid level in the tube remains where it is. (D) The air bubbles out at the bottom of the tube. (E) Any of the above depending on how hard the air flows.
30. (A) The liquid level in the tube rises to a level above the surface of the liquid surrounding the tube. The velocity will be greatest in the smaller diameter tube so the pressure will be less and the liquid will be forced up the tube.
31. Daily Double
32. A spring scale calibrated in kilograms is used to determine the density of a rock specimen. The reading on the spring scale is 0.45 kg when the specimen is suspended in air and 0.36 kg when the specimen is fully submerged in water. If the density of water is 1000 kg/m3, the density of the rock specimen is (A) 2.0 x 102 kg/m3 (B) 8.0 x 102 kg/m3 (C) 1.25 x 103 kg/m3 (D) 4.0 x 103 kg/m3 (E) 5.0 x 103 kg/m3
33. (E) 5.0 x 103 kg/m3 Apparent mass loss: 0.45 - 0.36 = 0.09 kg. Volume of water of 0.09/1000 = 9x10-5 m3. The density is then: 0.45/9 x10-5 = 5x103 kg/m3
34. An ideal gas may be taken from one state to another state with a different pressure, volume and temperature along several different paths. Quantities that will always be the same for this process, regardless of which path is taken. include which of the following? I. The change in internal energy of the gas II. The heat exchanged between the gas and its surroundings III. The work done by the gas (A) I only (B) II only (C) I and III only (D) II and III only (E) I, II, and III
35. (A) I only Temperature for an ideal gas is directly proportional to the internal kinetic energy. If ΔU = Q + W a variety of combinations of Q and W will result in the same overall change in internal energy in going from one state to another.
36. An electron e and a proton p are simultaneously released from rest in a uniform electric field E, as shown. Assume that the particles are sufficiently far apart so that the only force acting on each particle after it is released is that due to the electric field. At alater time when the particles are still in the field, the electron and the proton will have the same (A) direction of motion (B) speed (C) displacement (D) magnitude of acceleration (E) magnitude of force acting on them
37. (E) magnitude of force acting on them Because both particles have the same magnitude of charge the force will be the same on both.
38. A rope of negligible mass supports a block that weighs 30 N, as shown above. The breaking strength of the rope is 50 N. The largest acceleration that can be given to the block by pulling up on it with the rope without breaking the rope is most nearly (A) 6 m/s2 (B) 6.7 m/s2 (C) 10 m/s2 (D) 15 m/s2 (E) 16.7 m/s2
39. (B) 6.7 m/s2 50 - 30 = 3a therefore a = 6.7 m/s2
40. Which graph shows the maximum kinetic energy of the emitted electrons versus the frequency of the light?
41. A linear function with a negative y-intercept.
42. The hollow metal sphere shown above is positively charged. Point C is the center of the sphere and point P is any other point within the sphere. Which of the following is true of the electric field at these points? (A) It is zero at both points. (B) It is zero at C but at P it is not zero and is directed inward. (C) It is zero at C but at P it is not zero and is directed outward. (D) It is zero at P but at C it is not zero. (E) It is not zero at either point.
43. (A) It is zero at both points The electric field due to static charges is zero inside a conductor.
44. The spherical mirror shown above has a center of curvature at point c. Which point is nearest to the focal point? (A) a (B) b (C) c (D) d (E) e
45. (B) b "b" is at the estimated halfway point between the center of curvature "c" and the mirror
46. The frequencies of the first two overtones (second and third harmonics) of a vibrating string are f and 3f /2. What is the fundamental frequency of this string? (A) f /3 (B) f /2 (C) f (D) 2 f (E) 3 f
47. (B) f /2 Harmonics are integer multiple of the fundamental. Here the first harmonic is f, which must be twice the fundamental. Then, the second harmonic is 1.5 f or three times the fundamental.
48. An object is placed on the axis of a converging thin lens of focal length 2 cm, at a distance of 8 cm from the lens. The distance between the image and the lens is most nearly(A) 0.4 cm (B) 0.8 cm (C) 1.6 cm(D) 2.0 cm (E) 2.7 cm
49. (E) 2.7 cm
50. A radio station broadcasts on a carrier frequency of 100 MHz. The wavelength of this radio wave is most nearly (A) 3.0 x 10-3 m (B) 1.0 m (C) 3.0 m (D) 3.3 m (E) 3.0 x 106 m
More Related | 3,305 | 11,559 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.375 | 3 | CC-MAIN-2024-22 | latest | en | 0.781011 |
https://learnhtml.foobrdigital.com/matlab-fit/ | 1,679,677,044,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296945287.43/warc/CC-MAIN-20230324144746-20230324174746-00083.warc.gz | 410,293,034 | 43,789 | Categories
# Matlab fit
MATLAB fit method can be used to fit a curve or a surface to a data set. Fitting a curve to data is a common technique used in Artificial intelligence and Machine learning models to predict the values of various attributes.
For example, if we compare the weight of an item like rice with its price; ideally, it should increase linearly (Price will increase as the weight of rice will increase). If we fit a curve to this data of weight and price, we will get mostly a linear curve. Now someone looking at this linear curve can easily interpret the relation between the 2 attributes (weight and price in our example), without looking at the data.
## Syntax:
1. fitobject = fit (a, b, fitType) is used to fit a curve to the data represented by the attributes ‘a’ and ‘b’. The type of model or curve to be fit is given by the argument ‘fitType’
2. Various values which the argument ‘fitType’ can take are given in the table below:
## Table 1
Let us now understand how to fit a curve or a surface to data in MATLAB:
We will need some data to which we will fit the curve, for our examples, we will use some inbuilt data sets provided by MATLAB like ‘carsmall’ and ‘census’.
## Examples of Matlab fit
Let us discuss examples of Matlab fit.
## Example 1:
In this example, we will use the ‘carsmall’ data provided by MATLAB. The data is of various attributes of cars manufactured over the years 1970, 1976, and 1982. It has attributes like ‘Acceleration’, ‘Cylinders’, ‘Horsepower’ etc. which represent various features of a car. We will load this data to our workspace and will fit a curve to its attributes ‘Acceleration’ and ‘Displacement’. The steps to be followed for this example are:
1. Load the ‘carsmall’ data to the workspace
2. View the file loaded above to understand its attributes
3. Use the ‘fit’ function to fit a curve to the loaded data
4. Plot the model created in above step
## Code:
2. whos -file carsmall[Using ‘whos’ command to view the file loaded above]
3. C = fit(Acceleration, Displacement, ‘poly2’)[Using the ‘fit’ command to fit a curve to the data. The first 2 parameters represent the attributes to which we want to fit the curve and the 3rd parameter represents the type of curve which we want to fit (please refer to Table 1 for this)]
4. plot(C, Acceleration, Displacement)[Using ‘plot’ command to plot the model created in above step]
This is how our input and output will look like in MATLAB command window:
## Output 3:
As we can see in Output 3, we have obtained a curve that fits our data. Output 1 and Output 2 represent the data attributes and the model respectively.
In the same example, we can also fit a different type of curve as per our requirement. Let us try to fit ‘smoothingspline’ curve to the above data.
The code will be similar as in the above example with a change in line 3
## Code:
2. whos -file carsmall[Using ‘whos’ command to view the file loaded above]
3. C = fit(Acceleration, Displacement, ‘smoothingspline’)[Please note that the 3rd argument is now ‘smoothingspline’]
4. plot(C, Acceleration, Displacement)[Using ‘plot’ command to plot the model created in above step]
This is how our input and output will look like in the Matlab command window:
## Input 2:
Fitting the curve to the data:
## Input 3:
Plotting the model created above:
## Output 3:
As we can see in Output 3, we have obtained a smoothing spline curve that fits our data.
## Example 2:
In this example, we will use the ‘census’ data provided by MATLAB. The data is of the US and gives the population of the country in a particular year. It has 2 attributes ‘cdate’ and ‘pop’ representing ‘census date’ and ‘population’. We will load this data to our workspace and will fit a curve to it. The steps to be followed for this example are:
1. Load the census data to the workspace
2. View the file loaded above to understand its attributes
3. Use the ‘fit’ function to fit a curve to the loaded data
4. Plot the model created in above step
## Code:
`load census`[Using the ‘load’ command to load the census file to our workspace]
`whos -file census`[Using ‘whos’ command to view the file loaded above]
`C = fit(cdate, pop, 'poly2')`[Using the ‘fit’ command to fit a curve to the data. The first 2 parameters represent the attributes to which we want to fit the curve and the 3rd parameter represents the type of curve which we want to fit (please refer to Table 1 for this)]
`plot(C, cdate, pop)`[Using ‘plot’ command to plot the model created in above step]
This is how our input and output will look like in MATLAB command window:
## Input 2:
Fitting the curve to the data:
## Input 3:
Plotting the model created above:
## Output 3:
As we can see in Output 3, we have obtained a curve that fits our data. Output 1 and Output 2 represent the data attributes and the model respectively. | 1,193 | 4,875 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.953125 | 3 | CC-MAIN-2023-14 | longest | en | 0.885986 |
https://www.hackmath.net/en/word-math-problems/length?tag_id=150 | 1,611,800,999,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704835583.91/warc/CC-MAIN-20210128005448-20210128035448-00581.warc.gz | 810,728,518 | 10,690 | # Length + greatest common divisor (GCD) - math problems
#### Number of problems found: 21
• Length of a string
What is the smallest length of a string that we can cut into 18 equal parts and even 27 equal parts (in decimeters)?
• Self
A math text book is 2 2/9 inches thick. how many of these books will fit on a 120-inch self?
• Wide field
The field is 203 meters wide 319 meter long, what is the greater length of the rope by which length and width can be measured and find the exact number of time.
• Cutting paper
Divide a rectangular paper with dimensions 220mm and 308mm into squares of the same size so that they are as large as possible. Specify the length of the side of the square.
• Identical cubes
From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm?
1st blade 2,5 m, 2nd blade. .1.75 m. How many same long pieces of this two blades can be do the biggest? How long is one piece?
• The classroom
The classroom is 9 meters long. The width of the classroom is smaller and can be passed in equally long steps of 55 CM or 70 CM. Determine the width of the classroom.
• Square tiles
The room has dimensions of 12 meters and 5.6 meters. Determine the number of square tiles and their largest dimension to exactly cover the floor.
• Gardens colony
Gardens colony with dimensions of 180 m and 300 m are to be completely divided into the same large squares of the highest area. Calculate how many such squares can be obtained and determine the length of the square side.
• Four poplars
Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be?
• Glass panel
A rectangular glass panel with dimensions of 72 cm and 96 cm will cut the glazier on the largest square possible. What is the length of the side of each square? How many squares does the glazier cut?
• Pegs
From two sticks 240 cm and 210 cm long, it is necessary to cut the longest possible pegs for flowers so that no residues remain. How many pegs will it be?
• Trees in alley
There are four trees in the alley between which the distances are 35m, 15m and 95m. Trees must be laid in the spaces so that the distance is the same and the maximum. How many trees will they put in and what will be the distance between them?
• Pexeso
Drawing paper has dimensions of 60cm and 840mm. Pupils have to divide it into squares so that they can make a pexeso. What dimension must squares have if their side is to be larger than 3cm and less than 10cm?
• Cubes
Carol with cut bar 12 cm x 12 cm x 135 cm to the cubes. Find the sum of all the surfaces of the resulting cubes.
• Segments
Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
• Square gardens
The gardening colony with dimensions of 180 m and 300 m is to be completely divided into equally large square areas with the largest possible area. Calculate how many such square areas can be obtained and determine the side length of the square.
• Long bridge
Roman walked on the bridge. When he heard the whistle, he turned and saw running Kamil at the beginning of the bridge. If he went to him, they would meet in the middle of the bridge. Roman, however, rushed and so did not want to waste time returning 150m.
• Plumber
The plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it?
• Dividing
Divide the three line segment 13 cm, 26 cm and 19.5 cm long for parts so that the individual parts were equally long and longest. How long will the individual parts and how many it will?
Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.
We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.
Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...
Do you want to calculate greatest common divisor two or more numbers? Do you want to convert length units? Length - math word problems. Greatest common divisor (GCD) - math word problems. | 1,062 | 4,471 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.09375 | 4 | CC-MAIN-2021-04 | latest | en | 0.929391 |
https://www.econinfo.de/2016/03/12/revisiting-barrier-bond/ | 1,709,365,314,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947475757.50/warc/CC-MAIN-20240302052634-20240302082634-00671.warc.gz | 735,628,577 | 22,532 | # Revisiting barrier bond
In Analyse einer Barriere-Anleihe I was estimating the present value of a barrier bond emitted by Berliner Landesbank, which referred to the stock price of Daimler: The payout would be 100, if the price was either allways above the barrier of 70%, or, if it dipped below the barrier, but closed above the initial price at the maturity of the bond. In every other case, the buyer would get the value of the stock at maturity. For details on the bond, go here.
Using stochastic modelling on a 13 year history of the Daimler stock price, I estimated a present value at offering of 98.6% assuming a risk free rate of 2% for the 2 year maturity (I checked the sensitivity of the result to the risk free rate, but even at a -0.5% the mean present value is at 99.4%, so a slight loss).
Today I wanted to check what the actual payout would have been.
payoutEnd = function(basis, barriere, kurse)
{
basis = as.numeric(basis)
barriere = as.numeric(barriere)
kurse = as.numeric(kurse)
if(all(kurse >= barriere))
{
res = kurse[1]
} else if( last(kurse)>basis)
{
res = kurse[1]
} else
{
res = last(kurse)
}
return(res)
}
## [1] "DAI.DE"
Okay, so it seems the price never went below the barrier of 42.462, and the final payout was 100%:
payoutEnd(1,0.7, DAI.DE[,3]/DAI.DE[1,3])
## [1] 1
So, using hindsight, this would have been a good investment given the 7% coupon.
Diese Website verwendet Akismet, um Spam zu reduzieren. Erfahre mehr darüber, wie deine Kommentardaten verarbeitet werden. | 417 | 1,514 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.734375 | 3 | CC-MAIN-2024-10 | longest | en | 0.771039 |
https://www.onlinemath4all.com/proving-the-pythagorean-theorem.html | 1,591,135,236,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347426801.75/warc/CC-MAIN-20200602193431-20200602223431-00331.warc.gz | 837,186,080 | 13,152 | # PROVING THE PYTHAGOREAN THEOREM
In a right triangle, the two sides that form the right angle are the legs. The side opposite the right angle is the hypotenuse.
## The Pythagorean Theorem
In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
If a and b are legs and c is the hypotenuse,
a2 + b2 = c2
## Proving the Pythagorean Theorem
Step 1 :
Draw a right triangle on a piece of paper and cut it out. Make one leg shorter than the other.
Step 2 :
Trace your triangle onto another piece of paper four times, arranging them as shown. For each triangle, label the shorter leg a, the longer leg b, and the hypotenuse c.
Step 3 :
Find the area of the unshaded square.
c2 square units ----- (1)
Step 4 :
Label the unshaded square with its area.
Step 5 :
Trace your original triangle onto a piece of paper four times again, arranging them as shown. Draw a line outlining a larger square that is the same size as the figure you made in step 2.
Step 6 :
Find the area of the unshaded square at the top right and left of the figure in step 5.
a2 square units and b2 square units
Step 7 :
Label the unshaded squares with their areas.
Step 8 :
Find the total area of the unshaded regions in step 5.
(a2 + b2) square units -----(2)
Step 9 :
Because both (1) and (2) represent the total area of the unshaded region, they are equal.
So, we have
a2 + b2 = c2
Hence, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
## Reflect
1. Explain whether the figures in step 2 and step 5 have the same area.
Yes, the figures in step 2 and step 5 have the same area. Because, the outlines of the figures are the same size.
2. Explain whether the unshaded regions of the figures in step 2 and step 5 have the same area.
Yes, the shaded regions have the same area. Subtracting the area of the shaded region from the total area gives the same area for the unshaded region in each figure.
3. Write an equation relating the area of the unshaded region in step 2 and step 5 have the same area.
a2 + b = c2
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Sum of all three four digit numbers formed using 1, 2, 5, 6 | 1,089 | 4,540 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.78125 | 5 | CC-MAIN-2020-24 | longest | en | 0.834312 |
https://www.physicsforums.com/threads/parallel-rlc-circuit.689782/ | 1,600,533,733,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600400192778.51/warc/CC-MAIN-20200919142021-20200919172021-00790.warc.gz | 960,439,902 | 17,249 | # Parallel RLC Circuit
• Engineering
## The Attempt at a Solution
I found ω0 = 1/√LC when IR is at its maximum. (Purely resistive)
I have a feeling that the last part requires an approximation and then an expansion which gives 2 values of ω.
But the thing is, (1 + x)n ≈ 1 + nx + .....
only when x << 1
In this case it's L/RC << 1 which doesn't really fit..
Related Engineering and Comp Sci Homework Help News on Phys.org
SammyS
Staff Emeritus
Homework Helper
Gold Member
## The Attempt at a Solution
I found ω0 = 1/√LC when IR is at its maximum. (Purely resistive)
I have a feeling that the last part requires an approximation and then an expansion which gives 2 values of ω.
But the thing is, (1 + x)n ≈ 1 + nx + .....
only when x << 1
In this case it's L/RC << 1 which doesn't really fit..
[ IMG]http://i44.tinypic.com/530jdy.png[/PLAIN]
Well, what did you get for ω1 and ω2 ?
Well, what did you get for ω1 and ω2 ?
I can't do the expansion, because I can't find the small approximations in the square root!
SammyS
Staff Emeritus
Homework Helper
Gold Member
I can't do the expansion, because I can't find the small approximations in the square root!
You can find ω+ and ω- without an approximation.
However, I do see that the instructions do say to find approximate values assuming RC/L >> 1 .
Also notice that those values of ω are for (IR)2 = (I0)2/2 , so the square root goes away.
If they had said R2C/L >> 1, then I could see that helping.
Sorry. I can't be of more help.
You can find ω+ and ω- without an approximation.
However, I do see that the instructions do say to find approximate values assuming RC/L >> 1 .
Also notice that those values of ω are for (IR)2 = (I0)2/2 , so the square root goes away.
If they had said R2C/L >> 1, then I could see that helping.
Sorry. I can't be of more help.
Hmmm it's alright, let's leave this question up for other takers.
NascentOxygen
Staff Emeritus
Given RC/L ≫1, then for R>1Ω it follows that 4R2C/L ≫1.
Taking R>1Ω seems very reasonable for practical tuned circuits, I'd say.
rude man
Homework Helper
Gold Member
First: it's easier to use admittance and conductance rather than impedance and resistance when dealing with components connected in parallel. So for example for your circuit Y = G + jwC - j/wL where G = 1/R and Y = 1/Z.
Then: What is V as a function of w, where V is the voltage across your network? V is complex, but take |V|^2 which isn't.
Now, using |V|^2, what is I thru R? And I^2 thru R?
Then form I0^2/I^2 where I = Y*V. The V's cancel, giving you what for this ratio?
More when you get to this point.
First: it's easier to use admittance and conductance rather than impedance and resistance when dealing with components connected in parallel. So for example for your circuit Y = G + jwC - j/wL where G = 1/R and Y = 1/Z.
Then: What is V as a function of w, where V is the voltage across your network? V is complex, but take |V|^2 which isn't.
Now, using |V|^2, what is I thru R? And I^2 thru R?
Then form I0^2/I^2 where I = Y*V. The V's cancel, giving you what for this ratio?
More when you get to this point.
I have discussed this problem with my tutor, apparently the [RωC - R/(ωL)]2 = 1
which literally stems from the definition I = I0/√(2)
Then we get two values of ω.
rude man
Homework Helper
Gold Member
I have discussed this problem with my tutor, apparently the [RωC - R/(ωL)]2 = 1
which literally stems from the definition I = I0/√(2)
Then we get two values of ω. | 994 | 3,487 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.65625 | 4 | CC-MAIN-2020-40 | latest | en | 0.943394 |
http://m.thermalfluidscentral.org/encyclopedia/index.php?title=Main_Page&diff=prev&oldid=22 | 1,569,239,247,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514576355.92/warc/CC-MAIN-20190923105314-20190923131314-00540.warc.gz | 124,926,688 | 7,572 | # Main Page
(Difference between revisions)
Revision as of 21:35, 7 April 2009 (view source)← Older edit Revision as of 01:38, 8 April 2009 (view source)Newer edit → Line 25: Line 25: *[[Fluid Mechanics]] *[[Fluid Mechanics]] :[[Incompressible Flow]],[[inviscid flow]], [[potential flow]], [[boundary layer theory]], and [[Computational Fluid Dynamics (CFD)]]. :[[Incompressible Flow]],[[inviscid flow]], [[potential flow]], [[boundary layer theory]], and [[Computational Fluid Dynamics (CFD)]]. - *[[Combustion]] *[[Combustion]] - : [[Chemistry]] and thermal effects in combustion. + : [[Chemistry]] and thermal effects in combustion. + *[[Multiphase systems]] + : [[Melting and solidification]], [[sublimation]] and [[vapor deposition]], [[condensation]], [[evaporation]]and [[boiling]], and [[two-phase flow]]. *[[Application areas]] *[[Application areas]] : [[Heat exchanger]], [[heat pipe]], [[energy]] and [[fuel cells.]] : [[Heat exchanger]], [[heat pipe]], [[energy]] and [[fuel cells.]]
## Revision as of 01:38, 8 April 2009
Welcome to Thermalpedia
Thermalpedia is a comprehensive reference for professionals and students requiring information on the thermal and fluids science and engineering.
## Getting Started
Basic conduction, convection, mass transfer, radiation, and Computational Heat Transfer (CHT).
The properties of pure substances, first law and second law, entropy and availability, power and refrigeration cycles.
Incompressible Flow,inviscid flow, potential flow, boundary layer theory, and Computational Fluid Dynamics (CFD).
Chemistry and thermal effects in combustion.
Melting and solidification, sublimation and vapor deposition, condensation, evaporationand boiling, and two-phase flow.
Heat exchanger, heat pipe, energy and fuel cells.
Biotechnology, information technology, nanotechnology and security. | 442 | 1,840 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.609375 | 3 | CC-MAIN-2019-39 | longest | en | 0.762603 |
http://www.indiabix.com/electrical-engineering/passive-filters/ | 1,537,439,910,000,000,000 | text/html | crawl-data/CC-MAIN-2018-39/segments/1537267156460.64/warc/CC-MAIN-20180920101233-20180920121633-00353.warc.gz | 340,304,757 | 6,278 | # Electrical Engineering - Passive Filters
## Why Electrical Engineering Passive Filters?
In this section you can learn and practice Electrical Engineering Questions based on "Passive Filters" and improve your skills in order to face the interview, competitive examination and various entrance test (CAT, GATE, GRE, MAT, Bank Exam, Railway Exam etc.) with full confidence.
## Where can I get Electrical Engineering Passive Filters questions and answers with explanation?
IndiaBIX provides you lots of fully solved Electrical Engineering (Passive Filters) questions and answers with Explanation. Solved examples with detailed answer description, explanation are given and it would be easy to understand. All students, freshers can download Electrical Engineering Passive Filters quiz questions with answers as PDF files and eBooks.
## Where can I get Electrical Engineering Passive Filters Interview Questions and Answers (objective type, multiple choice)?
Here you can find objective type Electrical Engineering Passive Filters questions and answers for interview and entrance examination. Multiple choice and true or false type questions are also provided.
## How to solve Electrical Engineering Passive Filters problems?
You can easily solve all kind of Electrical Engineering questions based on Passive Filters by practicing the objective type exercises given below, also get shortcut methods to solve Electrical Engineering Passive Filters problems.
### Exercise :: Passive Filters - General Questions
1.
In a certain parallel resonant band-pass filter, the resonant frequency is 14 kHz. If the bandwidth is 4 kHz, the lower frequency
A. is 7 kHz B. is 10 kHz C. is 12 kHz D. cannot be determined
Explanation:
No answer description available for this question. Let us discuss.
2.
An RL low-pass filter consists of a 5.6 mH coil and a 3.3 k resistor. The output voltage is taken across the resistor. The circuit's critical frequency is
A. 93.8 kHz B. 93.8 Hz C. 861 Hz D. 86.12 kHz
Explanation:
No answer description available for this question. Let us discuss.
3.
In a series resonant band-pass filter, a lower value of Q results in
A. a higher resonant frequency B. a smaller bandwidth C. a higher impedance D. a larger bandwidth
Explanation:
No answer description available for this question. Let us discuss.
4.
The maximum output voltage of a certain low-pass filter is 15 V. The output voltage at the critical frequency is
A. 0 V B. 15 V C. 10.60 V D. 21.21 V
Explanation:
No answer description available for this question. Let us discuss.
5.
A parallel resonant band-pass filter consists of a 90 resistor in series with a parallel network made up of a 60 mH coil and a 0.02 F capacitor. The output is taken across the capacitor/coil. The coil winding has a resistance of 20 . What is the center frequency of the filter?
A. 459 Hz B. 4,591 Hz C. 999 Hz D. 2,176 Hz | 620 | 2,909 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.734375 | 4 | CC-MAIN-2018-39 | latest | en | 0.885446 |
http://wims.univ-savoie.fr/wims/wims.cgi?lang=en&+module=U1%2Fgeometry%2Fparamcomp.en | 1,670,665,302,000,000,000 | text/html | crawl-data/CC-MAIN-2022-49/segments/1669446710421.14/warc/CC-MAIN-20221210074242-20221210104242-00284.warc.gz | 58,133,044 | 3,208 | !! used as default html header if there is none in the selected theme. Parametric compose
# Parametric compose --- Introduction ---
This module is a graphical exercise on parametric curves in the cartesian plane.
A parametric curve is determined by two real functions $f$ and $g$ of a parameter $t$. This curve is therefore the set of points $\left(x=f\left(t\right),y=g\left(t\right)\right)$ for different values of t. On the other hand, we also have the graphs of the two coordinate functions $f$ and $g$ which are curves.
This exercise can either present the two curves of $f$ and $g$ and ask you to recognize the parametric curve $\left(x=f\left(t\right),y=g\left(t\right)\right)$ among others, or present the parametric curve and ask you to recognize the curves of $f$ and $g$.
Here are the configuration parameters of the exercise.
• Style
• Level of difficulty
• Number of questions in one session ( The score is attributed only at the end of a session)
Other exercises on:
In order to access WIMS services, you need a browser supporting forms. In order to test the browser you are using, please type the word wims here: and press Enter''. | 274 | 1,151 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 11, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2022-49 | longest | en | 0.847051 |
https://www.jiskha.com/display.cgi?id=1307327849 | 1,502,896,882,000,000,000 | text/html | crawl-data/CC-MAIN-2017-34/segments/1502886102307.32/warc/CC-MAIN-20170816144701-20170816164701-00437.warc.gz | 918,643,358 | 4,668 | posted by .
Prepare a 700- to 1,050-word paper in which you describe the use of statistics within your workplace or a company with which you are familiar. Address the following questions in your paper:
• How are statistics used in your workplace?
• What is one example of descriptive statistics used in your workplace?
• What is one example of inferential statistics used in your workplace?
• How is data at each of the four levels of measurement used in your workplace? If your workplace does not use all four levels, describe how such data could be used.
• What are the advantages of accurate interpretation of
• What is one example of descriptive statistics used in your workplace?
Why did you post this in the Jiskha Homework Forum?
The clues that could help you determine between expressions and equations are if it has simple arithmetic operations such as 3 + 5 x( (-2)^7 -3/2 then it’s an expression however if it is set up as P=Q which is equivalent with P-Q=0 it’s an equation The things to remember about expressions is that if it has signs and symbols of algebra then it’s an expression and if it has two expressions in the problem then it is an equation. Equations have equal sign whereas expressions don’t have an equal sign.
An example of an expression would be a+b
An example of an equation would be a+b=b+a
How are statistics used in your workplace.
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2.2 The Derivative as a Function
# 2.2 The Derivative as a Function - = 1 1 U x x x =< ≥...
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Derivative as a Function Section 2.2
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Definition of the Derivative of a Function The derivative of f at x is given by provided the limit exists. 0 ( ) ( ) '( ) lim h f x h f x f x h + - =
Notation for Derivatives ) ( ' x f dx dy ' y [ ] ) ( x f dx d [ ] y D x df dx
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(Alternate)Derivative at a Point The derivative of the function f at the point x = a is the limit provided the limit exists. ( ) ( ) '( ) lim x a f x f a f a x a - = -
Higher Derivatives
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Jerk l Jerk is the derivative of acceleration. l It is the 3rd derivative of the position function. l If a body’s position at time t is s(t), the body’s jerk at time t is 3 ( ) s da d s j t dt dt = =
Cases Where a Function is not Differentiable l A corner, where the one-sided derivatives differ. l A cusp, where the slopes of the secant lines approach from one side and from the other side. ( ) f x x = -∞ 2 3 ( ) f x x =
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l A vertical tangent, where the slopes of the secant lines approach either from both sides. l A discontinuity (which will cause one or both of the one-sided derivatives to be nonexistent. or -∞ 3 ( ) f x x = ( )
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Unformatted text preview: = ( ) 1, 1, U x x x = -< ≥ Thm. 2.1 Differentiability Implies Continuity If f is differentiable at x = c, then f is continuous at x = c. It is possible for a function to be continuous at x = c and not be differentiable at x = c. Thus, continuity does not imply differentiability. One-Sided Derivatives l A function y = f(x) is differentiable on a closed interval [a, b] if it has a derivative at every interior point of the interval, and if the limits exist at the endpoints. l The usual relationship between one-sided and two-sided limits holds for derivatives. A function has a (two-sided) derivative at a point iff the function’s right-hand and left-hand derivatives are defined and equal at that point. Joke Time What would America be called if we all drove pink cars? A pink carnation! Why should you never play cards in the jungle? It’s full of cheetahs!...
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2.2 The Derivative as a Function - = 1 1 U x x x =< ≥...
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Ask a homework question - tutors are online | 802 | 3,150 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2018-13 | latest | en | 0.875213 |
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Registered User
France, IdF, Lagny-sur-Marne
Joined Feb 2007
749 Posts
Quote:
Originally Posted by Montag DP Paul, I haven't done that. But, I don't really see the need either. Since you can already specify the Reynolds number, Cl, and Mach number for every operating point, you can just set up your operating points so that Re*sqrt(Cl) is constant, with the value determined based on the model weight, altitude, etc. Dan
Yes but you can only choose one of the following for all Re : "min-drag" or "min-sink" and "max-glide".
e.g. if I want min-sink at low Reynolds (thermalling) and max-glide at high Reynolds (to get through sinking air between two thermals).
Have you read Martin Simons series of articles on RC soaring here:
http://www.rcsoaringdigest.com/pdfs/Simons_UTSS.pdf
I suppose you have.
Paul
Apr 07, 2015, 11:25 AM
Sink stinks
United States, GA, Atlanta
Joined Apr 2005
4,626 Posts
Quote:
Originally Posted by Paul_BB Yes but you can only choose one of the following for all Re : "min-drag" or "min-sink" and "max-glide". e.g. if I want min-sink at low Reynolds (thermalling) and max-glide at high Reynolds (to get through sinking air between two thermals). Have you read Martin Simons series of articles on RC soaring here: http://www.rcsoaringdigest.com/pdfs/Simons_UTSS.pdf I suppose you have. Paul
Paul,
Here's how I would handle that problem. You can let me know if I'm being dense. In either of those cases (thermalling or flying between thermals), the lift is going to be known, so you can compute the Cl based on the flight speed and wing planform. Then compute the Reynolds number and Mach number as well for that flight condition. Finally, optimize the airfoil for 'min-drag' at each of these operating points. The reason being that if Cl is specified, all three types of optimization amount to minimizing the drag, even though the objective function may be computed differently.
Dan
Apr 07, 2015, 12:06 PM
Registered User
France, IdF, Lagny-sur-Marne
Joined Feb 2007
749 Posts
Quote:
Originally Posted by Montag DP Paul, Here's how I would handle that problem. You can let me know if I'm being dense. In either of those cases (thermalling or flying between thermals), the lift is going to be known, so you can compute the Cl based on the flight speed and wing planform. Then compute the Reynolds number and Mach number as well for that flight condition. Finally, optimize the airfoil for 'min-drag' at each of these operating points. The reason being that if Cl is specified, all three types of optimization amount to minimizing the drag, even though the objective function may be computed differently. Dan
Thanks Dan,
I'll think about it and give it a try tomorrow.
Regards,
Paul
Apr 09, 2015, 11:57 PM
Registered User
Joined Mar 2015
3 Posts
Quote:
Originally Posted by Montag DP Everyone, I've uploaded a new version which includes a constraint to generate symmetrical airfoils....
Thanks for that, I'll give it a spin tonight.
Apr 10, 2015, 01:30 AM Registered User France, IdF, Lagny-sur-Marne Joined Feb 2007 749 Posts Well, it didn't work. But don't bother Dan.
Apr 10, 2015, 01:57 AM Registered User Brisbane, Australia Joined Feb 2002 1,242 Posts Dan, I'll admit I was a bit confused by the choice of "min-drag" or "min-sink" and "max-glide". Since the analysis is being performed on a 2D aerofoil, and not a complete wing, I couldn't see how you could calculate min sink or max glide conditions ? And isn't the min-drag optimisation being performed for each operating point independently, with the penalty functions and weights being used to determine the overall optimal aerofoil ? | 930 | 3,654 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.6875 | 3 | CC-MAIN-2015-18 | latest | en | 0.920556 |
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# Number 691920
six hundred ninety one thousand nine hundred twenty
### Properties of the number 691920
Factorization 2 * 2 * 2 * 2 * 3 * 3 * 5 * 31 * 31 Divisors 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 31, 36, 40, 45, 48, 60, 62, 72, 80, 90, 93, 120, 124, 144, 155, 180, 186, 240, 248, 279, 310, 360, 372, 465, 496, 558, 620, 720, 744, 930, 961, 1116, 1240, 1395, 1488, 1860, 1922, 2232, 2480, 2790, 2883, 3720, 3844, 4464, 4805, 5580, 5766, 7440, 7688, 8649, 9610, 11160, 11532, 14415, 15376, 17298, 19220, 22320, 23064, 28830, 34596, 38440, 43245, 46128, 57660, 69192, 76880, 86490, 115320, 138384, 172980, 230640, 345960, 691920 Count of divisors 90 Sum of divisors 2401074 Previous integer 691919 Next integer 691921 Is prime? NO Previous prime 691919 Next prime 691921 691920th prime 10440611 Is a Fibonacci number? NO Is a Bell number? NO Is a Catalan number? NO Is a factorial? NO Is a regular number? NO Is a perfect number? NO Polygonal number (s < 11)? NO Binary 10101000111011010000 Octal 2507320 Duodecimal 294500 Hexadecimal a8ed0 Square 478753286400 Square root 831.81728762992 Natural logarithm 13.44722562098 Decimal logarithm 5.8400558840998 Sine 0.073922392848939 Cosine -0.9972639970617 Tangent -0.074125199612881
Number 691920 is pronounced six hundred ninety one thousand nine hundred twenty. Number 691920 is a composite number. Factors of 691920 are 2 * 2 * 2 * 2 * 3 * 3 * 5 * 31 * 31. Number 691920 has 90 divisors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 31, 36, 40, 45, 48, 60, 62, 72, 80, 90, 93, 120, 124, 144, 155, 180, 186, 240, 248, 279, 310, 360, 372, 465, 496, 558, 620, 720, 744, 930, 961, 1116, 1240, 1395, 1488, 1860, 1922, 2232, 2480, 2790, 2883, 3720, 3844, 4464, 4805, 5580, 5766, 7440, 7688, 8649, 9610, 11160, 11532, 14415, 15376, 17298, 19220, 22320, 23064, 28830, 34596, 38440, 43245, 46128, 57660, 69192, 76880, 86490, 115320, 138384, 172980, 230640, 345960, 691920. Sum of the divisors is 2401074. Number 691920 is not a Fibonacci number. It is not a Bell number. Number 691920 is not a Catalan number. Number 691920 is not a regular number (Hamming number). It is a not factorial of any number. Number 691920 is an abundant number and therefore is not a perfect number. Binary numeral for number 691920 is 10101000111011010000. Octal numeral is 2507320. Duodecimal value is 294500. Hexadecimal representation is a8ed0. Square of the number 691920 is 478753286400. Square root of the number 691920 is 831.81728762992. Natural logarithm of 691920 is 13.44722562098 Decimal logarithm of the number 691920 is 5.8400558840998 Sine of 691920 is 0.073922392848939. Cosine of the number 691920 is -0.9972639970617. Tangent of the number 691920 is -0.074125199612881 | 1,182 | 2,789 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2020-16 | latest | en | 0.43164 |
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# Jani
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• I
• Korybut
#### Korybut
TL;DR Summary
Need some clarifying commentary on the proof
Hello!
According to the attached proposition on ##C^\infty## manifold space of derivations ##D_m M## is isomorphic to Tangent space ##T_m M##.
Cited here another proposition (1.4.5) states the following
1. For constant function ##D_m(f)=0##
2. If ##f\vert_U=g\vert_U## for some neighborhood ##U## of ##m##, then ##D_m(f)=D_m(g)##.
I don't get the following.
1. Where ##C^\infty## is important? I think that this is important due to algebraic reasons. In Teylor's formula all terms should of the same ##C^k## and this happens only for ##C^\infty##. Am I right?
2. I don't get this ##h##-thing completely. Even without it I can apply derivation ##D_{m_0}## to both sides of (1.4.19) and get statement of the proposition. What am I missing?
## Answers and Replies
Summary:: Need some clarifying commentary on the proof
Hello!
According to the attached proposition on ##C^\infty## manifold space of derivations ##D_m M## is isomorphic to Tangent space ##T_m M##.
View attachment 296438
Cited here another proposition (1.4.5) states the following
1. For constant function ##D_m(f)=0##
2. If ##f\vert_U=g\vert_U## for some neighborhood ##U## of ##m##, then ##D_m(f)=D_m(g)##.
I don't get the following.
1. Where ##C^\infty## is important?
This is simply because it is easier to bother with smooth functions than to administrate an additional parameter in a proof that is very technical anyway. What are the assumptions in 1.4.5?
I think that this is important due to algebraic reasons. In Teylor's formula all terms should of the same ##C^k## and this happens only for ##C^\infty##. Am I right?
2. I don't get this ##h##-thing completely. Even without it I can apply derivation ##D_{m_0}## to both sides of (1.4.19) and get statement of the proposition. What am I missing?
I guess that your quotation of 1.4.5 is incomplete. What do we have outside of ##U##? How can ##f\vert_U=g\vert_U## determine the behaviour of ##D_m(f)## outside of ##U##? Either you have an additional property of ##M##, e.g. a transitive operation, or ##f\vert_{M/U}=g\vert_{M/U}=0.## The latter would explain the role of ##h.##
Korybut
This is simply because it is easier to bother with smooth functions than to administrate an additional parameter in a proof that is very technical anyway. What are the assumptions in 1.4.5?
Do you mean that one can prove this isomorphism ##T_m M=D_m M## without assuming that manifold is of ##C^\infty##?
This is simply because it is easier to bother with smooth functions than to administrate an additional parameter in a proof that is very technical anyway. What are the assumptions in 1.4.5?
I guess that your quotation of 1.4.5 is incomplete. What do we have outside of ##U##? How can ##f\vert_U=g\vert_U## determine the behaviour of ##D_m(f)## outside of ##U##? Either you have an additional property of ##M##, e.g. a transitive operation, or ##f\vert_{M/U}=g\vert_{M/U}=0.## The latter would explain the role of ##h.##
Indeed. Sorry for that here is the full proposition with the proof
Proof of this proposition also uses this ##h##-thing. I used to think that it was made just to make the proof look fancier. Now I believe that I miss something very subtle...
It looks it is very important for derivations to act only on functions that are defined globally on whole manifold. (1.4.19) holds only in some neighbourhood. However while l.h.s. is well-defined for entire manifold, on the other hand r.h.s. is defined only in this neighbourhood and with this ##h##-trick acquires definition on the entire manifold.
Why it is so important for derivation to be applied only on globally defined function? I know that according to the definition ##D_m\, :\, C^k(M)\rightarrow \mathbb{R}##. But this is derivation a point which looks like very local operation... Ahhhh
Please help)
Do you mean that one can prove this isomorphism ##T_m M=D_m M## without assuming that manifold is of ##C^\infty##?
All I can see is, that we need an integrable second derivative. The theorem is probably meant to use for Lie algebras, i.e. Lie groups, i.e. analytic manifolds, i.e. smooth manifolds. Derivations are another point of view for the Leibniz rule or the Jacobi identity, or: how to differentiate a product?
Smooth manifolds are a lot more convenient than tangential spaces on ##C^k(M)## and the most interesting examples are smooth manifolds.
Indeed. Sorry for that here is the full proposition with the proof0View attachment 296443
Proof of this proposition also uses this ##h##-thing. I used to think that it was made just to make the proof look fancier. Now I believe that I miss something very subtle...
It looks it is very important for derivations to act only on functions that are defined globally on whole manifold. (1.4.19) holds only in some neighbourhood. However while l.h.s. is well-defined for entire manifold, on the other hand r.h.s. is defined only in this neighbourhood and with this ##h##-trick acquires definition on the entire manifold.
Why it is so important for derivation to be applied only on globally defined function? I know that according to the definition ##D_m\, :\, C^k(M)\rightarrow \mathbb{R}##. But this is derivation a point which looks like very local operation... Ahhhh
Please help)
The ##h-##thingy as you call it is the partition of the unity. It bridges the gap between local and global. Differentiation is a local property, but we want to make a statement about the global manifold, and that its tangents at ##m\in M## are derivatives in ##m## for any ##m.## Remember that the derivative of a one-dimensional function is a linear function that obeys the Leibniz rule. Proposition 1.4.7 is simply the multi-dimensional version. In order to get a global statement from a local property, it is useful to expand the local function by zero outside the local neighborhood. For example, the normal field of a submanifold is to be extended to the entire manifold. Or: In order to define the area integral, or to integrate over manifolds in general, coordinates must be chosen, which is only possible locally. The integrand must therefore be broken down in such a way that it remains locally integrable, but becomes zero outside the scope of the coordinate system. That is what ##h## is for. It is the analytical version of Urysohn's Lemma.
Korybut
All I can see is, that we need an integrable second derivative. The theorem is probably meant to use for Lie algebras, i.e. Lie groups, i.e. analytic manifolds, i.e. smooth manifolds. Derivations are another point of view for the Leibniz rule or the Jacobi identity, or: how to differentiate a product?
Smooth manifolds are a lot more convenient than tangential spaces on Ck(M) and the most interesting examples are smooth manifolds.
I do understand what you are talking about. But I believe the reason is simply formal. If ##f## is of class ##C^k(M)##. Then l.h.s. of (1.4.19) is ##C^k## and I can apply derivation that maps ##C^k## functions to real numbers. However the remainder in Teylor's formula is of class ##C^{k-2}## and it is not clear how one should apply the same derivation to this term.
One more time. Thanks a lot for your help!
Last edited:
Why it is so important for derivation to be applied only on globally defined function?
I am guessing that is how the definitions were given in the book (which one is it?). Otherwise you get something equivalent. The space of derivations at a point of ##C^\infty(M)## and the space of derivations at a point of the algebra of locally defined smooth functions around the point are isomorphic. But they have to be consistent with their definitions.
I am guessing that is how the definitions were given in the book (which one is it?). Otherwise you get something equivalent. The space of derivations at a point of ##C^\infty(M)## and the space of derivations at a point of the algebra of locally defined smooth functions around the point are isomorphic. But they have to be consistent with their definitions.
I also believe that all this machinery is because of this very specific definition that derivation works only on function that are defined globally on the whole manifold. Book is "Differential Geometry and Mathematical Physics" by Rudolph and Schmidt (very hard to read (for me) but rigorous).
I also believe that all this machinery is because of this very specific definition that derivation works only on function that are defined globally on the whole manifold. Book is "Differential Geometry and Mathematical Physics" by Rudolph and Schmidt (very hard to read (for me) but rigorous).
Yes, definition 1.4.4 page 24.
Korybut | 2,158 | 8,706 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.3125 | 3 | CC-MAIN-2023-23 | latest | en | 0.881481 |
https://www.stem.org.uk/resources/elibrary/resource/33416/integrated-mathematics-scheme-n1 | 1,603,422,595,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107880519.12/warc/CC-MAIN-20201023014545-20201023044545-00355.warc.gz | 914,944,375 | 11,849 | # Integrated Mathematics Scheme: N1
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From the Integrated Mathematics Scheme, this book is designed for students who were likely to be taking examinations equivalent to higher level GCSE. The book contains 30 units, split into three sections each containing ten units.
[b]Units 1 to 10[/b] cover:
Calculating long multiplication and long division without the use of a calculator, solving linear equations, changing inequalities, translation and reflection of shapes on a four quadrant grid, drawing straight line graphs, dealing with different units of length, properties of size A paper, direct proportionality using graphs and expressed as a function, enlargement and scale factors, maps and plans, line and rotational symmetry, regular polygons, ruler and compass constructions, loci and calculation of the mean including use of sigma notation.
[b]Units 11 to 20[/b] cover:
Probability, angles in triangles and quadrilaterals, bearings, similar triangles, circumference, arcs, areas and sectors of circles, radian measure, straight line graphs, simultaneous equations, simultaneous inequalities, timetables, arithmetic in base 2 and other number bases, addition and multiplication of matrices, translation by a vector, pictograms, bar charts and pie charts.
[b]Units 21 to 30[/b] cover:
Calculation of volume of prisms and cylinders, density, multiplying out brackets, factorising, difference of squares, algebraic fractions, squares and square roots, application of Pythagoras’ Theorem, substitution into a formula, change the subject of a formula, four rules for directed numbers, solution of quadratics, use of sine, cosine and tangent, finding area of triangle using sine, use of logarithms, laws of indices and exponential graph.
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89.2 MB | 474 | 2,359 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.96875 | 3 | CC-MAIN-2020-45 | latest | en | 0.921987 |
http://math.stackexchange.com/questions/148406/elements-of-order-6-in-an-abelian-group-of-order-360?answertab=oldest | 1,455,110,712,000,000,000 | text/html | crawl-data/CC-MAIN-2016-07/segments/1454701159376.39/warc/CC-MAIN-20160205193919-00271-ip-10-236-182-209.ec2.internal.warc.gz | 153,416,803 | 17,814 | # Elements of order $6$ in an Abelian group of order $360$
Let $A$ be a finite abelian group of order $360$ which does not contain any elements of order $12$ or $18$. How many elements of order $6$ does $A$ contain? I've got that $A$ is $C_2 \times C_6 \times C_{30}$ but not sure how to work out how many elements of order $6$ there are. Any help appreciated!
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Your title has a typo. Please check for typos in what is the most visible part of your question! – Mariano Suárez-Alvarez May 22 '12 at 21:04
An element has exponent $6$ if and only if each component has exponent $6$. There are $2$ possibilities for the $C_2$ component, $6$ for the $C_6$ component, and $6$ for the $C_{30}$ component (since $C_{30}$ has a unique subgroup of order $6$. That gives $72$ elements of exponent $6$.
Of these elements, you want to subtract those of exponent $3$ and those of exponent $2$, and then add back the element of exponent $1$ (which you subtracted twice).
To get an element of exponent $3$ you need each component to be of exponent $3$: there is one choice for the $C_2$ component, three choices for the $C_6$ component, and three choices for the $C_{30}$ component. This gives you $9$ elements.
To get an element of exponent $2$, you need each component to be of exponent $2$; there are two choices for each of the components. This gives you $8$ elements.
So: \begin{align*} \#(\text{elements of order 6}) &= \#(\text{elements of exponent 6}) - \#(\text{elements of exponent 3})\\ &\qquad -\#(\text{elements of exponent 2}) + \#(\text{elements of exponent 1})\\ &= 72 - 9 - 8 + 1 = 56. \end{align*}
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Escentially, since your group is $G = H \times I \times J$ an element of order $6$ means that every component must be of order $6$, $3$, $2$, $1$, this can be proven by looking at the map $G/(H \times J)\to I$. Hence you get elements of the following form (note the numbers represent the orders of the elements): $$(1,1,6)\; (1,6,1)\; (1,6,6)\; (1,2,6)\; (1,3,6)\; (1,2,3)\; (1,3,2)\; (1,6,3)\; (1,6,2)\; (2,1,6)\; (2,6,1)\; (2,6,6)\; (2,2,6)\; (2,3,6)\; (2,2,3)\; (2,3,2)\; (2,6,3)\; (2,6,2)\; (2,3,1)\; (2,1,3).$$ And you basically take how many elements of each order there is in each subgroup (i.e., $(1,6,1)$ is $1\times 2\times 1=2$), and just multiply them for each set.
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Moreover, the other answer is wrong by simply looking at the group ((Z2,+)X(Z3,+)) which has two elements of order 6 (1,2) and (1,1) but the components have no elements of order 6 – Pioter May 23 '12 at 2:30 | 836 | 2,500 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2016-07 | longest | en | 0.820929 |
https://z-scoretable.com/negative-z-score-table/ | 1,695,936,047,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510454.60/warc/CC-MAIN-20230928194838-20230928224838-00390.warc.gz | 1,173,231,714 | 14,940 | ### Negative Z-Score Table: Navigating the Left Side of the Bell Curve
In the world of statistics, understanding the distribution of data points is crucial. Among the various tools used to make sense of these distributions, Z-scores are incredibly pivotal. While both positive and negative Z-scores provide insights into the positioning of data points, the negative Z-score table specifically helps us interpret those data points that fall below the mean. To fully appreciate the significance of the negative Z-score table, we must first journey into the broader landscape of Z-scores and standard normal distributions.
## Z-Score Basics
At its core, a Z-score is a statistical measurement that describes a value’s relationship to the mean of a group of values. It’s expressed in terms of standard deviations from the mean. The formula for the Z-score is:
Where:
• Z = Z-score
• X = Individual data point
• μ = Mean of the dataset
• σ = Standard deviation of the dataset
A negative Z-score indicates that the data point is below the mean. The farther away the Z-score is from zero, the more unusual and significant that data point is, relative to the mean.
## The Standard Normal Distribution and Negative Z-Scores
The standard normal distribution, often visualized as a bell curve, is symmetric about the mean. The mean value of the standard normal distribution is zero, which divides the distribution into two halves. While the right half (positive side) represents positive Z-scores, the left half symbolizes negative Z-scores.
When we discuss the negative Z-score table, we’re focusing on this left half, exploring the probabilities associated with data points that fall below the mean.
## Diving into the Negative Z-Score Table
Much like its positive counterpart, the negative Z-score table provides probabilities corresponding to various Z-scores. However, given the symmetry of the standard normal distribution, many tables list only positive Z-scores, expecting the user to infer the corresponding negative values. Some comprehensive tables, though, provide explicit entries for negative Z-scores.
Reading a negative Z-score table is straightforward. The table lists Z-scores and their corresponding probabilities. The value found at the intersection of a specific row and column provides the cumulative probability up to that Z-score.
## Examples and Applications
Example 1: Let’s say students’ scores in a particular examination are normally distributed with a mean of 50 and a standard deviation of 10. If a student scores 40, we can use the negative Z-score table to determine their percentile rank.
First, calculate the Z-score:
Using the negative Z-score table, a Z-score of -1 corresponds roughly to the 16th percentile. This means the student scored higher than only about 16% of the examinees.
Example 2: In a factory, the diameters of a particular product are normally distributed with a mean diameter of 5 cm and a standard deviation of 0.2 cm. If products below 4.8 cm in diameter are deemed substandard, what proportion of products is substandard?
First, derive the Z-score:
Referring to the negative Z-score table, a Z-score of -1 again aligns with approximately the 16th percentile. This suggests that 16% of the products might be substandard based on the diameter criterion.
## Importance of the Negative Z-Score Table
• Scientific Research: In fields like psychology or medicine, the negative Z-score table helps researchers understand how certain data points compare to typical or average outcomes.
• Business Analytics: For businesses, understanding negative Z-scores can be crucial when assessing below-average performance, whether in sales, production quality, or other metrics.
• Academic Evaluation: Teachers can use the negative Z-score table to understand how students perform relative to class or school averages, aiding targeted support.
Check out everything you need to know about the Z table
## Summary
The negative Z-score table offers a focused lens into the realm of data points that fall below the mean in a standard normal distribution. While it’s easy to get absorbed by the table’s rows and columns, it’s essential to remember the broader narrative. Each Z-score and corresponding percentile paints a story, positioning data points within a larger dataset and offering context.
Statistics, with its vast methodologies and tools, provides us the means to make sense of data. Among these tools, the negative Z-score table stands as an unsung hero, guiding researchers, analysts, and professionals in interpreting and responding to data points on the left side of the bell curve. Whether you’re in academia, business, or any other field that relies on data, understanding the nuances of the negative Z-score table is undoubtedly a valuable skill. | 952 | 4,812 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.125 | 4 | CC-MAIN-2023-40 | latest | en | 0.858989 |
https://www.mathworks.com/matlabcentral/cody/problems/39-which-values-occur-exactly-three-times/solutions/744855 | 1,590,705,844,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347400101.39/warc/CC-MAIN-20200528201823-20200528231823-00081.warc.gz | 823,852,256 | 15,701 | Cody
# Problem 39. Which values occur exactly three times?
Solution 744855
Submitted on 24 Sep 2015 by Uthara Keerthan
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% x = [1 2 5 2 2 7 8 3 3 1 3 8 8 8]; y_correct = [2 3]; assert(isequal(threeTimes(x),y_correct))
y = [] a = 1 2 3 5 7 8 y = 2 y = 2 3
2 Pass
%% x = [1 1 1]; y_correct = [1]; assert(isequal(threeTimes(x),y_correct))
y = [] a = 1 y = 1
3 Pass
%% x = [5 10 -3 10 -3 11 -3 5 5 7]; y_correct = [-3 5]; assert(isequal(threeTimes(x),y_correct))
y = [] a = -3 5 7 10 11 y = -3 y = -3 5 | 272 | 677 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.203125 | 3 | CC-MAIN-2020-24 | latest | en | 0.592606 |
https://jeopardylabs.com/play/unit-5-lessons-6-10-math-expressions-5th-grade | 1,531,939,230,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676590314.29/warc/CC-MAIN-20180718174111-20180718194111-00471.warc.gz | 678,474,486 | 7,927 | Convert Mixed to Improper
Convert Improper to Mixed
Subtract Mixed Numbers
Fraction Trivia
3 and 1/2 =
What is 7/2
11/2 =
5 and 1/2
3 1/3 + 3 1/3 =
6 2/3
3 1/2 - 1 1/2 =
2
### 100
Fractions have been used for over 2,000 years but were not used as we know them no until ... (1,000 years ago, 500 years ago, or 5 days ago).
500 years ago.
10 and 1/10 =
101/10
3/2 =
1 and 1/2
10 1/5 + 10 1/5
20 2/5
### 200
100 2/5- 100 2/5 =
0
### 200
If you walk 1/2 of the way home and stop to rest. Then walk 1/2 of the remaining distance home and then stop and rest, and then walk 1/2 of that remaining distance home, when will you get home.
Never. You will only be splitting the remaining distance. You will never make it.
3 and 1/3
10/3
4/3 =
1 and 1/3
5 3/7 + 4 5/7=
10 1/7
5 1/9 - 1 8/9=
3 2/9
### 300
What fraction is a NFL football game divided into?
Fourths
5 and 1/5
26/5
### 400
10/4 =
What is 2 and 2/4 or 2 and 1/2
5 3/4 + 2 3/4
8 2/4 or 8 1/2
10 2/5 - 3 4/5 =
6 3/5
### 400
Approximately what fraction of your life is spent sleeping?
1/3. If you live to be 99 you will have spent roughly 33 of those years asleep. | 460 | 1,137 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2018-30 | latest | en | 0.898466 |
grafit-electro.ru | 1,558,568,730,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232256980.46/warc/CC-MAIN-20190522223411-20190523005411-00244.warc.gz | 85,413,448 | 7,280 | # Coefficient of performance
Definition of coefficient of performance (COP): Ratio of work or useful output to the amount of work or energy input, used generally as a measure of the . Coefficient of performance (COP), is an expression of the efficiency of a heat pump. Geothermal heat pump efficiency is traditionally measured using a ratio called “ coefficient of performance ” (COP). Note: In calculating the coefficient of performance , or any other heat-engine related quantities, the temperatures must be the values in Kelvins. It is defined as the heat removed from the cold reservoir Qcol divided by the work W done to . It is based on the relationship between the power (kW) .
Equations are presented which relate the actual value of the coefficient of performance of a heat pump to the theoretical Rankine coefficient of performance by . Definition of COEFFICIENT OF PERFORMANCE (COP): Ratio of realized work or useful output per the amount of supplied effort or energy input. COP is also the ratio of . First Law : For refrigeration cycles: Equation. This is a cycle diagram for a refrigeration cycle. This measures the energy efficiency of certain heating and cooling appliances, such as heat pumps. The steady-state performance of an electric compression heat pump at a given set of temperature conditions.
COPd(Tj)) means the coefficient of performance at a limited number of specified bins (j) with outdoor temperature (Tj), as declared by the manufacturer.
The coefficient of performance , on the one han describes the relationship between the energy produced in the form of heating output (kWh) and the electrical . Abstract: We study the coefficient of performance (COP) and its bounds of the Canot-like refrigerator working between two heat reservoirs at . This paper gives the coefficient of performance for a heat pump operated at minimum input power for given output heat power. European Seasonal Coefficient Of Performance ) equivalent to the index. Phys Rev E Stat Nonlin Soft Matter Phys.
Efficiencies and coefficients of performance of heat engines, . Bialystok University of Technology, Faculty of Civil Engineering and Environmental Engineering, Department of HVAC Engineering, ul. Significance of heat pump coefficient of performance. Abstract: This paper deals with the load aspects and economic aspects of three types of residential heat . There is a lot to consider when buying a heat pump, but perhaps one of the most important is the coefficient of performance. The coefficent of performance (also known as COP) specifies the ratio between the energy transfer of a heating pump and the total input of . The key performance parameters, such as the coefficient of performance , specific heating loa temperatures of the working fluid in the heat exchangers, . Примеры перевода, содержащие „ coefficient of performance “ – Русско- английский словарь и система поиска по миллионам русских переводов.
A heat pump is a refrigerator whose inside is the greatoutdoors and whose outside is the room to be heated. Thecoefficient of performance for a heat pump is the . This paper showed that the average coefficient of performance (COP) of an air- source heat pump (ASHP) water heater was better during a heating cycle with . Intimidating words that compare the cost of operating a heat pump against operating straight electric heat.
Graph of Cost for 100BTUs of Heat Say you could . In this article the authors propose a new ground source heat pump system with horizontal ground heat . This Demonstration illustrates how to calculate the coefficient of performance ( COP) of an ideal mechanical refrigeration system using a pressure-enthalpy . The observed coefficients of performance for real refrigerators are located in the region between the lower and upper bounds, which is in good . | 773 | 3,818 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.78125 | 3 | CC-MAIN-2019-22 | latest | en | 0.893333 |
https://newbedev.com/determine-the-base-where-a-given-equation-is-true | 1,713,533,422,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817398.21/warc/CC-MAIN-20240419110125-20240419140125-00366.warc.gz | 378,564,034 | 7,237 | Determine the Base where a Given Equation is True
APL (Dyalog Unicode), 30 bytesSBCS
⊢{3⊃e=×/2↑e←⍵⊥⍺:⍵⋄⍺∇⍵+1}1+⌈/∘,
Try it online!
Thanks to Adám for the help.
Explanation:
⊢{3⊃e=×/2↑e←⍵⊥⍺:⍵⋄⍺∇⍵+1}1+⌈/∘, ⍝
⊢ ⍝ left argument ⍺: the vector (do nothing)
1+⌈/∘, ⍝ right argument ⍵: our starting base.
, ⍝ start by flattening the matrix of arguments ⌈/ ⍝ reduce by max (find the highest number)
∘ ⍝ compose both of these together
1+ ⍝ increment by one
{ ⍵⊥⍺ } ⍝ convert inputs to the current base
{ e← } ⍝ store the converted values in 3
{ 2↑ } ⍝ take the first 2 values
{ ×/ } ⍝ multiply them together (reduce-multiply)
{ e= } ⍝ compare with e (the converted inputs)
{3⊃ } ⍝ only keep the result of the comparison with the 3rd element (expected result)
{ :⍵ } ⍝ if truthy, return the current base.
{ ⋄ } ⍝ otherwise...
{ ⍺∇⍵+1} ⍝ ...recurse with the base incremented
We use a helper function, In, to receive the input into a more palatable format. Otherwise the input is received a matrix of 3 columns.
'3 9 42' would give, for example (read top-down then left-to-right):
0 0 4
3 9 2
And for 'aA bB 36jk' (same here. a is 10, b is 11, A is 36, etc)
0 0 3
0 0 6
10 11 19
36 37 20
CJam, 5251 48 bytes
63,{_ea{i32b~\([G-35-9]=-_Xe>:X;}f%fbW%~*=\X>*}#
Test it here. The online tester doesn't support input via ARGV. The closest alternative is to put put the input like 6 9 42 into STDIN and use:
lS/:E;
63,{_E{i32b~\([G-35-9]=-_Xe>:X;}f%fbW%~*=\X>*}#
This prints -1 if no valid base up to 62 can be found.
Many thanks to Peter for the digit parsing code!
I fixed a lot of problems which added 14 bytes to the count. The following explanation is still for my original submission, and I'll update it some time tomorrow.
63,{_ea{i32b~\([G-35-9]=-_Xe>:X;}f%fbW%~*=\X>*}#
63, "Push the array [0 1 .. 62].";
{ }# "Find the first index for which the block returns
a truthy value.";
_ "Duplicate the current base.";
ea "Read ARGV into an array of strings.";
{ }f% "Apply this block to each character.";
i32b "Convert to code point, and then to base-32. The
most significant digit now identifies the 'type'
of digit.";
~\( "Unwrap the array. Swap the digits. Decrement.";
[G-35-9] "Push array [16 -35 -9] of digit offsets.";
=- "Select the relevant offset and subtract it from
the least significant digit.";
_ "Duplicate the current digit D.";
Xe>:X; "X := max(X,D). X is predefined as 1.";
fb "Convert all numbers to the current base.";
W% "Reverse the list of numbers.";
~ "Unwrap the array.";
*= "Multiply factors. Check equality with product.";
\ "Swap result with current base.";
X> "Ensure base is greater than X.";
* "Multiply boolean results.";
The index is printed automatically at the end of the program.
CJam, 53 bytes
lA,s'{,97>+'[,65>+f#_\$W=1e>)63,>_@Wa/W%f{fb~*=}1#\0+=
Takes the three input from STDIN like
6 9 42
Prints 0 if product in any base is not possible
Will try to golf it further.
Try it here | 1,108 | 3,667 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2024-18 | latest | en | 0.778525 |
https://au.mathworks.com/matlabcentral/cody/problems/33-create-times-tables/solutions/1852625 | 1,606,356,787,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141185851.16/warc/CC-MAIN-20201126001926-20201126031926-00081.warc.gz | 204,924,705 | 17,038 | Cody
# Problem 33. Create times-tables
Solution 1852625
Submitted on 19 Jun 2019 by Willion Bird
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
x = 2; y_correct = [1 2; 2 4]; assert(isequal(timestables(x),y_correct))
2 Pass
x = 3; y_correct = [1 2 3; 2 4 6; 3 6 9]; assert(isequal(timestables(x),y_correct))
3 Pass
x = 5; y_correct = [1 2 3 4 5; 2 4 6 8 10; 3 6 9 12 15; 4 8 12 16 20; 5 10 15 20 25]; assert(isequal(timestables(x),y_correct))
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 248 | 700 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.859375 | 3 | CC-MAIN-2020-50 | latest | en | 0.63835 |
https://community.monday.com/t/how-to-use-formula-to-calculate-sum-of-values-across-multiple-numbers-columns-based-on-condition-e-g-find-column-with-name-or-all-columns/72346 | 1,708,984,951,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947474663.47/warc/CC-MAIN-20240226194006-20240226224006-00814.warc.gz | 190,450,473 | 18,397 | # How to use formula to calculate Sum of values across multiple Numbers columns based on condition e.g find column with name or "all columns"
How to use formula to calculate Sum of values across multiple Numbers columns based on condition e.g find column with name or even “all columns”
I am used to google sheet or excel where I can perform sum of values easily with SUM(:) with any defined range I want.
So far in monday.com, I only can do this SUM(column1, column2, column3,…)
PS: these columns are date header e.g 2/12/2023, 9/12/2023, 16/12/2023
How can I achieve similar result in Monday.com?
Ideally if I can SUM over columns easily with something similar here will be great e.g SUM(where year column = 2023) | 176 | 719 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2024-10 | latest | en | 0.775602 |
http://www.ask.com/web?q=Examples+of+Stem+Leaf+Plots&o=2603&l=dir&qsrc=3139&gc=1 | 1,484,658,932,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560279915.8/warc/CC-MAIN-20170116095119-00168-ip-10-171-10-70.ec2.internal.warc.gz | 345,074,509 | 15,041 | Web Results
## Stem-and-leaf display - Wikipedia
en.wikipedia.org/wiki/Stem-and-leaf_display
A stem-and-leaf display is a device for presenting quantitative data in a graphical format, similar ... In this example, the leaf represents the ones place and the stem will ... This allowed the ste...
## Stem-and-Leaf Plots - Purplemath
www.purplemath.com/modules/stemleaf.htm
Explains how to create a stem-and-leaf plot from a data set. ... Here are some more examples of stem-and-leaf plots, containing a few additional details.
## Stem and Leaf Plots - Math is Fun
www.mathsisfun.com/data/stem-leaf-plots.html
A Stem and Leaf Plot is a special table where each data value is split into a "stem " (the first digit or digits) and a "leaf" (usually the last digit). Like in this example: ...
## Stem and leaf plots - Khan Academy
Stem-and-leaf Plots. ... Practice: Reading stem and leaf plots · Next tutorial. Picture graphs, bar graphs, and histograms. Current time:0:00Total duration:5:58 ...
## Stem and Leaf Plots Examples, Stem and Leaf Plots Worksheet, and ...
www.beaconlearningcenter.com/documents/1600_01.pdf
Jul 23, 2003 ... common place value is used to form the leaves. 2. EXAMPLE: Make a stem and leaf plot of the algebra test scores given below. Then complete ...
## Stem & Leaf Plots Examples - Shmoop
www.shmoop.com/basic-statistics-probability/stem-leaf-plots-examples.html
Pre-Algebra giving you a hard time? Shmoop's free Basic Statistics & Probability Guide has all the explanations, examples, and exercises you've been craving.
Sep 1, 2011 ... This example shows how to make a stem and leaf plot. Remember that the leading values become our stems and the trailing values the leaves. | 417 | 1,716 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2017-04 | latest | en | 0.830577 |
https://stage.gcfglobal.org/en/googlespreadsheets/creating-complex-formulas/1/ | 1,726,771,842,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652055.62/warc/CC-MAIN-20240919162032-20240919192032-00124.warc.gz | 485,024,127 | 10,530 | search
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# Google Sheets: Creating Complex Formulas
### Introduction
You may have experience working with formulas that contain only one operator, such as 7+9. More complex formulas can contain several mathematical operators, such as 5+2*8. When there's more than one operation in a formula, the order of operations tells Google Sheets which operation to calculate first. To write formulas that will give you the correct answer, you'll need to understand the order of operations.
Watch the video below to learn how to create complex formulas.
#### Order of operations
Google Sheets calculates formulas based on the following order of operations:
1. Operations enclosed in parentheses
2. Exponential calculations (3^2, for example)
3. Multiplication and division, whichever comes first
4. Addition and subtraction, whichever comes first
Click the arrows in the slideshow below to learn how the order of operations is used to calculate formulas in Google Sheets.
• While this formula may look complicated, we can use the order of operations step by step to find the right answer.
• First, we'll start by calculating anything inside parentheses. In this case, there's only one thing we need to calculate: 6-3=3.
• As you can see, the formula already looks simpler. Next, we'll look to see if there are any exponents. There is one: 2^2=4.
• Next, we'll solve any multiplication and division, working from left to right. Because the division operation comes before the multiplication, it's calculated first: 3/4=0.75.
• Now, we'll solve our remaining multiplication operation: 0.75*4=3.
• Next, we'll calculate any addition or subtraction, again working from left to right. Addition comes first: 10+3=13.
• Finally, we have one remaining subtraction operation: 13-1=12.
• Now we have our answer: 12. And this is the exact same result you would get if you entered the formula into Excel.
#### Creating complex formulas
In the example below, we'll demonstrate how Google Sheets solves a complex formula using the order of operations. The complex formula in cell D6 calculates the sales tax by adding the prices together and multiplying by the 5.5% tax rate (which is written as 0.055).
Google Sheets follows the order of operations and first adds the values inside the parentheses: (D3+D4+D5) = \$274.10. Then it multiplies by the tax rate: \$274.10*0.055. The result will show that the tax is \$15.08.
It's especially important to follow the order of operations when creating a formula. Otherwise, Google Sheets won't calculate the results accurately. In our example, if the parentheses are not included, the multiplication is calculated first and the result is incorrect. Parentheses are often the best way to define which calculations will be performed first in Google Sheets.
#### To create a complex formula using the order of operations:
In the example below, we'll use cell references along with numerical values to create a complex formula that will calculate the subtotal for a catering invoice. The formula will calculate the cost of each menu item first, then add these values.
1. Select the cell that will contain the formula. In our example, we'll select cell C5.
2. Enter your formula. In our example, we'll type =B3*C3+B4*C4. This formula will follow the order of operations, first performing the multiplication: 2.79*35 = 97.65 and 2.29*20 = 45.80. It then will add these values to calculate the total: 97.65+45.80.
3. Double-check your formula for accuracy, then press Enter on your keyboard. The formula will calculate and display the result. In our example, the result shows that the subtotal for the order is \$143.45.
Google Sheets will not always tell you if your formula contains an error, so it's up to you to check all of your formulas. To learn how to do this, read our article on why you should Double-Check Your Formulas.
### Challenge!
1. Open our example file. Make sure you're signed in to Google, then click File > Make a copy.
2. Select the Challenge sheet. Let's say we want to compare two discounts. The first discount takes 20% off the total, and the second discount takes \$30 off the total.
3. In cell D6, create a formula that calculates the total using the 20% off discount.
Hint: Because we're taking 20% off, 80% of the total will remain. To calculate this, multiply 0.80 by the sum of the line totals.
4. In cell D7, create a formula that subtracts 30 from the total. | 1,015 | 4,458 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.6875 | 5 | CC-MAIN-2024-38 | latest | en | 0.910001 |
http://en.wikipedia.org/wiki/Kolmogorov_extension_theorem | 1,433,019,244,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207932705.91/warc/CC-MAIN-20150521113212-00188-ip-10-180-206-219.ec2.internal.warc.gz | 78,081,243 | 11,359 | # Kolmogorov extension theorem
In mathematics, the Kolmogorov extension theorem or Daniell-Kolmogorov extension theorem (also known as Kolmogorov existence theorem or Kolmogorov consistency theorem) is a theorem that guarantees that a suitably "consistent" collection of finite-dimensional distributions will define a stochastic process. It is credited to the Soviet mathematician Andrey Nikolaevich Kolmogorov[1] and also to British mathematician Percy John Daniell who discovered it independently in the slightly different setting of integration theory. [2]
## Statement of the theorem
Let $T$ denote some interval (thought of as "time"), and let $n \in \mathbb{N}$. For each $k \in \mathbb{N}$ and finite sequence of times $t_{1}, \dots, t_{k} \in T$, let $\nu_{t_{1} \dots t_{k}}$ be a probability measure on $(\mathbb{R}^{n})^{k}$. Suppose that these measures satisfy two consistency conditions:
1. for all permutations $\pi$ of $\{ 1, \dots, k \}$ and measurable sets $F_{i} \subseteq \mathbb{R}^{n}$,
$\nu_{t_{\pi (1)} \dots t_{\pi (k)}} \left( F_{\pi (1)} \times \dots \times F_{ \pi(k)} \right) = \nu_{t_{1} \dots t_{k}} \left( F_{1} \times \dots \times F_{k} \right);$
2. for all measurable sets $F_{i} \subseteq \mathbb{R}^{n}$,$m \in \mathbb{N}$
$\nu_{t_{1} \dots t_{k}} \left( F_{1} \times \dots \times F_{k} \right) = \nu_{t_{1} \dots t_{k} t_{k + 1}, \dots , t_{k+m}} \left( F_{1} \times \dots \times F_{k} \times \mathbb{R}^{n} \times \dots \times \mathbb{R}^{n} \right).$
Then there exists a probability space $(\Omega, \mathcal{F}, \mathbb{P})$ and a stochastic process $X : T \times \Omega \to \mathbb{R}^{n}$ such that
$\nu_{t_{1} \dots t_{k}} \left( F_{1} \times \dots \times F_{k} \right) = \mathbb{P} \left( X_{t_{1}} \in F_{1}, \dots, X_{t_{k}} \in F_{k} \right)$
for all $t_{i} \in T$, $k \in \mathbb{N}$ and measurable sets $F_{i} \subseteq \mathbb{R}^{n}$, i.e. $X$ has $\nu_{t_{1} \dots t_{k}}$ as its finite-dimensional distributions relative to times $t_{1} \dots t_{k}$.
In fact, it is always possible to take as the underlying probability space $\Omega = (\mathbb{R}^n)^T$ and to take for $X$ the canonical process $X\colon (t,Y) \mapsto Y_t$. Therefore, an alternative way of stating Kolomogorov's extension theorem is that, provided that the above consistency conditions hold, there exists a (unique) measure $\nu$ on $(\mathbb{R}^n)^T$ with marginals $\nu_{t_{1} \dots t_{k}}$ for any finite collection of times $t_{1} \dots t_{k}$. Kolmogorov's extension theorem applies when $T$ is uncountable, but the price to pay for this level of generality is that the measure $\nu$ is only defined on the product σ-algebra of $(\mathbb{R}^n)^T$, which is not very rich.
## Explanation of the conditions
The two conditions required by the theorem are trivially satisfied by any stochastic process. For example, consider a real-valued discrete-time stochastic process $X$. Then the probability $\mathbb{P}(X_1 >0, X_2<0)$ can be computed either as $\nu_{1,2}( \mathbb{R}_+ , \mathbb{R}_-)$ or as $\nu_{2,1}( \mathbb{R}_- , \mathbb{R}_+)$. Hence, for the finite-dimensional distributions to be consistent, it must hold that $\nu_{1,2}( \mathbb{R}_+ , \mathbb{R}_-) = \nu_{2,1}( \mathbb{R}_- , \mathbb{R}_+)$. The first condition generalises this obvious statement to hold for any number of time points $t_i$, and any control sets $F_i$.
Continuing the example, the second condition implies that $\mathbb{P}(X_1>0) = \mathbb{P}(X_1>0, X_2 \in \mathbb{R})$. Also this is a trivial condition that will be satisfied by any consistent family of finite-dimensional distributions.
## Implications of the theorem
Since the two conditions are trivially satisfied for any stochastic process, the powerful statement of the theorem is that no other conditions are required: For any reasonable (i.e., consistent) family of finite-dimensional distributions, there exists a stochastic process with these distributions.
The measure-theoretic approach to stochastic processes starts with a probability space and defines a stochastic process as a family of functions on this probability space. However, in many applications the starting point is really the finite-dimensional distributions of the stochastic process. The theorem says that provided the finite-dimensional distributions satisfy the obvious consistency requirements, one can always identify a probability space to match the purpose. In many situations, this means that one does not have to be explicit about what the probability space is. Many texts on stochastic processes do, indeed, assume a probability space but never state explicitly what it is.
The theorem is used in one of the standard proofs of existence of a Brownian motion, by specifying the finite dimensional distributions to be Gaussian random variables, satisfying the consistency conditions above. As in most of the definitions of Brownian motion it is required that the sample path are continuous almost surely, one then uses kolmogorov continuity theorem to construct a continuous modification of the process constructed by Kolmogorov extension theorem.
## References
1. ^ Øksendal, Bernt (2003). Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin. ISBN 3-540-04758-1.
2. ^ J. Aldrich, But you have to remember PJ Daniell of Sheffield, Electronic Journal for History of Probability and Statistics, Vol. 3, number 2, 2007 | 1,508 | 5,415 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 40, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.234375 | 3 | CC-MAIN-2015-22 | latest | en | 0.747119 |
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Calling All 2011 Booth Applicants!!
Author Message
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26 Jul 2010, 04:54
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@ BruceLee
Buddy I hardly find any comfort in the fact that it's not so very different from last year, cause I would be thinking about it for the very first time.
About this essay - yah even i feel that that it needs to be more interactive but I was thinking of being more explainatory than what a presentation would allow. Guess I would be trying for something in between presentation and an essay.
Nevertheless I would have to really outdo myself to make it sound interesting.
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Count me in for R1!
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In for R1
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27 Jul 2010, 10:46
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amit0505 wrote:
@ BruceLee
Buddy I hardly find any comfort in the fact that it's not so very different from last year, cause I would be thinking about it for the very first time.
About this essay - yah even i feel that that it needs to be more interactive but I was thinking of being more explainatory than what a presentation would allow. Guess I would be trying for something in between presentation and an essay.
Nevertheless I would have to really outdo myself to make it sound interesting.
There is another business school where recommenders are asked about the attitutude of candidate for dealing with ambiguity. Booth is asking it directly from its students. According to researchers, leaders use ambiguity to their advantage. They look at ambiguity as an opportunity instead of a problem.
This essay is definitely a "make or break" essay as it will show how you act if you are given ambiguous problems. And it is not that difficult. Just a bit of soul searching, creativity and self promotion is needed.
_________________
Regards,
George Jacobs
http://www.htbconsultants.com Affordable MBA Essay Review/Editing Service
mba.xpert@gmail.com
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count me in for R2, respectt...
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Booyakasha - big up yourself Matador
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MBAEssay wrote:
There is another business school where recommenders are asked about the attitutude of candidate for dealing with ambiguity. Booth is asking it directly from its students. According to researchers, leaders use ambiguity to their advantage. They look at ambiguity as an opportunity instead of a problem.
This essay is definitely a "make or break" essay as it will show how you act if you are given ambiguous problems. And it is not that difficult. Just a bit of soul searching, creativity and self promotion is needed.
I don't think they're looking at it as a test for how you deal with ambiguity. They're just giving you an opportunity to say whatever you would like to say. If you focus on it as "make or break" you're doing yourself a disservice. My powerpoint was good but it wasn't outstanding. I worried about it for months, ran out of time, and then just decided to tell my story. In the end, I put it together from start to finish in about 4 hours, and half of that was fixing small things. Just tell your story. If you can get creative with it, then it will be even better.
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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29 Jul 2010, 08:51
1
KUDOS
I agree with shana22.
Taking it as a test of ambiguity seems somewhat farfetched. Ambiguity and broad direction are two different things and I think the essay #3 is the latter.
And since the essay is probably the most important part of the app, all essays are make or break in my opinion. I like how Booth adcom changed the direction though. I think last year, it specifically said "you can include notes at the bottom, but don't make it like essays" or something like that.
This year, the format seems really free, but I can't think of any other format than ppt.
Video? unless I am good with cutting and editing scenes, it would be nothing more than me babbling in front of camera.
Word doc? another essay?! nope.
ppt? AAAHHH... I think i can handle that
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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29 Jul 2010, 09:05
1
KUDOS
chostein wrote:
This year, the format seems really free
Essay Question 3 Guidelines
We have set forth the following guidelines:
* The content is completely up to you. Acceptable file formats are PowerPoint or PDF.
* There is a strict maximum of four pages, though you can provide fewer if you choose.
* The document will be printed in color and added to your file for review; therefore, flash, hyperlinks, embedded videos, music, etc. will not be viewed by the committee. You are limited to text and static images to convey your points.
* The file will be evaluated on the quality of content and ability to convey your ideas, not on technical expertise or presentation.
* Files need to be less than 9 megabytes in order to upload. If your file is too large you may save your file as a PDF and upload your essay.
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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29 Jul 2010, 09:10
1
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Thanks, hazay.
I guess there are more stuff for the essay #3. I thought what was mentioned in pg.1 of this thread is everything :p
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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29 Jul 2010, 09:23
1
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chostein wrote:
I guess there are more stuff for the essay #3
Your comment was on the format, not the content required.
And you ve got everything
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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30 Jul 2010, 02:18
1
KUDOS
When you have blank pages to fill, whatever anyone says is a point of view and not a rule.
So I guess its natural for people to have different opinions about it.
I was going through the chat transcript and there were a few questions on the 3rd essay. I found the answer quite useful. So I thought I will paste them here. Hope it helps.
John: Hi, I have a query regarding how to approach the third essay question (PPT one). Should we relate any perwsonal o pofessional experience here that demonstates the quality of "How to think", ability to navigate thru ambiguity ?
Kurt: Again to reiterate an answer from earlier, it is your choice. Focus on what you want to convey to the committee that essentially completes your story. Content might focus on your professional life, personal life, a combination. The choice is up to you. That in essence is the ambiguity you need to navigate for us.
israstro: can u pls give example of ways to deal with Essay Question 3?
Joanna: Hi Israstro. Unfortunately there are literally hundreds of ways to approach this essay---and we have no preference. It truly is up to you how you convey your message to the committee using these 4 pages of white space! We are looking to see how strategic you are in using this space to complete your story effectively.
mattia: Regarding Essay 3, is there a specific font, font size or any other type of fomatting we would need to pay attention to?
Donna: We do not have any specific fonts. Keep in mind that using uncommon fonts may not print correctly on our printers.
G-256413371: Can you please explain what criteria you will be using to rate Essay #3? Is creativity more important than content?
Kurt: Content and substance always trumps creativity and flare. Essay 3 is an opportunity for you to complete your strategic message to the committee. We provide a fixed number of opportunities/tools for you convey your message in (essays, resume, recommendations etc). Even with these tools there is always potential to add greater texture to your story. That is what Essay 3 is for. From our perspective we are looking to see how strategic you are in using this space to complete your story effectively rather than can you simply be creative for creativity's sake.
Dele: Good morning! I was looking over the essays for the fall admissions process for 2011, and noted that there isn't an essay concerning whether there was any extra information that we would like ad com to know. I know that this was an essay of the past, and I was wondering, would it hurt an applicant if they were to construct an essay concerning possible employement gaps, lack of work experience, or low GPA's?
Kurt: Dele that is essentially what essay 3 can provide you. Since the creation of this question that was its intent, to allow you some "white space" to complete your story to the committee.
ANTONIOS: Good morning. I am a little confused about essay No3
Joanna: Essay 3 is an opportunity for you to complete your strategic message to the committee. We provide a fixed number of opportunities/tools for you convey your message in (essays, resume, recommendations etc). Essay three gives you a more open opportunity to share more of your story. We are looking to see how strategic you are in using this space to complete your story effectively.
http://www.chicagobooth.edu/fulltime/chat/transcript/2010-07-22.aspx
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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30 Jul 2010, 10:35
1
KUDOS
please count me in for rd 1
Question for those who may be able to answer this: On the application, under the extracurricular section, which is more preferred? Bullet-point listing the extracurriculars or adcoms prefer to see a small paragraph (or a short essay) talking about all the extras. I have several things I'd like to mention, but I'm not sure whether I should use the bullet-point format, or I should incorporate everything into a short essay.
Thanks!
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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31 Jul 2010, 15:50
1
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I am reapplying to Round 1. Any plans for a Google Doc roll-call spreadsheet?
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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01 Aug 2010, 12:47
1
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In for Round 1.
Question for current/prospective students or alums: I have not yet made my campus visit to Booth. Do you think its crucial? I can do a visit in the next few weeks, but since there are no ongoing classes, the only visit option is an "abbreviated schedule" visit that includes an info session and a tour, amounting to a total of about 1.5hr. Is this something I should consider?
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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02 Aug 2010, 10:33
2
KUDOS
The question of "is the campus visit crucial" always pops up, and the correct answer is..it is entirely up to you. You need to demonstrate to the school that you know enough about the school and made an informed choice based on your personal chemistry with the school when you put in your application. Visiting school and attending classes can help you to throw in personal anecdotes both in application and interview. But then you can do the same by meeting alumni/current students or just talking to them over phone/email and reading up about Professors. If you can complete your story without visiting, then perhaps it is fine to not visit.
But, in my case, I fell in love with Booth when I attended the Booth Live event. That perhaps resulted in me putting in that extra love in my application, which perhaps helped in getting accepted.
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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02 Aug 2010, 17:43
1
KUDOS
count me in for rd 1
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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02 Aug 2010, 19:06
1
KUDOS
Count me in for round 1!
Does anyone have a copy of the recommender questions? I wanted to see them before sending them to my recommenders.
Daniel
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Re: Calling All 2011 Booth Applicants!! [#permalink]
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03 Aug 2010, 07:33
1
KUDOS
danielduq wrote:
Count me in for round 1!
Does anyone have a copy of the recommender questions? I wanted to see them before sending them to my recommenders.
Daniel
It is a letter, there is no direct question as far as I know.
Recommenders are provided the following guidelines:
Please provide a written letter of recommendation. Be sure to include how the applicant ranks comparative to his/her peer group. Other items to consider are the applicant's:
* most salient strengths
* areas of development, including efforts the applicant has taken to show improvement
* team skills and leadership ability
* initiative, curiosity and motivation
* other matters which you feel we should know about the applicant
Re: Calling All 2011 Booth Applicants!! [#permalink] 03 Aug 2010, 07:33
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Display posts from previous: Sort by | 4,528 | 16,773 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2017-13 | longest | en | 0.903413 |
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Last year, Professor Steven Strogatz of Cornell University wrote a series of op-eds for the New York Times that discussed the presence of mathematics in unlikely places. I discussed one of these columns here. Now, either those articles were well-received, or Professor Strogatz is well-connected, because this year he’s back in the Times with a much more ambitious series of articles. This time around, Strogatz is attempting to “[write] about the elements of mathematics, from preschool to grad school, for anyone out there who’d like to have a second chance at the subject.”
Preschool to grad school is a significant amount of ground to cover, but thus far Strogatz has used his articles to assault this goal with gusto. To date, he has tackled counting, patterns in addition, negative numbers, division, and basic high school algebra. This doesn’t really do justice to his content, though. Along the way he . . . → Read More: Math in the News(paper)
## Decimal Point Fail, Ctd
I apologize for my silence over the past few weeks – I have been out of the country learning math and eating pancakes. While I get back into the swing of things, I’ve got a couple of points to mention that relate to earlier posts regarding our collective inability to correctly use the decimal point.
The first is a picture from a flyer advertising maid service. Here’s the ad (sent in to me by a dedicated foot soldier in the army that is my readership, a.k.a. my mother):
Names and phone numbers have been cropped out to protect the innocent. But in a case such as this, are there really any innocents? Although we’ve seen decimal point errors on signs before, this one is arguably the most egregious of all. Presumably the intended price is \$100 – if that’s the case, then not only is the decimal point . . . → Read More: Decimal Point Fail, Ctd
## The Cheapest Salad Bar in the World
Last week, I went to a number theory conference in Utah. The conference was very good, and I learned quite a lot, which I suppose is the goal of any such conference. The location of the conference itself was also quite nice – it was close to the mountains, a lake, and the home of Blendtec, famous for their “Will it Blend” series of videos.
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# GMAT Club Tests 14 Math + 6 Verbal - Free for GC Members
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CIO
Joined: 02 Oct 2007
Posts: 1218
Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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08 Jan 2010, 10:02
You can try to find similar scores in this thread:
result-correlation-between-gmat-and-gmat-club-s-tests-30989.html
People who took the real GMAT posted their GMAT Club Tests scores in that thread. Hope this helps.
johnnymac wrote:
Is there a way to determine approximately what GMAT score one scored based on the percentile scores? I understand it would be an approximation but it would be nice to see where I stand.
I received m25 -96%, v06 - 89%
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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01 Apr 2010, 23:30
I think the kudos points should not be the only criteria for the tests.Some other criteria should also be considered.
Manager
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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05 Apr 2010, 21:27
I hear the quality is goo, will have to see...
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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26 Apr 2010, 03:50
Hi,
I'd like to ask about the free options. Is it still true that when I have accumulated 200 posts all tests would be available upon a click?
Thanks.
CIO
Joined: 02 Oct 2007
Posts: 1218
Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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26 Apr 2010, 05:25
Hi,
Yes, the Free GMAT Club Tests policy is still in action. Please remember that your posts have to be quality posts and not just one-liners .
calvinhobbes wrote:
Hi,
I'd like to ask about the free options. Is it still true that when I have accumulated 200 posts all tests would be available upon a click?
Thanks.
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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26 Apr 2010, 06:23
dzyubam wrote:
Hi,
Yes, the Free GMAT Club Tests policy is still in action. Please remember that your posts have to be quality posts and not just one-liners .
calvinhobbes wrote:
Hi,
I'd like to ask about the free options. Is it still true that when I have accumulated 200 posts all tests would be available upon a click?
Thanks.
Thanks. Are there any policies still in action? Do I need to register on anything when I become qualified? Thanks again.
CIO
Joined: 02 Oct 2007
Posts: 1218
Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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26 Apr 2010, 06:31
Your access to GMAT Club Tests will be enabled automatically when you reach 200 posts and have been a member for 90 days.
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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10 May 2010, 12:30
Hi,
I thought we could access the tests free once we had 100 posts and 25 kudos, however im still unable to get access to them. Am i missing something here??.
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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10 May 2010, 23:31
Hi,
You got the access! Enjoy!
Silvers wrote:
Hi,
I thought we could access the tests free once we had 100 posts and 25 kudos, however im still unable to get access to them. Am i missing something here??.
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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14 May 2010, 03:26
i have 100+ posts and 26 kudos ...and i still dont have access to the 25 tests ? why ?
Intern
Joined: 25 May 2010
Posts: 9
Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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25 May 2010, 09:44
Is it 100-25 or 200-50?
Also, I checked the other thread and I think to get about GMAT700 we need about 35V (assuming 50Q), correct?
I got 34 in v06 sample so I'm feeling pretty good if this is true.
CIO
Joined: 02 Oct 2007
Posts: 1218
Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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25 May 2010, 12:57
Here are three ways you can get access to GMAT Club Tests for free:
1. 50 kudos
2. 100 forum posts and 25 kudos
3. 200 forum posts and 90+ days of membership
Here's a thread explaining GMAT Scores:
gmat-score-guide-to-gmat-scores-score-reports-83890.html
It seems that you should have 720 or more if you get Q50 and V36. See this debrief:
journey-670-to-720-q50-v36-long-85083.html
ponderer wrote:
Is it 100-25 or 200-50?
Also, I checked the other thread and I think to get about GMAT700 we need about 35V (assuming 50Q), correct?
I got 34 in v06 sample so I'm feeling pretty good if this is true.
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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31 May 2010, 07:04
i tried to access to the GMAT Club tests, but i couldn't!! is there anything wrong with it? it kept asking me to log in even though i did already!! can someone help and tell how to get access to the tests? Thanks!
CIO
Joined: 02 Oct 2007
Posts: 1218
Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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31 May 2010, 23:54
Judging from your other posts, you should have had your free access to GMAT Club Tests.
tt11234 wrote:
i tried to access to the GMAT Club tests, but i couldn't!! is there anything wrong with it? it kept asking me to log in even though i did already!! can someone help and tell how to get access to the tests? Thanks!
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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13 Jul 2010, 07:05
I gave m25 today, scored a 90.2percentile... 32correct n 5wrong with 2 silly mistakes
n was left with 15mins.
What is the rating like, compared to the original gmat level quant?
CIO
Joined: 02 Oct 2007
Posts: 1218
Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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13 Jul 2010, 08:21
You must be really good at math! You can look up the correlation in this long thread:
result-correlation-between-gmat-and-gmat-club-s-tests-30989.html
Good luck with your GMAT!
ssowmya2108 wrote:
I gave m25 today, scored a 90.2percentile... 32correct n 5wrong with 2 silly mistakes
n was left with 15mins.
What is the rating like, compared to the original gmat level quant?
_________________
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Intern
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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14 Jul 2010, 04:33
@dzyubam
thnx for ur reply.. but my main prob is with verbal
n i have 1 week to go
i've decided to stick to mgmat and MR verbal guides
CIO
Joined: 02 Oct 2007
Posts: 1218
Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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14 Jul 2010, 10:05
Sounds like a good plan. MGMAT guides are very good. Do your best not to burn out during this last week.
ssowmya2108 wrote:
@dzyubam
thnx for ur reply.. but my main prob is with verbal
n i have 1 week to go
i've decided to stick to mgmat and MR verbal guides
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Manager
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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26 Oct 2010, 02:02
Alas, when I registered for GMAT, I didn't even knew that I can do some free online test. When I joined GmatClub I came to know about the various new concept which I if I would search in books will take one year.
I wish I could give the GMAT CLUB test, but till now I am not able to reach to the 200 post mark and also the condition of three month membership. I'll complete my 3 months on 17th Nov, 2010. Which is too late for me because in between I have to write my GMAT.
I am not so much financially strong to buy any test.
Anyways, it's my fate. I appreciate the initiative taken by gmatclub for it's member. I'll always be an admirer of this forum.
_________________
I don't want kudos.. I want to see smile on your face if I am able to help you.. which is priceless.
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink]
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14 Nov 2010, 16:05
I wanna ask that now i am working gmat on my iphone , gmat Toolkit. In these test,the questions are same to iphone version or different. Thank you in advance
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Re: GMAT Club Tests 25 Math + 6 Verbal - Free for GC Members [#permalink] 14 Nov 2010, 16:05
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# GMAT Club Tests 14 Math + 6 Verbal - Free for GC Members
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Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 3,768 | 13,670 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2017-26 | longest | en | 0.905124 |
https://yourgametips.com/destiny-2/what-percentage-is-25-of-80/ | 1,696,006,656,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510520.98/warc/CC-MAIN-20230929154432-20230929184432-00361.warc.gz | 1,197,299,253 | 40,911 | What percentage is \$25 of \$80?
What percentage is \$25 of \$80?
31.25
How is a billion written?
1,000,000,000 (one billion, short scale; one thousand million or milliard, yard, long scale) is the natural number following 999,999,999 and preceding 1,000,000,001. One billion can also be written as b or bn. In standard form, it is written as 1 × 109.
What is 1000000000000000000000000 called?
septillion
What comes next after billion?
After a billion, of course, is trillion. Then comes quadrillion, quintrillion, sextillion, septillion, octillion, nonillion, and decillion.
How many millions make a billion?
1000 millions
How much is a zillion?
Zillion may represent ANY very large power of a thousand, certainly larger than a trillion, and maybe even a vigintillion or centillion ! Just as a million had spawned the Chuquet illions, the “zillion” also had many follow ups.
How many millions make a crore?
10 Million
How much is a billion dollars really?
The USA meaning of a billion is a thousand million, or one followed by nine noughts (1,000,000,000). Increasingly in this country we are using the USA meaning of a billion for these big numbers, and a trillion for the old UK meaning of one followed by twelve noughts.
Can you live off 200 million dollars?
One can live a very comfortable lifestyle in literally any country of the world. Even with the most conservative investment management, \$200 million will yield at least \$5 – 10 million per year. Take good chunk away in taxes and you’re still left with plenty enough for quite an opulent lifestyle.
Can you spend a billion dollars in a lifetime?
You could spend \$5,000 a day for more than 500 years before you would run out of money. … Breaking it down even farther, it means you would have to spend over \$100,000 every day for the next 25 years in order to spend one billion dollars.
Can you live off 5 million dollars?
Can you retire with 5 million dollars? For most people, the answer would be: Heck yes! I’d retire in a heartbeat! Using the 4% safe withdrawal rate as a guideline, the annual income will be around \$200,000.
How long would it take to spend a billion dollars at 1 million dollars a day?
Imagine someone gave you a million dollars and told you to spend \$1,000 every day and come back when you ran out of money. You would return, with no money left, in three years. If someone then gave you a billion dollars and you spent \$1,000 each day, you would be spending for about 2,740 years before you went broke.
How long can you live off 1 million dollars?
However, if you are no longer working, just how long will a million dollars last in retirement? The financial technology company SmartAsset looked at average household expenses and found that, nationwide, a \$1 million nest egg should last 23.46 years.
Can I retire at 55 with 300k?
In the UK, you don’t need to wait until the state pension age to retire. You can generally access your pension pot from the age of 55. This means retiring at 55 is a very real possibility for Britons in their mid-fifties. To find out if you can retire at 55, speak to a retirement planning adviser as soon as you can.
Can you live off interest of 1 million dollars?
The Rule of 4 says that you should withdraw no more than 4% of your total portfolio each year. Assuming you’re earning at least 4% in returns, you can effectively live off of interest-earned without touching your principal balance. With a \$1 million portfolio, this is \$40,000 per year.
Can you retire at 60 with 500k?
If you retire with \$500k in assets, the 4% rule says that you should be able to withdraw \$20,000 per year for a 30-year (or longer) retirement. So, if you retire at 60, the money should ideally last through age 90. If 4% sounds too low, consider that you’ll take an income that increases with inflation.
How long will 500k last in retirement?
Key Takeaways. It may be possible to retire at 45 years of age, but it will depend on a variety of factors. If you have \$500,000 in savings, according to the 4% rule, you will have access to roughly \$20,000 for 30 years.
Is 500000 enough to retire on?
Assuming you have \$500,000 in retirement, you could realistically withdraw \$20,000 your first year of retirement. That amount would shrink incrementally each subsequent year, assuming zero portfolio growth. That’s assuming, however, that you wait until your full retirement age to claim Social Security benefits.
What is a reasonable amount of money to retire with?
Most experts say your retirement income should be about 80% of your final pre-retirement salary. 3 That means if you make \$100,000 annually at retirement, you need at least \$80,000 per year to have a comfortable lifestyle after leaving the workforce.
Is \$800000 enough to retire on?
If you expect to have a relatively safe retirement income of \$60,000 a year, you will need \$800,000 saved up by the time you retire. Your income gap is now just \$24,000 a year, which you will draw from your retirement savings of \$800,000 to close the gap.
How many times my salary do I need to retire at 55?
seven times
How much do I need to retire at 59?
How much money do you need to retire comfortably? According to AARP, one common rule of thumb is that you’ll need 70% to 80% of your pre-retirement income after you retire. So if you made an average of \$75,000 per year during your working years, you may only need \$52,500 to \$60,000 in retirement.
Can I retire at 60 with 300K?
The short answer is, Yes. It is possible to retire at 55 with 300K in the UK.
What is the best age to retire at?
65
Can you retire 2 million?
Inflation, market risk, withdrawal rate, unexpected expenses in retirement, and increasing life expectancy are all factors that suggest you may need as much as \$2 million to retire comfortably. That number may scare you, but it’s a reminder to ensure you’re making the right financial moves today. | 1,412 | 5,943 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2023-40 | latest | en | 0.9549 |
https://www.jmp.com/support/help/en/16.0/jmp/histogram-options-for-continuous-variables.shtml | 1,618,373,090,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038076819.36/warc/CC-MAIN-20210414034544-20210414064544-00577.warc.gz | 956,281,442 | 2,877 | Basic Analysis > Distributions > Options for Continuous Variables > Histogram Options for Continuous Variables
Publication date: 04/12/2021
## Histogram Options for Continuous Variables
Histogram
Shows or hides the histogram. See Histograms.
Replaces the histogram with a shadowgram. To understand a shadowgram, consider that if the bin width of a histogram is changed, the appearance of the histogram changes. A shadowgram overlays histograms with different bin widths. Dominant features of a distribution are less transparent on the shadowgram.
Note that the following options are not available for shadowgrams:
Std Error Bars
Show Counts
Show Percents
Vertical
Changes the orientation of the histogram from a vertical to a horizontal orientation.
Std Error Bars
Draws the standard error bar on each level of the histogram using the standard error. The standard error bar adjusts automatically when you adjust the number of bars with the hand tool. See Resize Histogram Bars for Continuous Variables and Standard Error Bars.
Set Bin Width
Changes the bin width of the histogram bars. See Resize Histogram Bars for Continuous Variables.
Histogram Color
Changes the color of the histogram bars.
Count Axis
Adds an axis that shows the frequency of column values represented by the histogram bars.
Note: If you resize the histogram bars, the count axis also resizes.
Prob Axis
Adds an axis that shows the proportion of column values represented by histogram bars.
Note: If you resize the histogram bars, the probability axis also resizes.
Density Axis
The density is the length of the bars in the histogram. Both the count and probability are based on the following calculations:
prob = (bar width)*density
count = (bar width)*density*(total count)
When looking at density curves that are added by the Fit Distribution option, the density axis shows the point estimates of the curves.
Note: If you resize the histogram bars, the density axis also resizes.
Show Percents
Labels the proportion of column values represented by each histogram bar.
Show Counts
Labels the frequency of column values represented by each histogram bar. | 415 | 2,158 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2021-17 | latest | en | 0.807034 |
http://slideplayer.com/slide/4231971/ | 1,524,232,032,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125937780.9/warc/CC-MAIN-20180420120351-20180420140351-00081.warc.gz | 291,187,888 | 25,143 | # Uniform Circular Motion
## Presentation on theme: "Uniform Circular Motion"— Presentation transcript:
Uniform Circular Motion
Circular Motion ACT 1 B C A v Use this to motivate circular motion involves acceleration. Answer: B A ball is going around in a circle attached to a string. If the string breaks at the instant shown, which path will the ball follow?
Circular Motion
Uniform Circular Motion
For a particle in uniform circular motion, the velocity vector v remains constant in magnitude, but it continuously changes its direction.
Acceleration in Uniform Circular Motion
v2 v1 R R v1 v2 v centripetal acceleration aave= Dv / Dt Acceleration toward center Acceleration is due to change in direction, not speed. Object turns “toward” center must be a force on object toward center.
Centripetal Acceleration
Centripetal Acceleration ACT
Which motion has the largest centripetal acceleration?
Preflight “Gravity, Normal Force, Friction”
Consider the following situation: You are driving a car with constant speed around a horizontal circular track. On a piece of paper, draw a Free Body Diagram (FBD) for the car. How many forces are acting on the car? A) B) C) D) 4 W FN SF = ma = mv2/R a=v2/R R 0% 28% 44% f correct “Gravity, Normal Force, Friction” “Fn = Normal Force, W = Weight, the force of gravity, f = centripetal force.” 16
Common Incorrect Responses
Acceleration: SF = ma Centripetal Acceleration Force of Motion (Inertia not a force) Forward Force, Force of velocity Speed Centrifugal Force (No such thing!) Centripetal (really acceleration) Inward force (really friction) Internal Forces (don’t count, cancel) Car Engine
Circular Motion Requires Net Force
Net force may be provided by the tension in a string, the normal force, or friction, among other sources – as with any net force.
Preflights Consider the following situation: You are driving a car with constant speed around a horizontal circular track. On a piece of paper, draw a Free Body Diagram (FBD) for the car. The net force on the car is W FN A. Zero B. Pointing radially inward C. Pointing radially outward SF = ma = mv2/R a=v2/R R f 22% 67%11% correct “This is why many racetracks have banked roadways” “Centripetal force is always pointing inward" “Ever spin stuff in a bowl? It gravitates outward.” 16
Dip ACT Suppose you are driving through a valley whose bottom has a circular shape. If your mass is m, what is the magnitude of the normal force FN exerted on you by the car seat as you drive past the bottom of the hill A. FN < mg B. FN = mg C. FN > mg a=v2/R R correct FN v SF = ma FN - mg = mv2/R FN = mg + mv2/R mg 20
Dip Example While driving on a country road at a constant speed of 17.0 m/s, you encounter a dip in the road. The dip can be approximated by a circular arc with a radius of 65.0 m. What is the normal force exerted by the car seat on an 80.0 kg passenger at the bottom of the dip?
Merry-Go-Round ACT Bonnie sits on the outer rim of a merry-go-round with radius 3 meters, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. Klyde’s speed is: Klyde Bonnie (a) the same as Bonnie’s (b) twice Bonnie’s (c) half Bonnie’s Bonnie travels 2 p R in 2 seconds vB = 2 p R / 2 = 9.42 m/s Klyde travels 2 p (R/2) in 2 seconds vK = 2 p (R/2) / 2 = 4.71 m/s 33
Rounding a Corner A 1,200 kg car rounds a corner of radius r = 45.0 m. If the coefficient of friction between the tires and the road is ms = 0.82, what is the maximum speed the car can have on the curve without skidding? Question: How does this result depend on the mass of the car?
Banked Curves
Revolving in a Circle Vertical: Radial:
An energetic father places his 20 kg child in a 5.0 kg cart to which is attached a 2.0 m long rope. He then holds the end of the rope and spins the cart and child in a circle, keeping the rope parallel to the ground. If the tension in the rope is 100 N, what is the cart’s tangential speed? Vertical: m = 25 kg r = 2 m T = 100 N v = ? Radial:
50 •• Driving in your car with a constant speed of 12 m/s, you encounter a bump in the road that has a circular cross-section, as indicated in Figure 6–30. If the radius of curvature of the bump is 35 m, find the apparent weight of a 67-kg person in your car as you pass over the top of the bump. w N
51•• Referring to Problem 50, at what speed must you go over the bump if people in your car are to feel “weightless?”
Centrifuge A centrifuge rotates at a rate such that the bottom of a test tube travels at a speed of 89.3 m/s. The bottom of the test tube is 8.50 cm from the axis of rotation. What is the centripetal acceleration acp at the bottom of the test tube in m/s and in g (where 1 g = 9.81 m/s2)? | 1,250 | 4,735 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2018-17 | latest | en | 0.843619 |
http://math.furman.edu/~jpoole/euclidselements/eubk3/prop01/prop1~5.htm | 1,540,175,557,000,000,000 | text/html | crawl-data/CC-MAIN-2018-43/segments/1539583514443.85/warc/CC-MAIN-20181022005000-20181022030500-00216.warc.gz | 232,614,070 | 1,319 | THE ELEMENTS Book III Proposition 1 Similarly we can prove that no other point except F can be the center of the circle. Therefore the point F is found to be the center of the circle ABC Being what it was required to do. Previous Page Return to Propositions | 60 | 266 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2018-43 | latest | en | 0.863738 |
http://www.conceptdraw.com/examples/engineering-drawing-image-welding | 1,508,627,639,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187824899.75/warc/CC-MAIN-20171021224608-20171022004608-00823.warc.gz | 428,201,526 | 7,708 | # Butt weld geometry
## Butt weld geometry
This engineering drawing shows different types of geometry of butt welds.
"Welds can be geometrically prepared in many different ways. The five basic types of weld joints are the butt joint, lap joint, corner joint, edge joint, and T-joint (a variant of this last is the cruciform joint). Other variations exist as well - for example, double-V preparation joints are characterized by the two pieces of material each tapering to a single center point at one-half their height. Single-U and double-U preparation joints are also fairly common - instead of having straight edges like the single-V and double-V preparation joints, they are curved, forming the shape of a U. Lap joints are also commonly more than two pieces thick - depending on the process used and the thickness of the material, many pieces can be welded together in a lap joint geometry." [Welding. Wikipedia]
This engineering drawing example was redesigned using the ConceptDraw PRO diagramming and vector drawing software from the Wikimedia Commons file: Butt Weld Geometry.GIF.
[commons.wikimedia.org/wiki/File:Butt_Weld_Geometry.GIF]
The engineering drawing example "Butt weld geometry" is included in the Mechanical Engineering solution from the Engineering area of ConceptDraw Solution Park. Read more
Welding joint diagram
Used Solutions
## Welding symbols
This engineering drawing present weld type symbols and fillet weld symbols.
The weld type symbol is typically placed above or below the center of the reference line, depending on which side of the joint it's on. The symbol is interpreted as a simplified cross-section of the weld.
"Fillet welding refers to the process of joining two pieces of metal together whether they be perpendicular or at an angle. These welds are commonly referred to as Tee joints which are two pieces of metal perpendicular to each other or Lap joints which are two pieces of metal that overlap and are welded at the edges. The weld is aesthetically triangular in shape and may have a concave, flat or convex surface depending on the welder’s technique. Welders use fillet welds when connecting flanges to pipes, welding cross sections of infrastructure, and when fastening metal by bolts isn't strong enough." [Fillet weld. Wikipedia]
The engineering drawing example Welding symbols is included in the Mechanical Engineering solution from Engineering area of ConceptDraw Solution Park. Read more
Welding joint symbols
Used Solutions
## Welded joints types
"A welding joint is a point or edge where two or more pieces of metal or plastic are joined together. They are formed by welding two or more workpieces (metal or plastic) according to a particular geometry. Five types of joints referred to by the American Welding Society: butt, corner, edge, lap, and tee. These configurations may have various configurations at the joint where actual welding can occur." [Welding joint. Wikipedia]
The engineering drawing example "Welded joints types" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Mechanical Engineering solution from the Engineering area of ConceptDraw Solution Park. Read more
Welding joints
Used Solutions
## Elements location of a welding symbol
"The symbols and conventions used in welding documentation are specified in national and international standards such as ISO 2553 Welded, brazed and soldered joints -- Symbolic representation on drawings and ISO 4063 Welding and allied processes -- Nomenclature of processes and reference numbers. The US standard symbols are outlined by the American National Standards Institute and the American Welding Society and are noted as "ANSI/AWS".
In engineering drawings, each weld is conventionally identified by an arrow which points to the joint to be welded. The arrow is annotated with letters, numbers and symbols which indicate the exact specification of the weld. In complex applications, such as those involving alloys other than mild steel, more information may be called for than can comfortably be indicated using the symbols alone. Annotations are used in these cases." [Symbols and conventions used in welding documentation. Wikipedia]
The example chart "Elements of welding symbol" is redesigned using the ConceptDraw PRO diagramming and vector drawing software from the Wikipedia file: Elements of a welding symbol.PNG.
[en.wikipedia.org/wiki/File:Elements_of_a_welding_symbol.PNG]
The diagram example "Elements location of a welding symbol" is contained in the Mechanical Engineering solution from the Engineering area of ConceptDraw Solution Park. Read more
Welding joint symbol chart
Used Solutions
## Mechanical Engineering
This solution extends ConceptDraw PRO v.9 mechanical drawing software (or later) with samples of mechanical drawing symbols, templates and libraries of design elements, for help when drafting mechanical engineering drawings, or parts, assembly, pneumatic, Read more | 969 | 4,972 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.171875 | 3 | CC-MAIN-2017-43 | longest | en | 0.943589 |
https://www.exceldemy.com/excel-count-characters-in-cell-without-spaces/ | 1,701,341,713,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100184.3/warc/CC-MAIN-20231130094531-20231130124531-00266.warc.gz | 864,768,198 | 74,563 | # How to Count Characters in Cell without SpacesĀ in Excel (4 Methods)
Get FREE Advanced Excel Exercises with Solutions!
We need to count words while publishing an article, submitting an assignment, to see how many characters are going onto a business card, etc. We are going to learn the ways for Excel to count characters in cell without spaces. For your better understanding, we are going to use a sample dataset containing Name and Short Bio. We will see how many characters without space is in the Short Bio of each Name.
## How to Count Characters in Cell without Spaces in Excel: 4 Ways
We will use the LEN function with different combinations of SUBSTITUTE, SUM, SUMPRODUCT, and VBA to count characters in cells without spaces.
### Method 1: Count Characters in Cell without Spaces Using LEN Function
In our first method, we will see the combination of LEN and SUBSTITUTE functions to count characters without spaces.
Steps:
• Type the following formula in Cell D5.
`=LEN(SUBSTITUTE(C5," ",""))`
• Now, press the ENTER key.
Here, the SUBSTITUTE function will remove all the spaces and keep only the characters.
`=SUBSTITUTE(C5," ","")` yields the result PrincipalowneroftheCharlotteHornetsoftheNBA
And the LEN function counts the number of characters.
• Finally, drag down using the mouse right key to AutoFill rest of the series.
### Method 2: SUMPRODUCT and LEN Functions to Count Characters in Cell without Spaces
Earlier we have seen counting characters for a single cell. In this method, we will count characters in the range C5:C8. Thereās an easy way to do it.
Steps:
• First Type the following formula in Cell D6.
`=SUMPRODUCT(LEN(SUBSTITUTE(C5:C8," ","")))`
• After that, press the ENTER key.
Thatās it. LEN along with the SUBSTITUTE function counts the number of characters in each cell from C5 to C8 and the SUMPRODUCT totals those numbers and gives us the ultimate result.
### Method 3: Count Characters in Cell without Spaces Using SUM and LEN Functions
We can also use a combination of SUM, LEN, and SUBSTITUTE functions to count characters in a specific range.
Steps:
• First, type the following formula in cell D6.
`=SUM(LEN(SUBSTITUTE(C5:C8," ","")))`
• And, press the CTRL+SHIFT+ENTER key.
Here, the formula will operate as an ARRAY formula if we press CTRL+SHIFT+ENTER altogether.
### Method 4: Count Characters in Cell without Spaces by VBA
In this last section of the article, we will see a VBA code to count characters without spaces in Excel.
Steps:
• First, right-click on the sheet and go to View Code.
• After that, copy and paste the VBA code below.
VBA Code:
• After that, press the F5 or play button to run the code.
Done.
Read More: Excel VBA: Count Characters in Cell
## Practice Section
The single most crucial aspect in becoming accustomed to these quick approaches is practice. As a result, weāve attached a practice workbook where you may practice these methods.
Download Practice Workbook
## Conclusion
These are 4 different methods in Excel to Count Characters in Cell without Spaces. Based on your preferences, you may choose the best alternative. Please leave them in the comments area if you have any questions or feedback
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We will be happy to hear your thoughts
Advanced Excel Exercises with Solutions PDF | 829 | 3,854 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.0625 | 3 | CC-MAIN-2023-50 | longest | en | 0.880246 |
https://physics.stackexchange.com/questions/360336/why-are-the-masses-m-w-m-z-and-the-coupling-constants-e-g-related-in-ele | 1,718,551,267,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861665.97/warc/CC-MAIN-20240616141113-20240616171113-00788.warc.gz | 407,572,893 | 40,423 | Why are the masses $m_{W}/m_{Z}$ and the coupling constants $e/g$ related in electroweak unification?
Gottfried and Weisskopf write in their book, in the chapter on electroweak theory, that
$\frac{m_W}{m_Z} + \left(\frac{e}{g}\right)^2 = 1$
In this expression, $m_W$ and $m_Z$ are the masses of the $W$ and $Z$ bosons, and $e$ and $g$ are the electromagnetic and the weak coupling constants. I want to understand the equation; so I have a question. Why exactly is the boson mass ratio related to the coupling ratio?
After all, this expressions seems to tell that mass is due to coupling strength. But why is mass ratio related in this "elliptical" way to coupling ratio?
I also have another, minor question. I suppose that by $e^2$ the authors mean what is called the fine structure constant $\alpha$, and by $g^2$ what is called $\alpha_w$. Is this correct? Yes, it is, within a factor of $4 \pi$ for both of them.
Thank you in advance for all your help to make this clearer. Also any book or article on that equation would be helpful. I will improve the question with all comments that I get.
Despite the beautiful answer below, to me it remains a deep fascination why the mass of a particle should depend on the coupling, and why a charged particle (the W) is less massive than a similar neutral one (the Z) - naively, I would expect that electric charge adds to mass. Maybe I can ask this in other terms: why is the Higgs mechanism the way it is? Where does it come from? Since nobody knows yet, a more realistic question is: what is the simplest way to explain mass generation in weak bosons? The rotation in the abstract space is so hard to picture in concrete terms. Is there a simpler way?
After all, this expressions seems to tell that mass is due to coupling strength. But why is mass ratio related in this "elliptical" way to coupling ratio?
The relation between the couplings and the masses follows from the Higgs mechanism. It generates the masses for $W^{\pm}-,Z-$bosons. The masses depend on the $SU_{L}(2)$ gauge coupling $g_{1}$ and the $U_{Y}(1)$ gauge coupling $g_{2}$; precisely, the $W$-boson mass depends on the weak coupling $g \equiv g_{1}$ linearly, while the $Z$-boson mass is proportional to $\sqrt{g_{1}^{2}+g_{2}^{2}}$. From the other side, the EM coupling is proportional to $g_{2}/\sqrt{g_{1}^{2}+g_{2}^{2}}$. The ellipticity then follows from the simple trigonometric relation between the ratio $m_{Z}/m_{W}$ and $e/g_{1}$.
Such proportionality is the result of non-trivial "symmetry breaking" $G_{\text{electroweak}} \simeq SU_{L}(2)\times U_{Y}(1) \to U_{\text{EM}}(1)$, where $U_{\text{EM}}(1)$ (which is actually the EM gauge group) is the subgroup of $G_{\text{electroweak}}$ which isn't contained in $U_{Y}(1)$ or $SU_{L}(2)$ separately. Let's trace it explicitly.
The interaction of the $SU_{L}(2)\times U_{Y}(1)$ gauge bosons with the Higgs doublet $H$ is given by the lagrangian $$\tag 1 L_{H} = |D_{\mu}H|^{2}, \quad D_{\mu} \equiv \partial_{\mu} - i\frac{T_{H}}{2}g_{1}t_{a}W_{\mu}^{a}-i\frac{Y_{H}}{2}g_{2}B_{\mu},$$ where $W_{\mu,a}, a = 1,2,3$ are the $SU_{L}(2)$ gauge fields, $B_{\mu}$ is the $U_{Y}(1)$ gauge field, $t_{a}$ are the Pauli matrices, $T_{H} = 1$ is the weak isospin number for the Higgs doublet, and $Y_{H} = 1$ is the hypercharge number for the Higgs doublet.
After the Higgs driven electroweak crossover the $H$ acquires non-zero VEV, $H \to H + v\begin{pmatrix} 0 \\ 1\end{pmatrix}$, which generates the mass term $$\tag 2 L_{\text{mass}}= v^{2}g_{1}^{2}|W_{\mu}|^{2} + v^{2}(g_{2}B_{\mu}-g_{1}W_{\mu 3})^{2}$$ where $W_{\mu} \equiv \frac{1}{\sqrt{2}}(W_{\mu,1} -iW_{\mu,2})$.
One can introduce two linear combinations of $W_{\mu, 3}$ and $B_{\mu}$ called $Z$-boson and photon $A$, $$\tag 3 \begin{pmatrix} W_{\mu 3} \\ B_{\mu}\end{pmatrix} = \begin{pmatrix} \cos(\theta_{W}) & \sin(\theta_{W})\\ -\sin(\theta_{W}) & \cos(\theta_{W})\end{pmatrix}\begin{pmatrix} Z_{\mu} \\ A_{\mu}\end{pmatrix}, \quad \cos(\theta_{W}) = \frac{g_{1}}{\sqrt{g_{1}^{2}+g_{2}^{2}}}$$ which diagonalize $(2)$: $$L_{\text{mass}} = \frac{v^{2}g_{1}^{2}}{2}|W_{\mu}|^{2} + \frac{v^{2}(g_{1}^{2}+g_{2}^{2})}{2}Z^{2}$$ Note that the photon is massless, as it must be.
Therefore $m_{W} = \frac{vg_{1}}{\sqrt{2}}$ and $m_{Z} = \frac{m_{W}}{\cos(\theta_{W})}$, and $$\frac{m_{W}}{m_{Z}} = \cos(\theta_{W})$$ The only thing which is remained is the calculation of the coupling $e$ to the photon $A$ in terms of the constants $g_{1}, g_{2}$. By using $(3)$ and the explicit form of the covariant derivative $(1)$, one obtains $$e =g_{2}\cos(\theta_{W})= g_{1}\sin(\theta_{W})$$ Therefore, one obtains the desired result $$\left( \frac{m_{W}}{m_{Z}}\right)^{2}+\left(\frac{e}{g_{1}}\right)^{2} = \cos^{2}(\theta_{W}) +\sin^{2}(\theta_{W})= 1$$
I also have another, minor question. I suppose that by e2 the authors mean what is called the fine structure constant $\alpha$, and by $g^{2}$ what is called $\alpha_{W}$. Is this correct?
It depends on the units which you use. For the case of natural units, the relations read $\alpha = \frac{e^{2}}{4\pi}$ and $\alpha_{W} = \frac{g^{2}}{4\pi}$.
• Thank you very much for this beautiful explanation; I still dream of simplifying it so much that I am able to tell it to my grandparents. But this is not an easy task. Commented Oct 1, 2017 at 18:01
• I added some more questions above. Commented Oct 1, 2017 at 20:02
• @GiuliaTozzi : the most of the added questions are likely to open as another question. Commented Oct 1, 2017 at 20:14 | 1,829 | 5,529 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2024-26 | latest | en | 0.944342 |
https://aprove.informatik.rwth-aachen.de/eval/JAR06/JAR_TERM/TRS/Rubio/bn122.trs.Thm17:POLO_71:NO.html.lzma | 1,719,039,548,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862252.86/warc/CC-MAIN-20240622045932-20240622075932-00731.warc.gz | 89,073,732 | 1,814 | Term Rewriting System R:
[X, Y, Z]
plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
times(X, s(Y)) -> plus(X, times(Y, X))
Termination of R to be shown.
` R`
` ↳Dependency Pair Analysis`
R contains the following Dependency Pairs:
PLUS(plus(X, Y), Z) -> PLUS(X, plus(Y, Z))
PLUS(plus(X, Y), Z) -> PLUS(Y, Z)
TIMES(X, s(Y)) -> PLUS(X, times(Y, X))
TIMES(X, s(Y)) -> TIMES(Y, X)
Furthermore, R contains two SCCs.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳Polynomial Ordering`
` →DP Problem 2`
` ↳Polo`
Dependency Pairs:
PLUS(plus(X, Y), Z) -> PLUS(Y, Z)
PLUS(plus(X, Y), Z) -> PLUS(X, plus(Y, Z))
Rules:
plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
times(X, s(Y)) -> plus(X, times(Y, X))
The following dependency pairs can be strictly oriented:
PLUS(plus(X, Y), Z) -> PLUS(Y, Z)
PLUS(plus(X, Y), Z) -> PLUS(X, plus(Y, Z))
Additionally, the following usable rule using the Ce-refinement can be oriented:
plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
Used ordering: Polynomial ordering with Polynomial interpretation:
POL(plus(x1, x2)) = 1 + x1 + x2 POL(PLUS(x1, x2)) = 1 + x1
resulting in one new DP problem.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳Polo`
` →DP Problem 3`
` ↳Dependency Graph`
` →DP Problem 2`
` ↳Polo`
Dependency Pair:
Rules:
plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
times(X, s(Y)) -> plus(X, times(Y, X))
Using the Dependency Graph resulted in no new DP problems.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳Polo`
` →DP Problem 2`
` ↳Polynomial Ordering`
Dependency Pair:
TIMES(X, s(Y)) -> TIMES(Y, X)
Rules:
plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
times(X, s(Y)) -> plus(X, times(Y, X))
The following dependency pair can be strictly oriented:
TIMES(X, s(Y)) -> TIMES(Y, X)
There are no usable rules using the Ce-refinement that need to be oriented.
Used ordering: Polynomial ordering with Polynomial interpretation:
POL(TIMES(x1, x2)) = x1 + x2 POL(s(x1)) = 1 + x1
resulting in one new DP problem.
` R`
` ↳DPs`
` →DP Problem 1`
` ↳Polo`
` →DP Problem 2`
` ↳Polo`
` →DP Problem 4`
` ↳Dependency Graph`
Dependency Pair:
Rules:
plus(plus(X, Y), Z) -> plus(X, plus(Y, Z))
times(X, s(Y)) -> plus(X, times(Y, X))
Using the Dependency Graph resulted in no new DP problems.
Termination of R successfully shown.
Duration:
0:00 minutes | 787 | 2,436 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2024-26 | latest | en | 0.604244 |
https://cs.stackexchange.com/questions/103134/prove-that-there-always-exists-a-line-bisecting-each-of-two-point-sets | 1,713,530,107,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817398.21/warc/CC-MAIN-20240419110125-20240419140125-00046.warc.gz | 169,653,297 | 40,874 | # Prove that there always exists a line bisecting each of two point sets
A line $$\ell$$ for a set $$S$$ of points is bisecting if the open halfspaces on either side of $$\ell$$ contain at most $$\frac{|S|}{2}$$ points.
Now given point sets $$A$$ and $$B$$ in the plane, prove that we can always find a line $$\ell$$ such that $$\ell$$ bisects both $$A$$ and $$B$$ simultaneously. We can assume that no three points in $$A \cup B$$ lie on a line and no two points share an x-coordinate.
Note that I am not asking for an algorithm separating $$A$$ and $$B$$.
So far I have proven the following claim:
Let $$S$$ be a point set in the plane containing an even number of points. Prove that, for any point $$s \in S$$, a bisecting line $$\ell$$ for $$S \setminus \{s\}$$ also bisects $$S$$.
From this claim we can also infer that all separting lines for a point set $$P$$ with an odd number of points must pass through at least one point $$p \in P$$. However I am stuck on how to continue. Intuition suggests that one of the lines between points $$a \in A$$ and $$b \in B$$ must be simultaneously bisecting (if either of $$A$$ or $$B$$ contain an even number of points we can just remove one at random by the above claim). However I cannot seem to prove this is always the case.
Can you give me a hint for the next step?
• Note that this is a special case of the Ham sandwich theorem, which states that for $n$ measurable objects in the $n$-dimensional Euclidean space, one can always find a $n-1$-dimensional hyperplane such that the $n$ objects are divided in half (w.r.t. the given meaure). Here, $n = 2$ and the measure used is the counting measure. Barring this: Can we prove this theorem without using the ham sandwich theorem (i.e. using only discrete geometry)? Jan 20, 2019 at 16:56
• What do you mean "discrete geometry"? I am afraid it is either not well-defined or not suitable for the current situation of 2-dimension Euclidean space. Jan 20, 2019 at 18:25
• @Apass.Jack You're right, that's a bad formulation on my part. I meant: can we prove this without delving into measures and measure-theory? Jan 20, 2019 at 18:48
• In fact, we can make an algorithm to compute that line while proving the claim. The proof here is clear enough to me. Jan 20, 2019 at 18:52
• @Apass.Jack That proof only applies to pancakes and isn't applicable to point sets since they aren't continuously measurable. Jan 20, 2019 at 19:03
We can prove this using the geometric dual of $$P$$ and $$Q$$.
Take the line arrangement of $$P^*$$ and $$Q^*$$ in the plane and let us look at the median levels $$\Lambda_p$$ and $$\Lambda_q$$. Their intersection is definitely a possible solution because $$\Lambda_p$$ is the point set describing the dual of all bisecting lines for $$P$$, and vice-versa for $$Q$$.
Note the following: Since $$|P|$$ and $$|Q|$$ are odd, both median line arrangements have the same slope (and since all slopes are unique by assumption, they must correspond to the same lines) in the beginning and the end of the arrangement. Let us denote $$p^*$$ and $$q^*$$ as the respective lines. Then at the beginning (i.e. the largest x-value where no intersections occured yet), one must be above the other and at the end (i.e. the smallest x-value such that no intersections happen from now on forward), they must have switched places.
Since the levels $$\Lambda_p$$ and $$\Lambda_q$$ are piecewise continuous (actually even continuously extensible), by the intermediate value theorem they must intersect in at least one point $$c^*$$, which is the dual of a possible simultaneously bisecting line $$c$$. | 938 | 3,609 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 41, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.6875 | 4 | CC-MAIN-2024-18 | latest | en | 0.911587 |
https://brainly.com/question/161558 | 1,485,259,207,000,000,000 | text/html | crawl-data/CC-MAIN-2017-04/segments/1484560284405.58/warc/CC-MAIN-20170116095124-00232-ip-10-171-10-70.ec2.internal.warc.gz | 795,352,877 | 10,666 | 2014-10-23T15:25:33-04:00
1. Always give your graph a title in the following form: "The dependence of (your dependent variable) on (your independent variable). Let's say that you're doing a graph where you're studying the effect of temperature on the speed of a reaction. In this reaction, you're changing the temperature to known values, so the temperature is your independent variable. Because you don't know the speed of the reaction and speed depends on the temperature, the speed of the reaction is your dependent variable. As a result, the title of your graph will be "The dependence of reaction rate on temperature", or something like that.
2. The x-axis of a graph is always your independent variable and the y-axis is the dependent variable.For the graph described above, temperature would be on the x-axis (the one on the bottom of the graph), and the reaction rate would be on the y-axis (the one on the side of the graph)
3. Always label the x and y axes and give units.Putting numbers on the x and y-axes is something that everybody always remembers to do (after all, how could you graph without showing the numbers?). However, people frequently forget to put a label on the axis that describes what those numbers are, and even more frequently forget to say what those units are. For example, if you're going to do a chart which uses temperature as the independent variable, you should write the word "temperature (degrees Celsius)" on that axis so people know what those numbers stand for. Otherwise, people won't know that you're talking about temperature, and even if they do, they might think you're talking about degrees Fahrenheit.
4. Always make a line graphNever, ever make a bar graph when doing science stuff. Bar graphs are good for subjects where you're trying to break down a topic (such as gross national product) into it's parts. When you're doing graphs in science, line graphs are way more handy, because they tell you how one thing changes under the influence of some other variable.
6. Make sure your data is graphed as large as possible in the space you've been given.Let's face it, you don't like looking at little tiny graphs. Your teacher doesn't either. If you make large graphs, you'll find it's easier to see what you're doing, and your teacher will be lots happier.
So, those are the steps you need to follow if you're going to make a good graph in your chemistry class. I've included a couple of examples of good and bad graphs below so you know what these things are supposed to look like.
thanks
no problem
can u be my friend
sure lol
thanks again | 571 | 2,595 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2017-04 | latest | en | 0.939498 |
https://math.stackexchange.com/questions/2608137/a-statement-using-the-epsilon-delta-definition | 1,721,232,310,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514789.19/warc/CC-MAIN-20240717151625-20240717181625-00521.warc.gz | 335,659,695 | 37,113 | # A statement using the $\epsilon - \delta$ - definition
The exercise is as follows: Given a function $f : D \mapsto \mathbb R$ Are the following conditions stronger, weaker or not comparable with continuity?
$$\forall a \in D, \exists \epsilon \gt 0, \exists \delta \gt 0, \forall x \in D: |x-a| \lt \delta \Longrightarrow |f(x) - f(a)|\lt \epsilon$$
The solution that was given is:
It is weaker because $\forall \epsilon \gt 0 P(\epsilon) \Rightarrow \exists \epsilon \gt 0 : P(\epsilon)$
As an example $f(x)= \begin{cases} 0 & x \ne 0\\ 1 & x = 0 \end{cases}$
Now (c), because $\epsilon = 2, a\in D, \delta = 1, \forall x \in D : |x-a| \lt 1 \Longrightarrow |f(x) -f(a)|\le 1 \lt 2$
What I understand from this "solution" is that because of the quantifier $\exists$ is weaker than the quantifier $\forall$ the statement is weaker. Ok, from here on I don't understand it.
The example is a discontinuous function, ok. But I don't see the connection between the statement and the example. At least I'm not 100 % sure of it because I don't see why the statement suggests anything discontinuous.
• "Quantifier", not "quantor". Commented Jan 16, 2018 at 18:37
• Ok, in my language it is quantor. My apologies Commented Jan 16, 2018 at 18:39
• Why did you vote to close my question if I may ask? Commented Jan 16, 2018 at 18:40
• I'll edit it, sir. Commented Jan 16, 2018 at 18:59
• I don't know who voted or why; I think this is a well written question. Commented Jan 16, 2018 at 19:07
## 2 Answers
The function in the example satisfies the first statement since there exists an $\epsilon$ which makes the statement true; they show this by giving explicit values that indeed make it work.
However, that function is clearly discontinuous. The key is that the given statement is indeed weaker than the one defining continuity since, in that definition, it doesn't suffice to find one specific value of $\epsilon$ for which the rest of the statement holds, it needs to hold for all possible (positive) values of $\epsilon$. For the function in the example, it fails for any $\epsilon$ smaller than 1.
Letting go of this (mathematical) context, it's useful to see how for any statement "there exists (...)" is indeed weaker than "for all (...)"; which they wrote symbolically:
It is weaker because $\forall \epsilon \gt 0 P(\epsilon) \Rightarrow \exists \epsilon \gt 0 : P(\epsilon)$
If you're in a class with at least one student, take the property "is male" and consider the statements:
1. there exists a student $S$ in class: "$S$ is male"
2. for all students $S$ in class: "$S$ is male"
It should be clear that if the second statement is true, then the first is as well; but necessarily the other way around (e.g. a class with at least one man and at least one woman).
The statement is "stronger" in the following sense: A continuous function will always satisfy that statement, but it is not necessarily the case that a function that satisfies that statement will be continuous.
The example is intended to demonstrate this point since it satisfies the statement but is not continuous. | 822 | 3,101 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.8125 | 4 | CC-MAIN-2024-30 | latest | en | 0.896875 |
https://www.mathworks.com/matlabcentral/cody/problems/21-return-the-3n-1-sequence-for-n/solutions/244407 | 1,508,680,878,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825264.94/warc/CC-MAIN-20171022132026-20171022152026-00601.warc.gz | 957,161,583 | 11,484 | Cody
# Problem 21. Return the 3n+1 sequence for n
Solution 244407
Submitted on 14 May 2013 by Kushagra
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% n = 1; c_correct = 1; assert(isequal(collatz(n),c_correct))
2 Pass
%% n = 2; c_correct = [2 1]; assert(isequal(collatz(n),c_correct))
3 Pass
%% n = 5; c_correct = [5 16 8 4 2 1]; assert(isequal(collatz(n),c_correct))
4 Pass
%% n = 22; c_correct = [22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1]; assert(isequal(collatz(n),c_correct)) | 221 | 616 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2017-43 | latest | en | 0.476182 |
https://stevenpetric.com/attractions-canada/is-my-old-canadian-money-worth-anything.html | 1,660,943,398,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882573760.75/warc/CC-MAIN-20220819191655-20220819221655-00321.warc.gz | 495,894,006 | 19,602 | # Is my old Canadian money worth anything?
Contents
The value of one bill can range from \$20,000 to \$60,000 depending on its condition, according to the website Canada Currency. Other rare bank notes, such as the \$25 bill, can also fetch thousands of dollars.
## Are old Canadian dollar bills worth anything?
According to coinsandcanada.com, the rarest \$1 bills are the ones in perfect or near-perfect condition. Bills can be categorized: Good, Very Good, Fine, Very Fine, Extremely Fine, About Uncirculated and Uncirculated. The higher quality ones can be worth up to tens or even hundreds of times the value printed on them.
## How do I find out what old money is worth?
Multiply the weight of the coin by the percentage “fineness” of the coin (the percentage of the coin that is gold or silver). This will establish how much of the precious metal you have to sell. Multiply the result of the first calculation by the current price of the precious metal in the coin.
IT IS INTERESTING: Question: Can my Canada Goose fur get wet?
## Are Canadian \$2 bills worth anything?
The Value of the \$2 Bill Today
Depending on the condition of the bill (nearly perfect or signs of wear and tear) the value can be between \$3,000 to \$15,000. In some cases, the max value for the \$2 bill can be \$20,000.
## How much is a 1954 Canadian \$1 bill worth?
According to some specialists, the 1954 run of these Canadian paper bills can be worth as much as \$7,000 (for the \$20 bill) and as low as \$3,000 (for the \$1 bill).
## How much is a Canadian 1\$ bill worth?
The value of one bill can range from \$20,000 to \$60,000 depending on its condition, according to the website Canada Currency. Other rare bank notes, such as the \$25 bill, can also fetch thousands of dollars.
## How much is a two dollar bill worth?
Most large size two-dollar bills issued from 1862 through 1918, are highly collectible and are worth at least \$100 in well-circulated condition. Uncirculated large size notes are worth at least \$500 and can go up to \$10,000 or more.
## How do you know if money is worth anything?
What Constitutes Valuable Currency in the Eyes of Collectors?
1. Star Notes. …
2. Errors. …
3. Low and High Serial Numbers. …
4. Repeaters, Ladders and Other Patterns. …
6. Binary Numbers. …
7. Serial Numbers that Reflect a Specific Date. …
8. Consecutive Serial Numbers.
## How do I know if my paper money is worth anything?
If it’s been graded by a paper money grading company such as PCGS, it will have a grade that reflects its condition. The value of your old money will also be determined by its status of circulation. If you have an uncirculated note, it may look brand-new — highly circulated notes may have considerable wear and tear.
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## Are Canadian 1 and 2 dollar bills worth anything?
The \$1, \$2, \$25, \$500 and \$1,000 bills still retain their face value even though they are no longer legal tender. You can take them to your financial institution or send them to the Bank of Canada to redeem them. Or, you can decide to keep them.
## Do banks still take pennies in Canada 2021?
Yes, pennies continue to be legal tender in Canada and banks accept them for cash payments.
## Can you still get a 1000 dollar bill in Canada?
The \$1,000 denomination stopped being issued in 2000, and it is no longer considered legal tender. Essentially, you won’t be able to spend them in a cash transaction. This does not mean that the notes are worthless, however. The Bank of Canada says it will continue to honour them at face value.
## What \$1 bills are worth?
These Rare Dollar Bills Are Worth Serious Money
• Seven repeating digits in a row on \$1 bills (i.e., 18888888, 59999999)
• Seven of the same number on \$1 bills (i.e., 99909999, 00010000)
• Super repeaters on \$1 bills (i.e., 67676767)
• Double quads on \$1 bills (i.e., 44440000)
• Super radars on \$1 bills (ie: 01111110, 80000008)
## Are uncut dollar bills worth anything?
For the currency connoisseur, most of the uncut bills were Federal Reserve Bank of Boston issues. … But don’t expect to pay face value for the uncut sheets. A sheet of four uncut dollar bills will cost you \$11.50. The markup helps cover the Bureau of Engraving and Printing’s overhead and production costs.
IT IS INTERESTING: Is ginger ale a Canadian drink? | 1,069 | 4,401 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.640625 | 3 | CC-MAIN-2022-33 | latest | en | 0.952469 |
https://www.carboncollective.co/sustainable-investing/net-working-capital | 1,725,940,121,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651196.36/warc/CC-MAIN-20240910025651-20240910055651-00167.warc.gz | 661,003,971 | 26,939 | Net working capital is a liquidity ratio which shows whether a company can pay off its current liabilities with its current assets. It’s an important metric for management, creditors and company vendors because it measures the financial health of the company – in particular, the short-term liquidity and the ability to use company assets efficiently.
The net working capital formula is very similar to the working capital ratio and is used for current liabilities such as the company’s trade debts, accounts payable and any vendor notes set for repayment in the current year.
How does it measure the financial health of a company? Well, if the company can’t pay off its debts with current assets, management may be forced to use long-term assets, or any income product assets, to pay the debts.
This is a problem because selling those types of assets can affect the performance of the business and lead to reduced operations, lower sales volumes etc and it can also be an indicator of more serious organizational problems.
## Net Working Capital Formula
The net working capital formula is a very simple calculation which subtracts the current liabilities from the current assets, leaving you with your net working capital.
The current assets and liabilities are often found on the company balance sheet, but sometimes the balance sheet doesn’t separate current and non-current assets.
Current assets that would be included in the net working capital calculation are:
• Cash and cash equivalents
• Accounts receivable
• Stock inventory
• Short-term investments
Current liabilities would include:
• Accounts payable
• Unearned revenue
• Taxes payable
• Accrued expenses
In certain cases, you may also choose to include the current portion of long-term debt with current liabilities.
Although it’s a long-term obligation, the current portion of that debt needs to be repaid within the current year, so it makes sense to include it with other obligations that need to be met in the current year.
## Working Capital Ratio
Another useful metric is the working capital ratio, which measures the current assets against the liabilities.
The net working capital is an absolute amount, but the working capital ratio gives a number which can be used to quickly get a view on whether the company has enough assets to pay debt.
A working capital ratio higher than 1 means that the company can pay current debt with their current assets.
## Working Capital Turnover Ratio
This is another formula which looks at the relationship between net working capital and net sales to see how efficient the company is.
To calculate your average working capital, sum up the net working capital at the beginning of the year and end of the year and divide that by 2.
When a company has a high working capital turnover it means they are generating more revenue per \$1 of investment and is a good thing.
## Net Working Capital Analysis
It should go without saying that a positive net working capital is more favorable for a company. When you are net working capital positive you can show both creditors and your investors that the company is able to pay its debts with current assets – if needed.
A significant net working capital positive also indicates that the company has the available capital to invest for further growth without the need for additional funding.
That said, if the current assets are too high in relation to the current liabilities it would reduce the working capital turnover of the company, and this could be an indication that the company is not using its assets as efficiently as it could be.
### Negative Net Working Capital
When you have a negative net working capital, this says to investors and creditors that the company is not producing enough capital to pay its current debts.
Over time, this could result in the business needing to sell some of the long-term or income-producing assets they have to pay for current debts – like salaries, for example.
The company would also be unable to invest in growth without taking on more debt or investors and, over a long enough period, a negative trend of net working capital can lead to bankruptcy.
## Net Working Capital Example
Okay, let’s take a look at Frankie’s Pizzaria. Frankie owns a pizza place and has the below current assets and liabilities:
• Cash: \$5,000
• Accounts Receivable: \$2,000
• Stock (pizza ingredients): \$5,000
• Accounts Payable: \$3,000
• Accrued Expenses: \$1,000
So the first thing we need to do is get a total of all of the current assets and liabilities:
Now that we have those, we can run the net working capital formula:
Frankie has a healthy, positive net working capital and a good ratio of 3. What this means is that he can easily pay his current debts using only his current assets. The pizza place is very liquid and in good financial shape.
In fact, Frankie could use the liquidity of the business to continue growth by opening another pizza place or expanding the product offering to include burgers and hot dogs.
## Net Working Capital Calculator
You can use the net working capital calculator below to work out your net working capital and ratio.
## FAQs
### 1. What is net working capital?
Net working capital is the difference between current assets and liabilities. It's a measure of how much capital a company has within its operating cycle.
### 2. How do you calculate net working capital?
To calculate the net working capital, use the following formula:
Net Working Capital= Current Assets (CA) – Current Liabilities (CL).
### 3. What is a good net working capital ratio?
A net working capital ratio of 3 or more is considered good.
### 4. Do you include cash in net working capital?
No, you do not include cash in net working capital. It is a measure of current assets and liabilities excluding cash.
### 5. Can net working capital be negative?
Yes, net working capital can be negative if current liabilities are higher than current assets.
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Topics
## Sustainable Investing Topics
View our list of some topics below.
} | 1,283 | 6,502 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2024-38 | latest | en | 0.955088 |
http://www.jiskha.com/members/profile/posts.cgi?name=Alex&page=2 | 1,498,413,609,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320545.67/warc/CC-MAIN-20170625170634-20170625190634-00351.warc.gz | 576,190,956 | 11,993 | # Posts by Alex
Total # Posts: 3,757
Math
A section of stained glass is made by placing a circle at the top of a triangle with a base of 10 centimeters and a height of 8 centimeters. The diameter of the circle is equal to the height of the triangle. What is the area of the section of stained glass? Show your work. Use...
thanks 100%
Science
Relate to some objects your nose is in motion when you run. Relate to others it is not motion. Give one example of each
social studies
Yes, James is correct. D C D A
Linear Algebra
Hi, well I have the next question: How can I show that the sum of two eigen values is not another eigen value? I know that I can give an example, but is ther another way to solve?, please help...
Accounts
I have prepared Income Statement, Statement of Stockholders Equity and Balance Sheet of company and need to know if it is correct or not. imgur. com/HHPU5GO imgur. com/f2VQfNu imgur. com/QqBAarR
physics
Place a coin on top of a sheet of paper on a desk or table. Pull the paper horizontally with a quick snap. What concept of physics does this illustrate?
Math
A marketing expert determines that sales of television sets an be increased by 3 sets per week for each \$20 decrease in price. Weekly sales average 18 sets at \$440 each. What price should be given in order to receive \$10,800 in revenue?
Science
Classify the chemical equation as a combination/synthesis , single replacement, or combustion NaCl(aq) + AgNO3(aq) à AgCl(s) + NaNO3(aq)
Geology and soils
An oven tin containing a sample of moist soil was weighed and had a mass of 37.82 g; the empty tin had a mass of 16.15 g. After drying, the tin and soil were weighed again and had a mass of 34.68 g. Assuming GS = 2.70, determine the void ratio of the soil if the air-void ...
Physics
84grams
History
1.Why did the Portuguese think that they could find an easier way to reach Asia? * a.They had alliances with European nations to send out expeditions. b.They had a large country and a long tradition of Asian exploration. c.They had a large fleet and had defeated Spain in ...
History
I Got the others right but i need help with these.----> 1.Why did the Portuguese think that they could find an easier way to reach Asia? * a.They had alliances with European nations to send out expeditions. b.They had a large country and a long tradition of Asian ...
help
Maths
Show that: (3x-1)(x+5)(4x-3) = 12x^3 + 47x^2 - 62x +15 for all values of x. (3x-1)(x+5)(4x-3) = (?????)(4x-3) Expand into 6 terms: ???????? Simplify: ???????? Thank you.
Math
A pendulum of Length L cm has time period T seconds. T is directly proportional to the square root of L. The length of the pendulum is increased by 40%. What is the percentage increase in the time period? ???????? Multiplier for increasing L = 1.4 Multiplier for increasing T...
American government
Aluminium sulphate when dissolved in water forms aluminium hydroxide and sulphuric acid.Since, aluminium hydroxide is insoluble in water, a clear solution is not obtained. Al2(SO4)3 + 6H2O ?2Al(OH)3 + 3H2SO4Aluminium Aluminiumsulphate Hydroxide
Math
write the percent as a decimal and a fraction 365% Too confusing
Math
In a candy bar, 108 calories are from sugar. There are 240 calories in the candy bar. What percent of the calories are from sugar? I think the answer is 60.
Chemistry
What mass of zinc metal would be needed to produce 0.5 litre of hydrogen gas from dilute HCl
never mind i got it- it's just like matching
I am not sure how you got 40+4 and 30+35 btw thx for your help
Equation of the perpendicular bisector of line segment AB: y=5x/3 - 4 Coordinates of point D = (66/7, 82/7) Gradient of BC = 5/3 Coordinates of point C = (8,15) These are the right answers but how to find the area of quadrilateral? Apparently the answer is 629/14 square units
ABCD is a quadrilateral with angle ABC a right angle. The point D lies on the perpendicular bisector of AB. The coordinates of A and B are (7, 2) and (2, 5) respectively. The equation of line AD is y = 4x ? 26. find the area of quadrilateral ABCD
Physics
It seems 38J is incorrect too. Thanks though :)
Physics
A 5.0 kg block with a speed of 2.9 m/s collides with a 10 kg block that has a speed of 2.1 m/s in the same direction. After the collision, the 10 kg block is observed to be traveling in the original direction with a speed of 2.6 m/s. Suppose, instead, that the 10 kg block ends...
Physics
19.446
Sociology
Compare and contrast the similarities and differences of heterogeneity and diversity. Define each term and apply examples.
political science
1) Scenario: The President appoints Dan Evans to Senator Adams' seat when Adams resigns due to a personal scandal. This scenario is: a) Constitutional, because it is within the President’s powers to appoint Senators when one dies or resigns in the middle of his/her ...
calculus
Take the integral. The initial cost / fixed value (the omni-present +C) is 175. This equation is C(x). You want to know the cost of producing 8 units, so then calculate C(8).
chemistry
Industrial waste contains Zn(II) and cyanide. The waste is toxic to aquatic species like fish. 1- If the waste consists of water, Zn(II) and cyanide, what ligands might complex with Zn(II)? 2- Write chemical equilibria reactions the must be considered to determine toxicity of ...
Art History, college
Is there a difference between the Flamboyant style and the Late Gothic style of architecture?
Art History, college
Q:Describe, with specific examples, what kind of art the Hiberno-Saxons are best known for. Include a basic progression of this art-type’s development ? A: The kind of art that the Hiberno-Saxons are best known for is their illuminated manuscripts as many of the earliest ...
Trigonometry
Okay. Love the no help, now he thinks I'm stupid. My friend Nick is quizzing my on stuff I don't know. like this Given: A= 10km S30degreesW and B= 15km S40degreesW Find the resulting vector (magnitude and direction) of the combined vectors Please just help. He's 19...
Trignometry
Please Help!!! Given: A= 10km S30degreesW and B= 15km S40degreesW Find the resulting vector (magnitude and direction) of the combined vectors
Social Studies Lesson 1 Unit 7
thx xerano
Social Studies Pretest Lesson 1 Unit 7
Those answers are wrong. I got a 33 on my test.
Art History, college
Q:In which era did icons develop importance? A: I believe icons developed importance in the early 3rd century due to icons being associated with the early Byzantine and Eastern Orthodox Churches.
Math
The volume of a sphere is given by the formula: V = (4/3)(pi)R^3 Since we know V = 15000, this equation becomes 15000 = (4/3)(pi)R^3 Solve for R.
math
you are dealt 13-card bridge hand from a 52-card bridge deck. what is the probability that you will be dealt exactly 5 hearts? what is the probability that you will dealt at list 2 hearts? what is the probability that you will receive 5 hearts, 4 clubs, 2 diamonds, and 1 spade?
math
what divided by 7 equals 15
Algebra
A ball is thrown vertically upward from the ground with an initial velocity of 103 ft per sec. Determine what the maximum height will be
Physics
Physics
Ah, you subtract .23 from .747. Thanks! But what about part b? Do you find when net work = 0?
Physics
A 3.20 kg block starts at rest and slides a distance d down a frictionless 30.0° incline, where it runs into a spring (Fig. 8-6). The block slides an additional 23.0 cm before it is brought to rest momentarily by compressing the spring, whose spring constant k is 443 N/m. ...
Math
In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 72 and a standard deviation of 9. Grades are to be assigned according to the following rule: The top 10% receive A's. The next 20% receive B's. The middle ...
Math
In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 72 and a standard deviation of 9. Grades are to be assigned according to the following rule: The top 10% receive A's. The next 20% receive B's. The middle ...
Statistics
Note: For part c, the probability statement should read P(xbar < 3500). The bar denotes sampling means.
Statistics
(A) From the problem statement, N(7400, 2900). P(X < 3500) = .0893 (B) ... .0893? (C) This is a test of means. For this we make a new distribution, N(xbar, s), where xbar = mu, s = sigma / sqrt(n). N(7400, 1674.32) P(X < 3500) = .0099
Difficult Math
Uh... I'm guessing that .2 means 20%? Because you can't have .2 of a card? But then the total cards you have sums to over 100% and welp.
Science
Not enough information. Work is defined as (the sum of) Force(s) dot displacement. So we'd need the direction of the displacement vector. I guess you could argue that "carry" implies perfectly horizontal displacement. In which case, W = 0J. In that case, the ...
Algebra
From the problem statement we derive a system of equations. 4a + 3b = 64 a + b = 19 There are a variety of ways to solve this, but I'll use substitution. Isolate a variable. a = 19 - b ... And substitute that into the other equation. 4(19 - b) + 3b = 64 76 - 4b + 3b = 64 -...
Statistics
From the problem statement, N(32, 7). (A) 2 years is equivalent to 24 months. We want to know how many watches will break on average. P(X < 24) = .1265 = 12.65% (ouch) (B) This statement asks that we modify the warranty so that less than 16% of watches are refunded. We use ...
Physics
Yeah. Set up your static equilibrium equations relative to another pivot. I would recommend doing it at the 100 cm mark, where F is, but it doesn't really matter so long as it's not at the 0 cm mark.
Physics
What's N supposed to be? The knife? If so, you would have to pick a different pivot and repeat the process for it.
Physics
Start by drawing a picture. You have a meter stick of supposedly uniform mass, so the force due to gravity should be in the geometric center, pointing down. We know on the left end we have an upwards force due to the knife, and at the 40 cm mark a weight. Let's pick the ...
English
Inscribed on. Gotta love those English idioms.
Physics
As the problem states, this is a conservation of energy problem, so E(initial) = E(final) Let's pick our coordinate system to be point at which the ball initially rests. This makes the initial potential energy 0. When the ball is at its highest point, the velocity is ...
So we know that the result of doubling a number and subtracting 27 gives 407. Since your teacher wants a guess and check table, let's just start guessing numbers around the 200 mark, since we know double the number at some point.
Statistics
The standard normal curve is N(0, 1). That 6.6& of the curve lies right to the desired z means that .944 of it lies to the left. Use the inverse norm function with the above data in a calculator or look it up in a table. z = +1.589.
Algebra
Two fair eight-sided rolled. If a two is showing on one of the die, what is the probability that the sum is six or less?
SS
1: A,B,E 2: C 3: B 4: B is 100% right
Geometry
You're doing it right. Exact answer just means to keep your answer in symbolic form-- keep your constants. pi * 4^2 * 9 = 144pi (exact) If we wanted the approximate answer, we could substitute pi = 3.14, and then you get 452.
Graphing Linear Equations and Inequalities
Pretend that the inequality is an equals sign, so y = 2x. This is a line with slope of +2, and it's x and y intercepts at the origin. Now we want y to be less than 2x. This is represented as the area above / right of the line. To prove this to yourself, you could always ...
statistic
I suppose it would depend on how you're defining "overpaying." Certainly, we can assume that the distribution of houses is N(650, 90), and from that, we can conclude that Sam paid an amount one standard deviation above the mean. Whether that is overpaying or not ...
physics
Yeah, you have the right process. After you calculate the net force in x and y directions, construct a right triangle by drawing your vectors head-to-tail. |------ | / | / | / | / theta The hypotenuse has a length of ~3188 by Pythagorean theorem. To calculate the angle, we use...
Data
We calculate the number of ways each nationality can order their members. This is simple permutations. Canadians: 3! = 6 Americans: 4! = 12 Mexicans: 2! = 2 However, we can also manipulate the order of our diplomats (i.e. Canada, America, Mexico v. Canada, Mexico, America). ...
math
By how much does 17 exceed the difference of 5 and -5?
Science
In a tennis match the player hits the ball to serve the ball travels 24m from the servers raquet to the opponents Raquet at an average speed of 40 meters per second.calculate the time taken
Math
Suppose a tunnel is 44 feet wide and 22 feet high is in the shape of a parabola. A) Determinate an equation, f(x), of a parabola to represent this situation and B) provide a graph to support your work. Suppose lanes pass trought the tunnel that are each 12 feet wide. C) ...
Math
b a b c b 100% thx
economics
Economics
Math
The x-intercept of a graph is when y is 0. 5x - 12(0) = 60 x = 12 So our point is (12, 0). Likewise, the y-intercept is when x is 0. 5(0) - 12y = 60 y = -5 So our point is (0, -5). The distance between two points is given by the formula: Dist = sqrt{(x0 - x1)^2 + (y0 - y1)^2...
communications
what is the most distorted or misinterpreted topic on the internet?
Physics
A)A 100kg person is riding a 10kg bicycle up a 25degree hill. The hill is long and the coefficient of static friction is 0.9. How much force does the person have to apply in order for her to ride 10m up the hill at constant velocity? B) If the person now starts from rest from ...
math
Given that [sin(A-B)/cos(A+B)]=1/3[tan(A-B)], find the values of cosB if sinA=1/2
social studies
1. How did Washington handle the war between Britain and France? (1 point) The U.S. formed an alliance with France to fight against Britain. The U.S.&...
Physics
Six dogs pull a two-person sled with a total mass of 280 kg. The coefficient of kinetic friction between the sled and the snow is 0.080. The sled accelerates at 0.65 m/s2 until it reaches a cruising speed of 15 km/h. What is the team's maximum power output during the ...
Physics
A pile driver lifts a 450 kg weight and then lets it fall onto the end of a steel pipe that needs to be driven into the ground. A fall of 1.5 m drives the pipe in 45 cm. What is the average force exerted on the pipe?
HCC
A manufacturer of hospital supplies has a uniform annual demand for 80,000 boxes of bandages. It costs \$10 to store one box of bandages for one year and \$160 to set up the plant for prduction. Haw many times a year should the company produce boxes of bandages in order to ...
social studies
explain how the civic virtues of the ancient romans inspired the founding fathers vision of how citizens should conduct themselves in the united states
english
Tanya's pet hamster likes sleeping behind the computer. I have to pick out the prepositional phrase and then identify its object.
history,college
What are some secondary sources and primary sources about Joan of Arc's impact on how Christianity viewed females after Joan's death?
Math
A rectangular shaped desk has a length of 36 inches and a width of 16 inches. A desk with a similar shape has a width of 24 inches. What is the length of this desk?
Math
A 6-foot person standing 15 feet from a streetlight casts a 10-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the streetlight and the ground from the base of the ...
math
the tallest woman who ever lived cast a shadow of 10 feet while a 3 foot vertical stick cast a shadow of 3' 11". how tall was the woman to the nearest inch?
Art History, college
Q: How did the Babylonians make the Ishtar Gate blue (and all its other colors)? A: The Babylonians make the Ishtar Gate blue (and all its other colors) through the use of blue glazed enameled bricks for the blue which was thought to be made of the precious stone,lapis luzli, ...
Art History, college
Q:The Old Kingdom, or Old Dynasty, of Egypt is considered the golden age of Egypt. Using specific examples, explain why. A:The Old Kingdom, or Old Dynasty, of Egypt is considered the golden age of Egypt because of the monumental building efforts such as the funerary complex of...
Art History, college
Q:The Old Kingdom, or Old Dynasty, of Egypt is considered the golden age of Egypt. Using specific examples, explain why. A:The Old Kingdom, or Old Dynasty, of Egypt is considered the golden age of Egypt because of the monumental building efforts such as the funerary complex of...
Algebra
if tickets are sold for \$50, then 600 tickets are expected to be sold. For each \$1 reduction in price, an additional 20 tickets will be sold. Write an equation that gives revenue R from ticket sales when the ticket prices are reduced by "x" dollars.
History
All day long and in all places I am always fastening upon you, stirring you and persuading you and reproaching you. You will not easily find another like me. Use the passage to answer the question. 1. In the passage, what Greek philosopher describes his own method of seeking ...
History, college
What are some natural events mentioned in Robert Bartlett's book "The Natural and the Supernatural in the Middle Ages"?
Science
Yes
calculus
Sorry, supposed to be from 0 to 2pi
calculus
use Simpson's with n=10 to approx. f(x)= x sin x, 0¡Ü x ¡Ü2¦Ð round to 6 decimal places I know I set up the calculation correctly like this: (pi/15)(f(0)+4f(pi/5)+2f(2pi/5)+...+2f(8pi/5)+4f(9pi/5)+f(2pi) I keep getting a negative answer but...
math
Write a compound inequality that each graph could represent
Psychology
In Schachter and Singer's experiment, participants who received epinephrine injections reported euphoria in a happy situation and anger in an insulting situation. Why were the results difficult to interpret? a) Placebo injections produced the same results as epinephrine. ...
psychology
Goals are most effective at motivating increased efforts if the goals are a) challenging (somewhat better than you have done in the past). b) flexible (such as "do your best"). c) private. d) easy. a is my answer
History
1. That is correct as the traditional range for the Sioux people was from the Dakotas to Wyoming. 2. That is correct because the Aztecs lived in a swampy and marsh filled environment which means farming in terraces would be the best option for crops surviving floods. 3. That ...
Math
There are 11 kids in your math class. 3 of them are girls and 8 of them are boys. There are 6 bananas and 12 apples in the bowl.
Post a New Question | 4,847 | 18,775 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.125 | 3 | CC-MAIN-2017-26 | latest | en | 0.945514 |
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# Problems (Equilibrium of Particles)
1. The 40-kg block rests on the rough surface. Length of the spring is 180 mm in the
position shown. Unstretched length of the spring is 200 mm. Determine the coefficient
of friction required for the equilibrium. ( m = ? ) FBD of Block
W=mg
y
20o
## For spring: l=180 mm, lo=200 mm (spring is compressed)
Fspring kl 25000.2 0.18 50 N
## F x 0 : Fspring F friction mg sin 20 0 F friction 50 409.81sin 20 184.21 N
F friction
F friction mN m 0 .5
N
Problems (Equilibrium of Particles)
## 2. 4-kg sphere rests on the smooth parabolic surface. Determine the
reaction of the surface on the sphere and the mass mB required to hold it
in the equilibrium position.
mB
60o
A
y
y=2.5x2
x
0.4 m
Problems (Equilibrium of Particles)
## 3. A continuous cable of total length 4 m is wrapped
around the small pulleys at A, B, C and D. If each spring is
stretched 300 mm, determine the mass m of each block
for equilibrium. Neglect the weight of the pulleys and
cords. The springs are unstretched when d=2 m.
FBD of Pulley C
Fspring kl 5000.3 150 N
Fspring
F y 0
C
75
q q 150 2T sin q 0 T
T T sin q
C q 90 d 2 m
0 .7
C' q arcsin 44.4
T 107.1 N
0.7 m 1 m 1
q FBD of Pulley B
B T F x 0
mg B q 2T cos q m
g 0
A'
q 9.81
A
T m 15.6 kg
Problems (Equilibrium of Particles)
4. The pail and its contents have a mass of 10 kg. If the length of cable
ABC is 7 m, determine the horizontal distance x for equilibrium. Also find
the tension in the cable. The mass of the small pulley at B is small and can
be neglected.
4m
x
A 1m
B C
L=7 m, x = ? (for equilibrium). T=? y 4m
x
A x
C
1m
A
y
y1 B C
q q'
FBD of B
B
T From equilibrium of B :
T
B
q q' F x 0 : T cos q T cos q 0 q q
F y 0 : 2T sin q W 0 (*)
W=mg
x 4 x 7
From geometry: cos q 7 x ax 4a ax a x
a 7a 4
x x 4 y
cos q q 55.15 tan q 1.44 y 1.44 x
a 7x 7 x
4
y y 1 1.44 x 1.44 x 1
x 2.347 m
x 4 x x 4 x
## (*) 2T sin 55.15 109.81 0 T 59.817 N
Problems (Equilibrium of Particles)
r=200 mm
5. The cylinder of mass 1 kg having A
h=120 mm
a very small diameter is held against
a semi-cylinder with a much larger B
diameter by two identical springs, r
h
which are fixed to points C and C
on the ground. The springs are
unstretched when at point A. C
Knowing that the small cylinder is
in equilibrium at point B, what is the
spring constant? C
Problems (Equilibrium of Particles)
## 6. Two bodies weighing 150 N and 200 N, respectively, rest on a
cylinder and are connected by a rope as shown. Find the reactions of
the cylinder on the bodies, the tension in the rope and the angle q.
Assume all surfaces to be smooth.
W1=200 N
rope
W2=150 N
90q
q
Problems (Equilibrium of Particles)
SOLUTION 6 Fx 0
T cos q
FBD of Particle 1 N1 sin q T cos q 0 N1
sin q
y T
Fy 0
x q
N1 cos q T sin q 200 0
q T cos q
90q
N1 cos q T sin q 200 0
q sin q
W1=200 N
T cos 2 q T sin 2 q 200 sin q
T 200 sin q
Problems (Equilibrium of Particles)
Problems (Equilibrium of Particles)
7. It is aimed to hold the 48 kN load in equilibrium by the wire AB that passes from
the ring at C. In order to do this, another force 𝑃 parallel to the xy plane is applied
to the ring. Determine the tension in the wire and the vector expression of load 𝑃.
9m
1m B
A 12 m O 8m
12 m y
x C
P
Problems (Equilibrium of Particles)
8. A small peg P rests on a spring that is contained inside the smooth pipe. The
spring exerts an upward force of 284 N on the peg. Determine the point of
attachment A (x, y, 0) of cord PA so that the tension in cords PB and PC equals
130 N and 84 N, respectively. z
0.6 m
B
0.4 m 0.2 m C
0.3 m
y x y
x
A
z
Fspring = 284 N, , TC = 84 N; determine coordinates of point A (x, y, 0).
P FBD of peg P Coordinates
0.6 m 𝐴 𝑥, 𝑦, 0 𝐵 0, −0.4, 0
𝐶 −0.3,0.2,0 𝑃 0, 0, 0.6
B
0.4 m 0.2 m C TC
0.3 m TB Fspring T
x
y x y A
From equilibrium of peg P F 0
A
x x
Fx 0 TA
a
36 0 TA 36 1
a
xi yj 0.6k y y
TA TA
x 2 y 2 0 .6 2
F y 0 TA 72.22 24 0
a
TA 48.22 2
a
0 .6 0 .6
TB TB
0 .4 j 0 .6 k F z 0 284 TA
a
108.33 72 0 TA
a
103.67
0.72 x 3
130
1 TA
a 36 x 0.208 m
TB 72.22 j 108.33k 0.6 103.67
3 TA
0.3i 0.2 j 0.6k a
TC TC y
0 .7 TA
84
2 a 48.22
TC 36i 24 j 72k y 0.279 m
3 0.6 103.67
TA
Fspring 284k a TA = 119.845 N
Problems (Equilibrium of Particles)
9. The shear leg derrick is used to haul the 200 kg net of fish onto the dock.
Determine the compressive force along each of the legs AB and CB and the
tension in the winch cable DB. Assume the force in each leg acts along its axis..
Problems (Equilibrium of Particles)
10. Crate A weighing 580 N rests on the inclined surface by the cable AB and force
P which is parallel to the z-axis. Determine the tension in the cable AB and force P
for equilibrium. Since the crate is mounted on casters, the force exerted by the
incline on the crate is perpendicular to the incline.
y
1.5 m
3m
B
2.2 m
E P
C
A
3m
O D x
4m
z
Problems (Equilibrium of Particles)
## 11. If WA=WB=1400 N, determine the force P, TAB and the reactions
between the collars and bars.
Problems (Equilibrium of Particles)
12. The 100-kg collar A rests on the smooth straight fixed bar CD by
the cable AB. Determine the tension in the cable and the reaction
between the collar and bar CD.
C
Problems (Equilibrium of Particles)
## 13. Collar A weighing 170 N,
which can slide freely on the
4.5 m
quarter circle, is held in
equilibrium by cable AB.
a) Determine the tension in the
cable.
8
b) Determine the magnitude and 3.4 m 15
## the components of the contact
r =3.4 m
force acting on the collar from
the circle.
Problems (Equilibrium of Particles)
14. Smooth collars A, B and C, each weighing 360 N, are connected by the
wires AB and BC and may slide freely on the smooth rod having the shape
shown. Determine the magnitude of the horizontal force P which must be
applied to the collar A to maintain equilibrium. DEFG portion of the rod is
parallel to xy-plane.
FBD of collar A
W
Four unknowns
y
NAx
TAB NAy
x
z
FBD of collar C
FBD of collar B y
y
TBA
W
W
TCB
z
TBC x z
x
NCx
NBz Four unknowns NCz
Three unknowns
NBxy
FBD of collar C
y
W
TCB
z
x
NCx
NCz
F 0
TBC W N C 0
4i 4 j 7 k
F TBC TBC
9
1.5 m B
4.5 m xB W 360 j
E N C N Cx i N Cz k
6m
4
Fy 0 TBC 360 0
A (0;9;3) 9
1.5 x B
B (2;5;7) TBC 810 N
C (6;1;0) 4.5 6
FBD of collar B y
TBA
W
F
z
TBC x
NBz E
NBxy
F 0
TBC TAB W N B 0
F TBC TCB 360i 360 j 630k
B
2i 4 j 4 k
4.5 m TBA TBA
NBxy q 6
q E
W 360 j
6m
N B 0.6 N B xy i 0.8 N B xy j N Bz k
q 36.87o
2
Fx 0 0.6 N B xy 360 TBA 0
sin q 0.6 6
cos q 0.6 F
4
y 0 0.8 N B xy 360 TBA 360 0
6
TBA 1080 N
FBD of collar A
W
y
NAx
TAB NAy
x
z
F 0
TAB W N A P 0
TAB TBA 360i 720 j 720k
W 360 j
N A N Axi N A y j
P Pk
F z 0 720 P 0
P 720 N
Problems (Equilibrium of Particles)
15. Smooth collars A and B are connected by the spring. Spring has a
constant of 120 N/cm and its unstretched length is 30 cm. Determine the
magnitude of the force P which must be applied to the collar A to maintain
equilibrium and the reaction between the collar and bar. Neglect the weight of
the collars. Take A (40;0;40) and B (0;20;80).
z
A
20 cm
P 80 cm
40 cm 80 cm
40 cm
30 cm
y
x
z
FBD of collar A z
Q
Fspring B
z
A
P 40 cm
NAy q A
NAxz 20 cm
NAxz y P
40 cm 80 cm
80 cm
x x q 40 cm
30 cm 30 cm
y
F 0 Fspring P N A 0 x
40i 20 j 40k
Fspring 120(60 30) AB (0 40)i (20 0) j (80 40)k
60
Fspring 2400i 1200 j 2400k AB 40i 20 j 40k AB 60 cm
3 4 4 3
P Pi Pk N A N Axz i N Axz k N Ay j
5 5 5 5
3 4
Fx 0 2400 P N Axz 0
5 5
F y 0 1200 N Ay 0 N Ay 1200 N Correct sense
F
4 3
z 0 2400 P N Axz 0
5 5
N Axz 387 N P 3483.87 N
Problems (Equilibrium of Particles)
16. The 10-kg collar A and 20-kg collar B rest on the smooth fixed
bars by the cable AB and the force F. Determine the magnitude of the
force F required to maintain equilibrium of the system. The force F is
parallel to the bar CE.
AB 3.5 m y
(0;5;0) m
(0;3;0) m
F
3m
x
(4;0;0) m
z
(0;0;4) m
Problems (Equilibrium of Particles)
Coordinates of point A
y y
C
(0;5;0) m
(0;3;0) m 5m A
F yA
3m
x
3m xA E
4m
x
(4;0;0) m
z
(0;0;4) m
CE 52 42 6.4 m
3 4 xA 3 y
x A 2.125 m A y A 2.34 m
6.4 4 6.4 5
A(2.125, 2.34, 0)
Problems (Equilibrium of Particles)
## A(2.125, 2.34, 0) y B(0, yB, zB) Coordinates of point B
y
(0;5;0) m G
(0;3;0) m
F AB 3.5 m
B 3m
yB
3m
z D zB
z (4;0;0) m x 4m
(0;0;4) m
4 zB yB 12 4 y B
12 3z B 4 y B zB
4 3 3
AB 2.125 02 2.34 y B 2 z B2 3.52
2
4.417 1.889
2.77 y B2 15.34 y B 13.741 0 yB zB
1.1231 2 .5
## B(0, 1.1231, 2.5)
Problems (Equilibrium of Particles)
FBD of particle B y
A(2.125, 2.34, 0) B(0, 1.1231, 2.5) W G
y T
Bx
F B 3m
Byz yB
Byz
x
z
z D zB
4m
B Bx i B yz cos j B yz sin k
B Bx i 0.8B yz j 0.6 B yz k , W 209.81 j 196.2 j
T T
2.125 0i 2.34 1.123 j 0 2.5k
T 0.607i 0.347 j 0.714k
3.5
Fx 0 Bx 0.607T 0
Fy 0 0.8B yz 0.347T 196.2 0
Fz 0 0.6 B yz 0.714T 0
B yz 179.737 N , T 151.04 N | 5,279 | 9,762 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4 | 4 | CC-MAIN-2020-05 | latest | en | 0.557225 |
https://www.physicsforums.com/threads/simple-dc-circuit-strange-layout.114796/ | 1,508,671,193,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187825174.90/warc/CC-MAIN-20171022094207-20171022114207-00147.warc.gz | 944,063,545 | 16,243 | # Simple dc circuit, strange layout!
1. Mar 19, 2006
I'm having difficulty to understand a circuit from my textbook (figure attached). Essentially, the currents seem to go in opposite directions and ultimately meet. It looks strange (circled area), but maybe there is a simple explanation behind it. I wish I could redraw the circuit in a simpler fashion, which is often possible; I can't visualize it this time.
Here is what the problem states:
For the given circuit, find $$\frac{V_0}{V_s}$$ in terms of $$\alpha$$, $$R_1$$, $$R_2$$, $$R_3$$, and $$R_4$$. If $$R_1 = R_2 = R_3 = R_4$$, what value of $$\alpha$$ will produce $$\left| \frac{V_0}{V_s} \right| = 10$$?
Here is what I think (I may be wrong!):
1. The right side gives:
$$V_0 = \left( \frac{R_3 R_4}{R_3 + R_4} \right) \alpha I_0$$
2. The left side gives
$$V_s = \left( R_1 + R_2 \right) I_0$$
3. The first and second expressions yield
$$\frac{V_0}{V_s} = \frac{R_3 R_4}{\left( R_1 + R_2 \right) \left( R_3 + R_4 \right)} \alpha$$
4. If $$R_1 = R_2 = R_3 = R_4 = R$$, then
$$\frac{V_0}{V_s} = \frac{\alpha}{4}$$
5. If $$\left| \frac{V_0}{V_s} \right| = 10$$, then $$\alpha = \pm 40$$.
Any help is highly appreciated
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2. Mar 19, 2006
### Ouabache
Your math looks fine.. A good way to think about this kind of circuit representation is, the right circuit is dependent on the left.. On the left side, you have current $I_o$... The right side uses this same current $I_o$ and is scaled by $\alpha$ (also known as dependent-current-source). Don't worry about the connection node in between. That is your lowest potential (typically ground). In your diagram, both circuits are sharing this common ground.
You will see lots more of this kind of circuit diagram, if you learn about http://people.deas.harvard.edu/~jones/es154/lectures/lecture_3/bjt_models/bjt_models.html [Broken] of bipolar junction transistors.
Last edited by a moderator: May 2, 2017
3. Mar 19, 2006
### Cyrus
Wow, can we give this guy a prize for such a nice post?
4. Mar 20, 2006 | 680 | 2,126 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.15625 | 4 | CC-MAIN-2017-43 | longest | en | 0.850903 |
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Expert Advice and Techniques for Solving Complex Biostatistics Assignments
May 30, 2023
Claire Mitchell
Australia
Biostatistics
Dr. Claire Mitchell is a highly skilled biostatistician who specializes in evaluating and interpreting complex healthcare data. Dr. Mitchell has worked with various research teams and healthcare institutions in Australia and overseas and has a solid background in biostatistical theory and advanced analytical techniques.
Biostatistics is important in healthcare and medical research because it provides the tools and procedures needed to examine and interpret data. However, biostatistics assignments can be daunting and difficult for many students. The intricacies of statistical principles, as well as the use of statistical tools, can frequently cause confusion and frustration. In this article, we will look at expert suggestions and approaches for navigating difficult biostatistics assignments efficiently.
1. Learn the Fundamentals
Before solving any biostatistics assignment, it is critical to first grasp the fundamental ideas. Begin by examining fundamental statistical concepts such as hypothesis testing, probability distributions, sampling strategies, and data analysis techniques. Reinforcing your understanding of these fundamental ideas will give you a solid foundation for tackling more difficult challenges. You should be familiar with the following basic biostatistics concepts:
1.1 Hypothesis Testing
Biostatistics relies heavily on hypothesis testing. It entails developing a hypothesis regarding a population parameter, gathering data, and analyzing the information to see if it supports or contradicts the theory. Learn about the many sorts of hypotheses, such as null and alternative hypotheses, and the methods involved in hypothesis testing, such as choosing an acceptable test statistic and establishing the significance threshold.
1.2 Distributions of Probability
Probability distributions are mathematical functions that explain the probability of various outcomes in a random occurrence. Understanding probability distributions is critical for doing various statistical analyses in biostatistics. Examine popular distributions including the normal distribution, binomial distribution, and Poisson distribution. Learn about their qualities and characteristics, as well as how they are utilized in biostatistics to make inferences and draw conclusions.
1.3 Sampling Methods
The process of selecting a subset of individuals from a broader population to obtain data is referred to as sampling in biostatistics. There are several sampling strategies used, including basic random sampling, stratified sampling, and cluster sampling. Learn about the benefits, drawbacks, and proper application of each sample approach. Learn about sampling error and how it affects statistical analysis.
1.4 Data Analysis Techniques
In biostatistics, data analysis methods are used to summarize and analyze data. Examine descriptive statistics (such as measures of central tendency and variability), inferential statistics (such as confidence intervals, t-tests, and chi-square tests), regression analysis, and analysis of variance (ANOVA). Understand the assumptions and circumstances that must be met for each approach, as well as how to interpret the findings.
2. Seek Clarification When You Don’t Understand
If you have questions about a particular idea or work prompt, don't be afraid to ask your teacher or teaching assistant for clarification. Biostatistics can be complex, and a thorough understanding of the problem is essential for its proper execution. Before attempting the assignment, ask questions, visit office hours, or join study groups to ensure you have a good grasp of the content. When faced with difficult biostatistics tasks, it is critical to seek clarification to achieve a comprehensive knowledge of the problem and its needs. Here are some techniques for effectively seeking clarification:
2.1 Go over the Assignment Prompt again
Begin by thoroughly reviewing your instructor's assignment prompt or directions. Keep a record of any particular questions or tasks stated in the assignment. Keep in mind any criteria for data sources, statistical methodologies, or program needs. Understanding the assignment prompt thoroughly will assist you in identifying places where you may require additional clarification.
2.3 Online Discussion Forums
Participating in biostatistics-related online discussion forums or study groups can be quite beneficial in obtaining clarity. These platforms allow students to communicate with other students who may have similar questions or concerns. Post your questions and join discussions to obtain new perspectives and insights. Furthermore, you may discover that other students have already asked similar questions, saving you time in your search for answers.
2.4 Make Use of Online Resources and Tutorials
In addition to requesting help from your instructor or colleagues, make use of the numerous online resources and courses for biostatistics. Numerous websites, video tutorials, and online courses are available to illustrate statistical ideas and problem-solving strategies. These materials frequently include step-by-step explanations and examples, making complex subjects more approachable and clearer.
2.5 Review Supplementary Reference Materials
In some circumstances, reviewing extra reference materials might help clarify and improve your comprehension of difficult biostatistics concepts. Textbooks, academic publications, and research articles can provide alternative explanations and examples that might aid in the understanding of complex subjects. Explore relevant biostatistics literature using your institution's library resources or online databases.
2.6 Participate in Review Sessions or Workshops
Attend any biostatistics-related review sessions or workshops offered by your institution. These sessions are frequently intended to provide further clarity and support for difficult ideas. Participate actively in these sessions, ask questions, and engage in conversations to make the most of the opportunity to get clarification from qualified instructors or facilitators.
3. Break the Problem Down
When faced with a difficult biostatistics task, it is helpful to divide it into smaller, more manageable chunks. Analyze the assignment requirements and determine whether statistical techniques or approaches must be used. You can tackle the problem more systematically if you divide it into smaller components. This will reduce confusion and improve your overall knowledge of the task.
4. Make Use of Available Resources
Biostatistics projects frequently require the use of statistical software such as R, SPSS, or SAS. Learn about the software package recommended by your course or school. Use internet tutorials, user guides, and forums devoted to statistical software. These resources can help you browse and use the software more efficiently, saving you time and effort.
5. Use Real-World Examples to Practice
Practice applying biostatistics ideas to real-world instances to strengthen your comprehension. Examine published research papers or case studies on healthcare or medical research. Working through these examples will help you understand how biostatistics is utilized in practice and build the skills needed to successfully evaluate and analyze data.
6. Collaboration and Discussion
Participating in group conversations and collaborations with your peers might help you gain a better grasp of biostatistics. Collaboration and discussion are effective techniques for overcoming difficult biostatistics tasks. Engaging with peers and professionals in the subject can bring new insights, clear up misconceptions, and promote a deeper understanding of complicated concepts. Here are some ways to effectively collaborate and participate in biostatistics discussions:
6.1 Participate in Study Groups or Discussion Forums
Consider organizing study groups with classmates working on similar biostatistics tasks. Study groups provide a helpful environment in which you may exchange ideas, explore difficult concepts, and work together to solve challenges. You can improve your comprehension and problem-solving abilities by combining different perspectives and approaches.
If study groups aren't easily available, look into online discussion forums and biostatistics communities. These platforms enable students, researchers, and professionals to connect with a larger network of peers. Participate actively in debates, share your ideas, and solicit feedback from others to obtain new views and broaden your understanding.
6.2 Hold Regular Group Meetings
Establish a regular meeting schedule once you've joined a study group to collaborate efficiently. Plan and structure meetings so that they are focused on specific subjects or problem areas. Allow time for each member to present and discuss their methods to issue resolution or conceptual understanding. To establish an engaging and productive workplace, encourage open discussion, ask questions, and provide constructive feedback.
6.3 Divide and Conquer
Consider distributing the burden among group members when faced with a complex biostatistics job. Assign different areas or difficulties to each member, and then come back together to discuss and share your results. This method provides for a more in-depth examination of the task and encourages individual accountability. You can complete the job more quickly if you collaborate and combine your collective knowledge and talents.
6.4 Discuss Concepts with One Another
Explaining biostatistics topics to others is one of the most effective ways to solidify your comprehension of them. Take turns teaching difficult topics, statistical methodologies, or problem-solving procedures to members of your study group. Teaching others not only reinforces your understanding but also aids in identifying areas that may require additional clarification or research. Encourage group members to ask questions and participate in conversations to have a better understanding of the subject.
Seek input from specialists or professionals in the field of biostatistics in addition to interacting with peers. For assistance and clarification, contact your instructors, teaching assistants, or faculty members who specialize in biostatistics. They can provide useful insights, new resources, and assistance in navigating challenging assignments. Use office hours or scheduled appointments to discuss specific concerns or seek assistance on problem-solving tactics.
7. Make a Timetable
Assignments in biostatistics can be time-consuming, especially when dealing with huge datasets or sophisticated studies. Make a realistic timetable and provide enough time for each stage of the assignment. Breaking the task down into smaller milestones will allow you to stay organized and avoid last-minute rushing. Begin early to allow for unexpected obstacles and modifications.
8. Validate and Verify Results
In biostatistics, double-checking your calculations and verifying the accuracy of your results is critical. Check that you followed the necessary procedures, used the appropriate statistical tests, and correctly interpreted the results. A minor calculation or interpretation error can lead to incorrect findings. To authenticate your conclusions, cross-reference your work with reliable sources such as textbooks or statistical references.
9. Seek Professional Assistance
If, despite your best efforts, you find yourself continuously suffering with biostatistics assignments, don't be afraid to seek professional assistance. Online tutoring programs or academic support centers frequently provide aid from professional statisticians who can guide you through difficult problems and explain difficult topics. Using these tools might offer you the expertise you need to overcome obstacles in your work.
10. Reflect on and Learn from Your Mistakes
Every assignment, no matter how difficult, offers an opportunity for growth and learning. Take the time to reflect on and learn from your mistakes. Recognize the areas where you struggled and seek more practice or study materials to help you better understand those ideas. Accept the learning process and use each assignment to improve your biostatistics skills.
Conclusion
Biostatistics assignments can be difficult to complete, but with the appropriate strategy and mindset, they can be made more manageable. You can successfully traverse complex biostatistics assignments by understanding the fundamentals, getting clarification when necessary, breaking down problems, leveraging accessible resources, and practicing with real-world examples. Remember to work with your colleagues, manage your time properly, verify and confirm your results, and seek professional assistance as needed. Accept the learning process, and with perseverance, you will build a solid foundation in biostatistics, allowing you to flourish in your academic studies as well as future ambitions in healthcare and medical research. | 2,280 | 13,236 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2024-10 | latest | en | 0.909083 |
https://mathoverflow.net/questions/369253/creation-and-annihilation-operators-in-qft?noredirect=1 | 1,621,292,350,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243991870.70/warc/CC-MAIN-20210517211550-20210518001550-00023.warc.gz | 395,102,550 | 35,945 | # Creation and annihilation operators in QFT
As I said before, I'm not a QFT expert but I'm trying to understand the basics of its rigorous formulation.
Let's take Dimock's book, where the foundation of QM and QFT is discussed. If we consider, say, two particles, one living in a Hilbert space $$\mathcal{H}_{1}$$ and the other in another Hilbert space $$\mathcal{H}_{2}$$, the description of the state of the two-particle system is given in terms of the tensor product $$\mathcal{H}^{(2)}=\mathcal{H}_{1}\otimes \mathcal{H}_{2}$$. Of course, we could go furhter and study a system $$\mathcal{H}^{(N)}=\mathcal{H}_{1}\otimes \cdots \otimes \mathcal{H}_{n}$$. If all the particles are identical, then $$\mathcal{H}_{1}=\cdots = \mathcal{H}_{n} \equiv \mathcal{H}$$ and we must take into account symmetric and anti-symmetric subspaces of $$\mathcal{H}^{(N)}$$, which correspond to the fact that particles may be either bosons or fermions, respectivelly. At this point, one defines symmetrization and anti-symetrization operators. The next step is to consider a system of an arbitrary number of particles. At this point, one defines Fock spaces $$\mathcal{F}^{\pm}(\mathcal{H}) = \bigoplus_{n=0}^{\infty}\mathcal{H}_{n}^{\pm}$$ for bosons and fermions. Also, one defines creation and annihilation operators $$a(h)$$ and $$a^{\dagger}(h)$$ on $$\mathcal{F}^{\pm}(\mathcal{H})$$.
Now, as far as I understand, this is all quantum mechanics, not QFT. However, these ideas seem to find analogues in QFT, and this is the point where I get confused.
On section I.5 of Feldman, Trubowitz and Knörrer's book there is a quick discussion on (fermionic) QFT and it is stated that, in this context, creation and annihilation operators are special families $$\{\varphi^{\dagger}(x,\sigma):\hspace{0.1cm} x \in \mathbb{R}^{d}, \hspace{0.1cm} \sigma \in \mathcal{S}\}$$ and $$\{\varphi(x,\sigma):\hspace{0.1cm} x \in \mathbb{R}^{d}, \hspace{0.1cm} \sigma \in \mathcal{S}\}$$ on a Hilbert space $$\mathcal{H}$$. This is very different than the creation and annihilation operators mentioned above. For instance, these are now families of operators indexed by $$x$$ and $$\sigma$$. I believe this is a reflection of the fact that we passed from QM to QFT. But I'm really lost here and I don't know what's the difference between these two constructions and definitions. Can anyone help me, please? I'm mainly interested in understanding the second approach, since the first one I believe I understand (at least sufficiently well). If, in addition, you could suggest some reference where these ideas of Feldman, Trubowitz and Knörrer are discussed in more details and with rigor, I'd appreciate!
ADD: Based on Feldman, Trubowitz and Knörrer's book, it seems to me that the understanding of these objects (to be more precise, the objects they briefly describe in the first 2 pages of section I.5) is fundamental to understand the formulation of a bunch of QFT models (at least for fermions). Thus, I'd appreciate if someone could elaborate a little more on the structure behind these creation and annihilation operators and its connections to the quantum case that is needed to understand the rest of the discussion on FTK's book. In other words, I think I just need to better understand these first definitions (and how are they connected with the usual quantum case I (seem) to know) to be able to understand the rest of the text.
• Morally speaking, a linear functional on a function space is an integral. So $a(h) = \int a(x) h(x) dx$. Replace $a$ by $\varphi$ and make $h(x)$ multicomponent-valued to account for spin to get the FTK notation. If you shift the focus from rigor to motivation and historical context, you can't go wrong with Dirac's classic Principles of Quantum Mechanics (1930), §59–65. – Igor Khavkine Aug 15 '20 at 18:28
• The general idea is that in QFT -unlike QM- the wave functions themselves are "upgraded" to operators. If you wish to understand the basics, i suggest you first focus on the radiation field, that is QED (quantum electrodynamics). Among all field theories this is the first to be formulated (historically) and maybe the only one which has a rigorous formulation. – Konstantinos Kanakoglou Aug 16 '20 at 11:35
• Mandl's book: archive.org/details/… (especially the first few chapters), could provide a descent starting point. – Konstantinos Kanakoglou Aug 16 '20 at 11:36
• @IgorKhavkine this is something that came to my mind, too. But this is just a different way to represent these operators, right? I mean, is it all? And, besides, why doing that? (Sorry if my questions are really basic, I'm still getting acquainted with all this). – IamWill Aug 16 '20 at 15:40
• @KonstantinosKanakoglou thank you so much for the comments! I'm going to take a look at this book right now. – IamWill Aug 16 '20 at 15:41
The connection can be seen by taking $$H = L^2(\mathbb{R}^3)$$ in the first explanation. This is the Hilbert space of a nonrelativistic, spinless, three-dimensional particle. By direct summing the symmetric (antisymmetric) tensor powers of $$H$$ we get the Hilbert space of an ensemble of noninteracting Bosonic (Fermionic) nonrelativistic, spinless, three-dimensional particles, known as Fock space. The $$n$$th tensor power represents the states in which $$n$$ particles are present.
Now we have "creation" and "annihilation" operators which take states in the $$n$$th tensor power into the $$(n \pm 1)$$st tensor power. For each state $$h$$ in the original Hilbert space $$H$$ there is a creation operator which tensors with $$h$$ and symmetrizes (antisymmetrizes), taking the $$n$$th tensor power into the $$(n+1)$$st, and its adjoint which goes in the opposite direction and removes a tensor factor of $$h$$.
In the physics literature one usually works with idealized creation/annihilation operators for which the state $$h$$ is a fictional Dirac delta function concentrated at some point of $$\mathbb{R}^3$$. This is what is described in your second explanation. As is usual in physics, the Hilbert space is unspecified, but in the case of free fields it corresponds to the Fock space in the first explanation.
Fock space is inadequate to model interacting fields (indeed, here the mathematical issues become deep and fundamentally unresolved). However, it is not trivial; for instance, one can study free quantum fields against a curved spacetime background and derive Hawking radiation, the Unruh effect, etc. Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics by Wald is an excellent, mathematically rigorous explanation of this setting.
In QFT the intuition is that one has a separate Hilbert space at each point of space, and one takes their tensor product to get the Hilbert space of the entire field. I indicated how, intuitively, the Fock space models a "measurable tensor product" of a family of harmonic oscillators (Bosonic case) or two-state systems (Fermionic case) indexed by all the points of space in my answer here. See Section 2.5 of my book Mathematical Quantization for a full explanation.
• very nice! Bravo Nik. And thanks for filling us in with a more accurate pciture – Mirco A. Mannucci Aug 16 '20 at 16:50
• Thank you Mirco! – Nik Weaver Aug 16 '20 at 17:00
• @NikWeaver thank you so much for the amazing answer. This clarifies the things to me. Let me ask you something. You said that my second representation arises when the state $h$ is taken to be a delta. Dimock's book discusses many particle systems where $\mathcal{H}=L^{2}(\mathbb{R}^{3})$. In this case, $\mathcal{F}^{\pm}=\bigoplus_{n=0}^{\infty}\mathcal{H}^{\pm}$ , where $\mathcal{H}^{\pm} = L^{2}_{\pm}(\mathbb{R}^{3n})$ are, respectivelly, symmetric and anti-symmetric subspaces of $L^{2}(\mathbb{R}^{3n})$. continues... – IamWill Aug 17 '20 at 14:54
• At some point, Dimock states: "If $\psi \in L^{2}_{\pm}(\mathbb{R}^{3n})$ is a continuous function, then in $a(h)\psi$ we can take $h$ to be a $\delta$-function and define an operator $a(x)$ by $(a(x)\psi)(x_{1},...,x_{n-1}) = \sqrt{n}\psi(x,x_{1},...,x_{n-1})$." Question: according to you answer, this is precisely what my $\varphi^{\dagger}(x,\sigma)$ are, right? The only difference is that, in this case, the spins are not being taking into account, so that $\sigma$ is omitted. – IamWill Aug 17 '20 at 14:58
• Yes, I believe that is what the $\phi^{\dagger}(x,\sigma)$ are. Just be careful about $\psi$ needing to be continuous --- this makes the operator $a(x)$ unbounded on each summand, whereas $a(h)$ for $h \in L^2(\mathbb{R}^3)$ would be bounded on each summand ... – Nik Weaver Aug 17 '20 at 15:51
Disclaimer: I am not a mathematical physicist.
Even with one Hilbert space, namely the quantum harmonic oscillator, you can define "creation-annihilation" operators, except that in this case they simply raise or downgrade the energy level of the single particle system.
Now, you consider the Fock space $$\mathcal{F}^{\pm}(\mathcal{H}) = \bigoplus_{n=0}^{\infty}\mathcal{H}_{n}^{\pm}$$ the way you describe above: it is actually a functor, hence the infamous dictum that second quantization is a functor.
Therein, you define again the two operators, but you re-interpret them as ladder operators which, from the ground state, create and destroy particles. Formally they behave very much as with the toy harmonic oscillator, and that analogy is far-reaching:
basically it tells you that the quantum field described by the Fock functor can get "excited": particles are excitations of the void (in fact there are some beautiful pictures of quantum fields as (infinite) ensembles of (coupled ) harmonic oscillators, see here).
What has this to do with the second definition? If the quantum field creates and annihilates particles, it can do it at each point of your ambient space. Hence the indexes...
• Regarding whether each quantum field can be represented using creation and annihilation operators on a Fock space -- the answer is no. – Robert Furber Aug 16 '20 at 5:15
• Hello again Mirco! And thanks for the answer! You said that the Fock space formulation is already QFT, right? This is confusing to me. See, I know that, rigorously, a QFT theory is defined by Wightman axioms, right? But intuitively (since I'm not an expert), this seems really like a QM problem. What is you understanding on this? – IamWill Aug 16 '20 at 15:37
• @Iamwill you see the beaty of MO? You try to answer a question, and sometimes you mak a fool out of yourself :) . Now, assuming that one can take it (and I can), it is GOOD. Why? because you learn what you do not know. My picture was an oversimplification, and was based on the erroneous assumption that every QFT can somehow be "represented" as a Fock space, in other words, that the Hilbert space which is assumed by the Wightman axioms can be realized as a Fock tensor product. – Mirco A. Mannucci Aug 16 '20 at 16:21
• Robert disabused me of this. So, here i my new understanding (perhaps also faulty): some QFT can be so realized, but actually they are in a way the silly ones. Now, the exact picture still escapes me – Mirco A. Mannucci Aug 16 '20 at 16:21
• @MircoA.Mannucci I think to recognize one's mistake is as important as learning from others. In my opinion, this is a very nice humble behavior of yours! This is well done science for sure! – IamWill Aug 16 '20 at 16:30 | 3,054 | 11,346 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 30, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2021-21 | latest | en | 0.826181 |
https://stoicacademia.com/2021/08/05/1an-electron-that-is-a-certain-distance-from-a-proton-is-acted-on/ | 1,632,331,160,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057371.69/warc/CC-MAIN-20210922163121-20210922193121-00423.warc.gz | 580,505,418 | 11,666 | # 1) an electron that is a certain distance from a proton is acted on
1) An electron that is a certain distance from a proton is acted on by an electrical force. a) If the electron were moved twice the distance away from the proton, would the electrical force be: 1) 2 2) ½ 3) 4 4) ¼ b) If the initial electric Force is, F, and the electron were moved to one third he original distance toward the proton, what would be the new electrical force? 2) What is the magnitude and direction of the electric field at a point 0.75 m away from a point charge of +2.0 pC? 3) Two fixed charges -4.0 C and -5.0 C are separated a certain distance. a) Is the net electric field at a location halfway between the two charges: 1) Directed toward the -4.0 C charge 2) Zero 3) Directed toward the -5.0 C charge b) If the charges are separated by 20 cm, calculate the magnitude of the net electric field halfway between the two charges. 4) What is the speed of a proton whose kinetic energy is 12.9 keV? 5) An electron is accelerated by a uniform electric field (1000 V/m) pointing vertically upward. Use energy methods to get the magnitude and direction of its velocity after it moves 0.10 cm form rest. Does the electron gain or lose potential energy? 6) How much charge flows through a 12 –V battery when a 2.0 mF capacitor is connected across its terminals?
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Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result. | 659 | 2,731 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.796875 | 3 | CC-MAIN-2021-39 | latest | en | 0.905923 |
http://clay6.com/qa/13495/two-short-bar-magnets-have-their-magnetic-moments-1-2-am-2-and-1-0-am-2-the | 1,527,143,200,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865928.45/warc/CC-MAIN-20180524053902-20180524073902-00422.warc.gz | 62,824,614 | 26,615 | # Two short bar magnets have their magnetic moments $1.2\;Am^2$ and $1.0\;Am^2$. They are placed on a horizontal table parallel to each other at a distance of $20\;cm$ between their centers, such that their north poles pointing towards geographic south. They have common magnetic equatorial line. Horizontal component of earth's field is $3.6 \times 10^{-5}$ T. Then, the resultant horizontal magnetic induction at mid point of the line joining their centers is $\bigg(\large\frac{\mu _0}{4 \pi}$$=10 ^{-7} 11/m\bigg)$
$(a)\;3.6 \times 10^{-5}T \quad (b)\;1.84 \times 10^{-4}\;T \quad (c)\;2.56 \times 10^{-4}\;T \quad (d)\;5.8 \times 10^{-5}T$ | 211 | 645 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2018-22 | latest | en | 0.795479 |
https://www.physicsforums.com/threads/force-couple-system.475301/ | 1,643,217,075,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320304959.80/warc/CC-MAIN-20220126162115-20220126192115-00713.warc.gz | 967,019,424 | 14,191 | # Force couple system
This is not really a homework question just a review but i wanted someone to explain to me why the forces of the moments negative on Fb, Fc and Fd
#### Attachments
• qz2.2.png
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ehild
Homework Helper
The component of torque of a force F acting at a point r is equal to the vector product of the vector r and the force.
Mx=y Fz -z Fy,
My=z Fx -x Fz,
Mz=x Fy -y Fx.
You can also decide the sign from the direction of rotation the force would cause along an axis. Seeing from the positive x, y, or z axis, the moment is positive if it rotates anti-clockwise, and negative, if the rotation is clockwise.
ehild | 179 | 652 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2022-05 | latest | en | 0.884569 |
https://id.scribd.com/doc/57871347/Gann-Calculator-Explained | 1,582,257,523,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145438.12/warc/CC-MAIN-20200221014826-20200221044826-00396.warc.gz | 416,668,098 | 80,103 | Anda di halaman 1dari 5
# Gann Calculator Explained Introduction: Gann calculator in the initial days of its introduction got very good response
2.
Take the previous days last hour high and low for next days 1st hour trade provided global sentiments must be neutral during the non trading hours of our market.
3.
If the current price action of the script is trending then take the low or high follows the trend high or low.
4.
If you encounter congestion then take the high and low in greater time interval.
Now see some examples which I feel will thrill you. I will also explain how you will enter a trade. Example 1: consider the Nifty spot one hour data from 10 to 11 a.m on 12th august 2008.Its high was 4634 and low was 4598. Using this data in the intraday calculator I found that my key supports are 4600-4566-4498 and resistances are 4631-4666-4735. You can use this data in the calculator and test its accuracy. At 11:05 a.m. it has fallen and found support at 4565, 11:30 it touched high 4599 and fallen. Hence it is confirmed in the next half an hour nifty was very much within the band of my calculated support 1 and support 2. From trading point of view if I miss the chance to enter the short trade at 4611 then better in this junction I will wait or change my data points. Second observation is the bounce from the low 4565 failed to cross the 1st support 4600. So now the support turns into resistance as per basic technical analysis concept for next half an hour. In this junction also I can go short with my initial stoploss as 4611 and second stoploss as 4631 and target as 4565. See in the next half an hour nifty created new low of 4557 at 11:52 a.m. In this example I have used the past one hour high and low points for my observation and calculated all the resistance and support values for the next hour. It is not guaranteed that I will achieve my target or stop loss in the next one hour. It is just a mathematical assumption based on my observation. I will suggest all of you to treat this calculator as an alternative software tool as you treat all other indicators and tools. Example 2: consider reliance industry high and low in a time period from 10 a.m. to 12 p.m. on 13th august 2008. It was a trending day for reliance because it was creating higher high and higher low. My Swing high and swing low for this two hour period is 2353 and 2315 respectively. Using these two values on the gann calculator I got the following values: Long entry price was: 2331 target 2339-2347-2363-2412 Short entry price was: 2337 target 2329-2320-2304-2256 Since it was a trending market for RIL and it was creating the higher high and higher low and the current price is much above my second target point and trending upward. I will use this swing action to enter a buy trade keeping my 1st stoploss as 2339 which is my key resistance, which turn into the support and my target will be 2363. I will come out of the trade at 2363 or slightly below that because this is the 3rd level of target and important resistance point. Again I have observed that after touching the high of 2373.65 the price has started retracing back. Now I will change my swing low and high. The low as 2339 and high as 2373.65. The stock price 2339 is the low which the stock has made just before making this high of 2373.65. You can say this is the high following the low. Notice it carefully I have not taken the hourly high or low rather I have taken the latest low preceding the high. Why this deviation in principle? If the current price action is against the previous trending nature of the price then you need to make this deviation. In the second case scenario if the price continues its trending behaviour then also this deviation in principle will come in to focus. Using these two values 2373.65 and 2339 I got
Short entry price was: 2358 Long entry price was: 2355 This is congestion because the difference is only Rs 3 /- so now I will shift my focus to the 1st level of target for both the long and short. As per my calculation 1st long and short targets are 2363 and 2349. These two prices will act as my new long entry and short entry points. More precisely I will buy reliance above 2363 and sell below 2349. My stoploss for the sell entry will be 2358-2374-2398 and stoploss for buy trade will be 2355-2339-2314 Observe the second part of the calculator which flags the important support and resistance points. my entry points also coincide with the 1st level of resistance and support. As you can observe from the chart at 12:35 p.m after drifting to the level of 2362 the stock has a minor bounce back to 2366 and the greater downward action started once it has broken the level of 2349. My target level of short entry was 2342-2326-2277. You can say it as a coincident or a mathematical wonder. 1. At 1:30 p.m. stock touched 2341 and bounced back to 2349 level.
2. | 1,194 | 4,885 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.21875 | 3 | CC-MAIN-2020-10 | latest | en | 0.945579 |
http://mathhelpforum.com/advanced-algebra/134340-fields-elements.html | 1,481,152,457,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542250.48/warc/CC-MAIN-20161202170902-00193-ip-10-31-129-80.ec2.internal.warc.gz | 177,773,421 | 10,174 | Thread: fields and elements
1. fields and elements
Let K be a finite field with k elements. Let K*={x1,x2,...,xk-1}, the non-zero elements of K.
Show that product (x belonging to K*) x=x1x2...xk-1=-1.
Hint: Try to arrange, in the product, the elements in pairs a,b with ab=1, i.e. b=a^(-1) to the extent possible. Of course, a can not equal a^(-1) Which elements aren't paired?
I'm highly confused by this. I get it in the concrete example, i.e. in Z11, we get an arrangement of this form (2*6)(3*4)(5*9)(7*8) (1)(10), but I'm having trouble with it in the abstract.
Thanks.
2. Originally Posted by twittytwitter
Let K be a finite field with k elements. Let K*={x1,x2,...,xk-1}, the non-zero elements of K.
Show that product (x belonging to K*) x=x1x2...xk-1=-1.
Hint: Try to arrange, in the product, the elements in pairs a,b with ab=1, i.e. b=a^(-1) to the extent possible. Of course, a can not equal a^(-1) Which elements aren't paired?
I'm highly confused by this. I get it in the concrete example, i.e. in Z11, we get an arrangement of this form (2*6)(3*4)(5*9)(7*8) (1)(10), but I'm having trouble with it in the abstract.
Thanks.
DISCLAIMER: You may want to wait for verification by another member. I am NOT too experienced in field theory.
For every $k\in K-\{1,-1\}$ there exists some $k'$ such that $kk'=1$. Thus, $\prod_{k\in K}k=\prod_{k\in K-\{1,-1\}}k\cdot 1\cdot -1=(k_1k'_1)(k_2k'_2)\cdots =-1\cdot1\cdots=-1$ | 478 | 1,435 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.96875 | 4 | CC-MAIN-2016-50 | longest | en | 0.843383 |
https://jp.mathworks.com/matlabcentral/cody/problems/44384-find-the-nearest-prime-number | 1,721,634,850,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763517833.34/warc/CC-MAIN-20240722064532-20240722094532-00118.warc.gz | 291,800,879 | 22,775 | # Problem 44384. Find the nearest prime number
Happy 5th birthday, Cody! Since 5 is a prime number, let's have some fun looking for other prime numbers.
Given a positive integer x, find the nearest prime number. Keep in mind that the nearest prime may be less than x.
Examples
```nearestprime(5) = 5
nearestprime(36) = 37
nearestprime(200) = 199
```
NOTE: You may ignore cases in which two prime numbers are equally close to x. (e.g., x=12 --> 11 and 13 are both primes).
### Solution Stats
31.25% Correct | 68.75% Incorrect
Last Solution submitted on Jul 19, 2024
### Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting! | 183 | 699 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.1875 | 3 | CC-MAIN-2024-30 | latest | en | 0.868599 |
http://www.mathworksheets4kids.com/matrices/index.php | 1,511,414,855,000,000,000 | text/html | crawl-data/CC-MAIN-2017-47/segments/1510934806736.55/warc/CC-MAIN-20171123050243-20171123070243-00599.warc.gz | 404,305,412 | 8,282 | Home > Algebra > Matrices
# Matrices Worksheets
Matrix is an array of numbers in rows and columns. It plays an important role in the field of computer science. Learning matrices help to solve complex problems related to real life situations in an easy manner. Worksheets on matrices help you expertise in basics of matrix operations.
Order of Matrices Worksheets
Order of matrices determined by the number of rows and columns. If there are 2 rows and 3 columns then the order is 2 x 3
Do addition for matrices that have same order. Add the elements in corresponding positions. Choose the difficulty level you need.
Subtraction of Matrices Worksheets
As we do in addition, same procedure as to be followed. Both square and non square matrices included.
Complete revision of addition and subtraction of matrices. Add or subtract two or three matrices in a worksheet.
Multiplication of Matrices Worksheets
Process of multiplication is quite long than addition or subtraction. More concentration is required to multiply matrices.
Inverse of Matrices Worksheets
Inverse of A is A-1. If you multiply A and the inverse, then the result is unit matrix. Inverse of matrix works only for square matrices.
Determinants Worksheets
Value of square matrices often called as determinants. Few determinants can easily be evaluated using the properties. | 264 | 1,350 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2017-47 | latest | en | 0.878748 |
http://quant.stackexchange.com/questions/tagged/risk-management?sort=faq | 1,416,847,041,000,000,000 | text/html | crawl-data/CC-MAIN-2014-49/segments/1416400380866.29/warc/CC-MAIN-20141119123300-00193-ip-10-235-23-156.ec2.internal.warc.gz | 272,372,290 | 25,559 | # Tagged Questions
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### Is Unexpected Loss ever used in Basel II?
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### Regression in liquidity risk model of Jarrow/Protter
In the paper "Liquidity Risk and Risk Measure Computation" authors describe a linear supply curve model for liquidity risks in presence of market impact, i.e. impact-affected asset price $S(t,x)$ is ... | 2,754 | 12,804 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.515625 | 3 | CC-MAIN-2014-49 | longest | en | 0.921537 |
https://programs.programmingoneonone.com/2022/04/hackerearth-choose-k-numbers-problem-solution.html | 1,686,077,703,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224653071.58/warc/CC-MAIN-20230606182640-20230606212640-00019.warc.gz | 518,206,694 | 33,723 | # HackerEarth Choose K Numbers problem solution
In this HackerEarth Choose K Numbers problem solution, You are given an array Arri of size N. You have to find the maximum value of K such that after choosing K numbers from the array the DiffValue of chosen numbers is less than or equal to S.
DiffValue for a set of integers is defined as the largest possible difference among any two integers of the set. However if you choose K numbers from the array, value of all the chosen numbers get multiplied by K.
Hence print two integers i.e the largest value of number K and largest possible DiffValue corresponding to value of K.
## HackerEarth Choose K Numbers problem solution.
`#include <bits/stdc++.h>#define sflld(n) scanf("%lld",&n)#define sfulld(n) scanf("%llu",&n)#define sfd(n) scanf("%d",&n)#define sfld(n) scanf("%ld",&n)#define sfs(n) scanf("%s",&n)#define ll long long#define s(t) int t; while(t--)#define ull unsigned long long int#define pflld(n) printf("%lld\n",n)#define pfd(n) printf("%d\n",n)#define pfld(n) printf("%ld\n",n)#define lt 2*idx#define rt 2*idx+1#define f(i,k,n) for(i=k;i<n;i++)#define MAXN 100005#define FD freopen("out.txt", "w", stdout);#define FC fclose(stdout);using namespace std;int cost[MAXN],n,s,v[MAXN];bool cal(int k){ int i; f(i,0,n) { v[i]=(cost[i]*k); } bool fl=0; f(i,0,n-k+1) { if(v[i+k-1]-v[i]<=s) { fl=1; break; } } return fl;}int main(){ int t; sfd(t); while(t--) { int i,j; sfd(n); sfd(s); f(i,0,n) { sfd(cost[i]); } sort(cost,cost+n); int l=1,r=n; int k; while(l<=r) { ll m=(l+r)/2; // cout<<l<<" "<<r<<" "<<m<<endl; if(cal(m)) { k=m; l=m+1; } else r=m-1; } int mx=-1; f(i,0,n) { v[i]=(cost[i]*k); } f(i,0,n-k+1) { if(v[i+k-1]-v[i]<=s) { mx=max(mx,v[i+k-1]-v[i]); } } cout<<k<<" "<<mx<<endl; } return 0;}`
### Second solution
`#include <cstdio>#include <iostream>#include <set>#include <map>#include <queue>#include <algorithm>#include <stack>#include <math.h>#include <string>using namespace std;#define maxN 50000#define ll long long intll n,sum;ll a[maxN+5];bool valid(ll k){ ll i; for(i=0;(i+k)<=n;i++) if(((a[i+k-1]-a[i])*k)<=sum) return true; return false;}ll searchb(ll s,ll e){ ll m; while((e-s)>1) { m=s+(e-s)/2; if(valid(m)) s=m; else e=m-1; } if(valid(e)) return e; if(valid(s)) return s; return 0;}int main(){ ll t,i,k,val; scanf("%lld",&t); while(t--) { scanf("%lld%lld",&n,&sum); for(i=0;i<n;i++) scanf("%lld",&a[i]); sort(a,a+n); k=searchb(0,n); val=0; for(i=0;(i+k)<=n;i++) if((a[i+k-1]-a[i])*k<=sum) val=max(val,(a[i+k-1]-a[i])*k); printf("%lld %lld\n",k,val); } return 0;}` | 947 | 3,169 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2023-23 | longest | en | 0.501226 |
https://community.powerbi.com/t5/Desktop/Slicer-filter-another-slicer/m-p/619914 | 1,555,967,834,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578582584.59/warc/CC-MAIN-20190422195208-20190422221208-00414.warc.gz | 394,800,364 | 104,549 | cancel
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Frequent Visitor
## Slicer filter another slicer
Power BI Set up;
- 1 Table
- Slicer 1 (Between) for column A (Values)
- Slicer 2 (Between) for column B (Date)
Goal:
[Count values filtered by slicer 1 and slicer 2] divided by [Count Values filtered only by slicer 2]
I have tried filters ALL, ALLSELECT and ALL EXCEPT.
I can filter with slicer 1 from 0 to 10, but it doesn't work with slicer 1 from 3 to 10.
Thanks for your effort!
Boudewijn
1 ACCEPTED SOLUTION
Accepted Solutions
Community Support Team
## Re: Slicer filter another slicer
in my test,
[Count values filtered by slicer 1 and slicer 2] ---Measure
divided by
[Count Values filtered only by slicer 2] ---------Measure 2
Best Regards
Maggie
6 REPLIES 6
Super User
## Re: Slicer filter another slicer
Please post or share some sample data and the output expected to arrive at a solution.
Cheers
CheenuSing
Did I answer your question? Mark my post as a solution and also give KUDOS !
Proud to be a Datanaut!
Highlighted
Frequent Visitor
## Re: Slicer filter another slicer
I found the problem;
If the slicer 2 (between) for column B (date) is formatted as date (1-1-2018 / 31-12-2018), it will not work.
If the slicer 2 (between) for column B (date) is formatted as decimal (2018 / 2018), it work's.
What to do if I want to filter on date format???
Community Support Team
## Re: Slicer filter another slicer
Create a date table
New table-> enter the following formula
Table = CALENDARAUTO()
leave no relationship between this date table and your table
Create measures
MIN = MIN('Table'[Date])
Max = MAX('Table'[Date])
Measure =
CALCULATE (
COUNT ( Sheet3[index] ),
FILTER ( ALLSELECTED ( Sheet3 ), [columnB] >= [MIN] && [columnB] <= [Max] )
)
Measure 2 =
CALCULATE (
COUNT ( Sheet3[index] ),
FILTER ( ALL ( Sheet3 ), [columnB] <= [Max] && [columnB] >= [MIN] )
)
Best Regards
Maggie
Community Support Team _ Maggie Li
If this post helps, then please consider Accept it as the solution to help the other members find it more quickly.
Community Support Team
## Re: Slicer filter another slicer
in my test,
[Count values filtered by slicer 1 and slicer 2] ---Measure
divided by
[Count Values filtered only by slicer 2] ---------Measure 2
Best Regards
Maggie
Frequent Visitor
## Re: Slicer filter another slicer
Maggie, I'm really impressed, brilliant!! It is just what the doctor ordered! Thanks for your efforts!
Frequent Visitor
## Re: Slicer filter another slicer
Maggie, I'm really impressed, brilliant!! It is just what the doctor ordered! Thanks for your efforts! | 718 | 2,633 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.546875 | 3 | CC-MAIN-2019-18 | latest | en | 0.832285 |
http://question.onlinegdb.com/979/why-is-infinity-infinity-calculated-to-nan | 1,604,046,213,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107909746.93/warc/CC-MAIN-20201030063319-20201030093319-00527.warc.gz | 92,091,123 | 5,875 | # Why is INFINITY - INFINITY calculated to -NAN?
I have a C-function which tests that an x - x expression, where x is a double, is not reduced to 0.
Why, when x is INFINITY, does x - x give the wrong result -NAN (negative) instead of NAN (positive)?
/******************************************************************************************************************************
* Test that the compiler does not optimise x-x to zero. Also test that INF-INF is correctly calculated.
* The calculation expression is regarded highly prone to be reduced to zero by a sloppy compiler.
* Returns 0x1 if successful. Otherwise an even value less than 0xf is returned.
******************************************************************************************************************************/
static unsigned int
infInfSubtraction(void)
{
unsigned int res = 0x0u;
const unsigned long long pattInf = 0x7ff0000000000000uLL;
const unsigned long long pattNan = 0x7ff8000000000000uLL;
const unsigned long long pattZero = 0x0000000000000000uLL;
const double x = *(double*)&pattInf;
const double XsubX = x - x;
if (*(unsigned long long*)&XsubX == pattNan)
{
res = 0x1u; // Correct subtraction INFINITY - INFINITY = NAN
}
else if (*(unsigned long long*)&XsubX == pattZero)
{
res = 0x2u; // Incorrect subtraction INFINITY - INFINITY = 0
}
else
{
res = 0xeu;
}
return res;
} // infInfSubtraction() | 342 | 1,398 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.703125 | 3 | CC-MAIN-2020-45 | latest | en | 0.661325 |
https://iitbrain.com/simple-harmonic-motion/ | 1,726,324,672,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700651579.38/warc/CC-MAIN-20240914125424-20240914155424-00302.warc.gz | 281,223,251 | 8,885 | # 9 - Simple Harmonic Motion Questions Answers
Asked By: JAINIL
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Asked By: SAURABH SHARMA
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The quality factor of a sonometer wire is 2 x 10³. On plucking it makes 240 per second. Calculate the time in which the amplitude decreases to half the initial value.
Asked By: SINOVIYA V K
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Asked By: RISHI
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Joshi sir comment
Asked By: KANDUKURI ASHISH
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Asked By: TUSHAR GUPTA
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Joshi sir comment
small ring is threaded on an inextensible frictionless cord of length 2l.
The ends of the cord are fixed to a horizontal ceiling. In equilibrium, the
ring is at a depth h below the ceiling. Now the ring is pulled aside by a
small distance in the vertical plane containing the cord and released.
Find period of small oscillations of the ring. Acceleration of free fall is g.
Asked By: ABHISHEK KHANDELWAL
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Joshi sir comment
TWO PENDULUM HAVE TIME PERIODS T &5T/4. THEY STARTS SHM AT THE SAME TIME FROM THE MEAN POSITION . WHAT WILL BE THE PHASE DIFFERENCE B/W THEM AFTER D BIGGER PENDULUM COMPLETED ONE OSCILLATn ??
ans 900
Asked By: SARIKA SHARMA
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Joshi sir comment
When bigger pendulum will complete its one oscillation, the smaller one will complete [1+(1/4)] oscillation. so phase difference = 2π*(T/4)/T = π/2
2 comparable masses m1 and m2 r orbiting about their bodycenter o at distance r1 and r2 from their body center respectively with a common period T. the squar of time period ?
Asked By: SHUBHAM VED
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Joshi sir comment
According to the diagram
Gm1m2/(r1+r2)2 = m1r1ω2 = m2r2ω2
compare first part with either second or third part of the given equation for getting ω2 then find T2
Register | 595 | 2,050 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2024-38 | latest | en | 0.85887 |
http://www.apug.org/forums/viewpost.php?p=1568513 | 1,438,613,366,000,000,000 | text/html | crawl-data/CC-MAIN-2015-32/segments/1438042989891.18/warc/CC-MAIN-20150728002309-00100-ip-10-236-191-2.ec2.internal.warc.gz | 291,481,031 | 4,171 | A simple way to calculate exposure compensation is to use a ruler. I keep a small tape measure with me for this purpose.
Examples:
90mm = 3.5"
150mm = 6"
210mm = 8.25"
300mm = 12"
2. Now focus any one of your lenses at infinity It will be it's mm length from the film plane. I use the film plane and the center of the front standard to measure from.
3. In your mind convert the mm focal length to inches.
Round it off to the closest f/number.
In your mind call the resulting number an f/stop.
For example my 210mm lens is 8.25" which is my f/8 lens.
My 90mm lens is 3.5" which is my f/4 lens.
150mm lens is 5.9" which is my f/5.6 lens.
300mm lens is my f/11 lens (close enough to 12")
4. When you are focused for your photograph use the tape measure to measure the distance from the film plane to the front standard reference point.
Examples:
Lets say for example that you are using a 210mm lens and it is focused at 11 inches. 210mm = "f/8" and my "f/8 lens" at 11' is f/11. f/8 to f/11 = One stop bellows compensation.
Fast and accurate. Try it. | 304 | 1,056 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.390625 | 3 | CC-MAIN-2015-32 | latest | en | 0.936696 |
http://michaelashcroft.net/dpwr4/diode-characteristics-graph-7280cf | 1,619,037,657,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618039550330.88/warc/CC-MAIN-20210421191857-20210421221857-00064.warc.gz | 66,919,923 | 8,902 | For forward bias, So, on this graph, we can see the potential difference, or voltage, across the diode on the horizontal axis and the current through the diode on the vertical axis. The current increases slowly in the beginning and then rapidly when the reverse voltage becomes a certain value. Breakdown is the knee of diode characteristics curve. Ideal Diode Characteristics Threshold Voltage. The graph shows the reverse V-I characteristics of the given p-n junction diode. Zener diode source. Below is a graph of the I-V characteristics curve of an ideal diode: Ideal Diode Characteristics Curve. In the next tutorial about diodes, we will look at the small signal diode sometimes called a switching diode which is used in general electronic circuits. A layer of metal is deposited on a thin epitaxial layer of the n-type silicon. What really happens inside the diode during the forward bias ? associated with a diode. In today’s tutorial, we will have a look at the Voltage Current Characteristic of Diode. Unfortunately, actual diode behavior isn't quite ideal. For all the practical purposes, a diode is considered to be an open switch when reverse biased. Input Characteristics: Input impedance = R i = V BE / I B (V CE is constant) 2. As reverse bias voltage is raised depletion region continues to increase in width and no current flows. To know more about diode let us look at on important graph of a diode which is the Current vs Voltage I-V Curve. The straight line on the graph represents the load line and the curve on the graph represents the diode characteristic equation. It can be noted that, initially the current increase very slowly. You can see that when the diode receives forward voltage, it instantly conducts an infinite amount of current which it can supply to a circuit. The VI characteristic of the diode shows the relation between diode current and voltage. Arrange the sliding contact of the rheostat to minimum. (Supervisory Control and Data Acquisition), Programmable Logic Controllers (PLCs): Basics, Types & Applications, Diode: Definition, Symbol, and Types of Diodes, Thermistor: Definition, Uses & How They Work, Half Wave Rectifier Circuit Diagram & Working Principle, Lenz’s Law of Electromagnetic Induction: Definition & Formula. Simulator Procedure (as performed through the Online Labs) Select the characteristics of diode from the drop down list. The first quadrant is the forward biased region. Volt-ampere characteristics of diode in forward bias condition.2. This makes sense as Ohm’s law is only relevant to components at constant temperatures. हिंदी This kind op plots can often be seen in datasheets. The diode equation is plotted on the interactive graph below. The forward characteristics of a diode is non linear. We use semiconductor materials (Si, Ge) to form variety of electronic devices. The graph showing the forward bias voltage and forward current is known as the forward characteristics, and that showing the reverse bias voltage and reverse current is known as the reverse characteristics. A plot onto a lin-log scale as in figure 11 shows more details withing the full current range. Fig. For diodes, only tiny currents of a few microamps (millionths of an amp) flow at low voltages.Putting more than about 1.5 volts across them normally makes them "turn on" allowing current to flow.. That defines how the current flows through the component and how the voltage is measured across it. This article will help to explain the characteristics which make up zener diodes, specifically how the voltage across a zener diode varies with the current flowing through it. N = 1, for Ge Zener Diode Characteristics. Care must be taken when designing circuits containing diodes not to exceed the breakdown voltage. Using Excel, graph the I-V characteristics. Materials Required: Diode Characteristics Kit , Power Supply, Ammeter (0-20mA), Voltmeter (0-20V), Connecting Leads. If a potential difference is applied in the direction with very high resistance, it is said to be reverse bias. To redo the experiment, click on the ‘Reset’ button. The corresponding voltage represents the knee voltage of that diode. Connections are made as per the connection diagram. PN Junction diode characteristics provide us the information about the habitual working of the diode. Select the diode … The diode is 2 terminal semiconductor devices that used to rectify alternating current into the direct current. This depletion region has a predefined width, say W. This width will vary for a Silicon diode and a Germanium diode. Semi-thermal diodes are mainly used to protect other electronic components. The i v characteristic curves which is short for current voltage characteristic curves or simply i v curves of an electrical device or component are a set of graphical curves which are used to define its operation within an electrical circuit. If you can remember this bit, then you can go to the top of the class. The figure depicted under the section Forward Characteristic shows that Forward Voltage and Reverse Voltage are usually plotted on the horizontal line of the graph. We are a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for us to earn fees by linking to Amazon.com and affiliated sites. In reverse biasing P- terminal is connected to negative terminal of the battery and N- terminal to positive terminal of battery. This article will help to explain the characteristics which make up zener diodes, specifically how the voltage across a zener diode varies with the current flowing through it. interface or a boundary between two semiconductor material types This results in lack of charge carriers at the junction and thus the junction is called depletion region. Comments. Forward Voltage represented to the right and Reverse Voltage to the left. A diode is a device that has very low resistance in one direction and a very high resistance in the other direction. Funded by MeitY (Ministry of Electronics & Information Technology), English chung chinngee. The semiconductor diode starts conducting current after exceeding the threshold of the forward voltage value specified by the manufacturer in the data sheet. Understand the basic diode clipping circuits completely. The V-I characteristics of a diode can be forward or reverse. Ideally, diodes will block any and all current flowing the reverse direction, or just act like a short-circuit if current flow is forward. The first graph shows the i v characteristic of a thorlabs sld830s a20 830 nm super luminescent diode sled. VI characteristics of PN junction diode is a curve between the voltage and current through the circuit. Characteristics of LED (Light Emitting Diode) Before connecting an LED is a circuit and start using it, there are few characteristics of LED that are worth knowing (actually, they are very important). Semiconductor Diode – Current-voltage characteristic. The forward and reverse current voltage (IV) characteristics of a diode are generally compared on a single characteristic curve. The characteristics, voltage, and breakdown levels are clearly understood through this graphical representation. All of these pretty graphs are indicating one thing. For a certain value of voltage, it shows a sharp increase. Drawing the transfer characteristics for the circuit becomes easy, if you understand the circuit completely and able to get it's output waveform. It is presented for the visual demonstration of the breakdown region only.) Repeat the process by increasing the forward current in equal steps by changing the rheostat slider. Forward and reverse current values are shown on the vertical axis of the graph. Move the sliding contact of the rheostat to provide a reverse bias voltage.Note the voltmeter and micro ammeter readings. The I-V Characteristics Curve of a zener diode, shown below, is the curve which shows the current-voltage relationship of a zener diode. Note down readings in the observation table. The forward current increases slowly in the beginning and … When we apply voltage across the terminals of PN junction, we call it as diode. It is known as the reverse breakdown voltage. Diode characteristics & Design of Rectifier circuits. Arrange the sliding contact of the rheostat to maximum. A plot onto a lin-lin scale graph is displayed in figure 10. However, with further increase in reverse voltage, the current shows a rapid rise at a certain value. Fig. When reverse voltage is fed to the diode, it conducts no current at all, no matter how great this reverse voltage is. Diode Characteristics by Kenneth A. Kuhn Oct. 3, 2007, rev. Figure 5: Diode package and Symbol Electronics 1 - Diode Characteristics 5. Useful mathematical relations are shown and illustrated with plots. Now, gently move the rheostat contact to provide a positive bias voltage. Developed by Amrita Vishwa Vidyapeetham & CDAC Mumbai. The above graph is the VI characteristics curve of the PN junction diode. Hello, fellows, I hope all of these pretty graphs are indicating that a forward-biased diode is biased. Enter your email below to receive free informative articles on electrical & Electronics engineering and micro ammeter readings DiodeTopics. 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Is 2 terminal semiconductor devices that used to rectify alternating current into the direct current on important graph of through! | 3,780 | 18,827 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.90625 | 3 | CC-MAIN-2021-17 | latest | en | 0.910932 |
http://www.topnotchpapers.com/mathematics-2/ | 1,603,431,084,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107880656.25/warc/CC-MAIN-20201023043931-20201023073931-00542.warc.gz | 175,718,493 | 8,315 | Get 10% Off with
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Avoid the Hustle
# Mathematics
Category: Mathematics
Situation: You have been contracted to locate and describe an important archeological site. After days of searching, you find the site and see that there is a tower on the site. The tower is clearly leaning to one side. The problem is that a gorge full of very dangerous crocodiles separates you from the tower and so you can clearly not cross the gorge.
1. Describe a method to calculate the height of the tower. Include what measurements you will need to take, what instruments you will need, and a diagram.
2. Describe a method to calculate the angle that the tower is leaning? Include what measurements you will need to take, what instruments you will need, and a diagram.
3. Describe a method to calculate the coordinates of the tower. Include what measurements you will need to take, what instruments you will need, and a diagram. | 202 | 944 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.75 | 3 | CC-MAIN-2020-45 | latest | en | 0.934927 |
https://es.mathworks.com/matlabcentral/cody/problems/528-find-the-largest-value-in-the-3d-matrix/solutions/108902 | 1,591,525,273,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590348526471.98/warc/CC-MAIN-20200607075929-20200607105929-00264.warc.gz | 330,414,362 | 15,837 | Cody
# Problem 528. Find the largest value in the 3D matrix
Solution 108902
Submitted on 10 Jul 2012 by Daniel Armyr
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% Test 1 A = 1:9; A=reshape(A,[3 1 3]); y_correct = 9; assert(isequal(islargest(A),y_correct))
2 Pass
%% Test 2 A = 9:17 A=reshape(A,[3 1 3]); y_correct = 17; assert(isequal(islargest(A),y_correct))
A = 9 10 11 12 13 14 15 16 17 | 179 | 521 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.53125 | 3 | CC-MAIN-2020-24 | latest | en | 0.650203 |
https://www.rdsharmasolutions.in/rd-sharma-class-7ex-20-2-chapter-20-mensuration-i-perimeter-and-area-of-rectilinear-figures/ | 1,680,312,105,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949694.55/warc/CC-MAIN-20230401001704-20230401031704-00237.warc.gz | 1,068,542,563 | 44,190 | # RD Sharma Class 7 ex 20.2 Solutions Chapter 20 Mensuration I (Perimeter and Area of Rectilinear Figures)
In this chapter, we provide RD Sharma Class 7 ex 20.2 Solutions Chapter 20 Mensuration I (Perimeter and Area of Rectilinear Figures) for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Class 7 ex 20.2 Solutions Chapter 20 Mensuration I (Perimeter and Area of Rectilinear Figures) Maths pdf, Now you will get step by step solution to each question.
# Mensuration I (Perimeter and Area of Rectilinear Figures) Exercise 20.2
### Question: 1
A rectangular grassy lawn measuring 40 m by 25 m is to be surrounded externally by a path which is 2 m wide. Calculate the cost of leveling the path at the rate of Rs 8.25 per square metre.
### Solution:
We have,
Length AB = 40 m and breadth BC = 25 m
Area of lawn ABCD = 40 m x 25 m = 1000 m2
Length PQ = (40 + 2 + 2 ) m = 44 m
Breadth QR = ( 25 + 2 + 2 ) m = 29 m
Area of PQRS = 44 m x 29 m = 1276 m2
Now, Area of the path = Area of PQRS – Area of the lawn ABCD
= 1276 m2 – 1000 m2 = 276 m2
Rate of leveling the path = Rs. 8.25 per m2
Cost of leveling the path = Rs.( 8.25 x 276) = Rs. 2277
### Question: 2
One metre wide path is built inside a square park of side 30 m along its sides. The remaining part of the park is covered by grass. If the total cost of covering by grass is Rs 1176, find the rate per square metre at which the park is covered by the grass.
### Solution:
We have,
Side of square garden (a) = 30 m
Area of the square garden including the path = a2= (30)2 = 900 m2
From the figure, it can be observed that the side of the square garden, when the path is not included, is 28 m.
Area of the square garden not including the path = (28)2 = 784 m2
Total cost of covering the park with grass = Area of the park covering with green grass x Rate per square metre
1176 = 784 x Rate per square metre
Rate per square metre at which the park is covered with grass = Rs. (1176 ÷ 784 ) = Rs. 1.50
### Question: 3
Through a rectangular field of sides 90 m x 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the field. if the width of the roads is 3 m, find the total area covered by the two roads.
### Solution:
Length of the rectangular sheet = 90 m
Breadth of the rectangular sheet = 60 cm
Area of the rectangular field = 90 m x 60 m = 5400 m2
Area of the road PQRS = 90 m x 3 m = 270 m2
Area of the road ABCD = 60 m x 3 m = 180 m2
Clearly, area of KLMN is common to the two roads.
Thus, area of KLMN = 3 m x 3 m = 9 m2
Hence, Area of the roads = Area (PQRS) + Area (ABCD) – Area (KLMN)
= (270 + 180) m2 – 9 m2 = 441 m2
### Question: 4
from a rectangular sheet of tin, of size 100 cm by 80 cm, are cut four squares of side 10 cm from each corner. Find the area of the remaining sheet.
### Solution:
Length of the rectangular sheet = 100 cm
Breadth of the rectangular sheet = 80 cm
Area of the rectangular sheet of tin = 100 cm x 80 cm
= 8000 c m2
Side of the square at the corner of the sheet = 10 cm
Area of one square at the corner of the sheet = (10 cm)2 = 100 cm2
Area of 4 squares at the corner of the sheet = 4 x 100 cm2 = 400 cm2
Hence, Area of the remaining sheet of tin = Area of the rectangular sheet – Area of the 4 squares
Area of the remaining sheet of tin = (8000 – 400) cm2 = 7600 cm2
### Question: 5
A painting 8 cm long and 5 cm wide is painted on a cardboard such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.
### Solution:
We have, Length of the cardboard = 8 cm and breadth of the cardboard = 5 cm
Area of the cardboard including the margin = 8 cm x 5 cm = 40 c m2
From the figure, it can be observed that,
New length of the painting when the margin is not included = 8 cm – (1.5 cm + 1.5 cm)
= (8 – 3) cm = 5 cm
New breadth of the painting when the margin is not included = 5 cm – (1.5 cm + 1.5 cm)
= (5 – 3) cm = 2 cm
Area of the painting not including the margin = 5 cm x 2 cm = 10 cm2
Hence, Area of the margin = Area of the cardboard including the margin – Area of the painting
= (40 – 10) cm2 = 30 cm2
### Question: 6
Rakesh has a rectangular field of length 80 m and breadth 60 m. In it, he wants to make a garden 10 m long and 4 m broad at one of the corners and at another corner, he wants to grow flowers in two floor-beds each of size 4 m by 1.5 m. In the remaining part of the field, he wants to apply manures. Find the cost of applying the manures at the rate of Rs 300 per area.
### Solution:
Length of the rectangular field = 80 m
Breadth of the rectangular field = 60 m
Area of the rectangular field = 80 m x 60 = 4800 m2
Again, Area of the garden = 10 m x 4 m = 40 m2
Area of one flower bed = 4 m x 1.5 m = 6 m2
Thus, Area of two flower beds = 2 x 6 m2 = 12 m2
Remaining area of the field for applying manure = Area of the rectangular field – (Area of the garden + Area of the two flower beds)
Remaining area of the field for applying manure = 4800 m2 – (40 + 12) m2
= (4800 – 52 ) m2 = 4748 m2
Since 100 m2 = 1 acre → 4748 m2 = 47.48 acres
So, cost of applying manure at the rate of Rs. 300 per are will be Rs. (300 x 47.48) = Rs. 14244
### Question: 7
Each side of a square flower bed is 2 m 80 cm long. It is extended by digging a strip 30 cm wide all around it. Find the area of the enlarged flower bed and also the increase in the area of the flower bed.
### Solution:
We have ,
Side of the flower bed = 2 m 80 cm = 2.80 m [since 100 cm = 1 m ]
Area of the square flower bed = (Side)2 = (2.80 m )2 = 7.84 m2
Side of the flower bed with the digging strip = 2.80 m + 30 cm + 30 cm
= (2.80 + 0.3 + 0.3) m
= 3.4 m
Area of the enlarged flower bed with the digging strip = (Side) 2 = (3.4)2 = 11.56 m2
Thus, Increase in the area of the flower bed = 11.56 m2 – 7.84 m2 = 3.72 m2
### Question: 8
A room 5 m long and 4 m wide is surrounded by a verandah. If the verandah occupies an area of 22 m2 , find the width of the varandah.
### Solution:
Let the width of the verandah be x m.
Length of the room AB = 5 m and BC = 4 m
Area of the room = 5 m x 4 m = 20 m2
Length of the verandah PQ = (5 + x + x) = (5 + 2x) m
Breadth of the verandah QR = ( 4 + x + x) = (4 + 2x) m
Area of verandah PQRS = (5 + 2x) x (4 + 2x) = (4×2 + 18x + 20 ) m2
Area of verandah = Area of PQRS – Area of ABCD
→ 22 = 4x2 + 18x + 20 – 20
22 = 4x2 + 18x
11 = 2x2 + 9x
2x2 + 9x – 11 = 0
2x2 + 11x – 2x – 11 =0
x(2x+11)-1(2x+11)=0
(x- 1)(2x+11)= 0
When x – 1 = 0, x = 1
When 2x + 11 = 0, x = -11/2
The width cannot be a negative value. So, width of the verandah = x = 1 m.
### Question: 9
A square lawn has a 2 m wide path surrounding it. If the area of the path is 136 m2 , find the area of the lawn.
### Solution:
Let ABCD be the square lawn and PQRS be the outer boundary of the square path.
Let side of the lawn AB be x m.
Area of the square lawn = x2
Length PQ = (x m + 2 m + 2 m) = (x + 4) m
Area of PQRS = (x + 4)2 = (x2 + 8x + 16) m2
Now, Area of the path = Area of PQRS – Area of the square lawn
136 = x2 + 8x + 16 – x2
136 = 8x + 16
136 – 16 = 8x
120 = 8x
x = 120/ 8 = 15
Side of the lawn = 15 m Hence, Area of the lawn = (Side)2 = (15 m)2 = 225 m2
### Question: 10
A poster of size 10 cm by 8 cm is pasted on a sheet of cardboard such that there is a margin of width 1.75 cm along each side of the poster. Find (i) the total area of the margin (ii) the cost of the cardboard used at the rate of Re 0.60 per c m2 .
### Solution:
We have,
Length of poster = 10 cm and breadth of poster = 8 cm
Area of the poster = Length x Breadth = 10 cm x 8 cm = 80 cm2
From the figure, it can be observed that,
Length of the cardboard when the margin is included = 10 cm + 1.75 cm + 1.75 cm = 13.5 cm
Breadth of the cardboard when the margin is included = 8 cm + 1.75 cm + 1.75 cm = 11.5 cm
Area of the cardboard = Length x Breadth = 13.5 cm x 11.5 cm = 155.25 c m2
Hence,
(i) Area of the margin = Area of cardboard including the margin – Area of the poster
= 155.25 c m2 – 80 c m2
= 75.25 c m2
(ii) Cost of the cardboard = Area of cardboard x Rate of the cardboard Rs 0.60 per cm2
= Rs. (155.25 x 0.60)
= Rs. 93.15
### Question: 11
A rectangular field is 50 m by 40 m. It has two roads through its centre, running parallel to its sides. The widths of the longer and shorter roads are 1.8 m and 2.5 m respectively. Find the area of the roads and the area of the remaining portion of the field.
### Solution:
Let ABCD be the rectangular field and KLMN and PQRS the two rectangular roads with width 1.8 m and 2.5 m, respectively.
Length of the rectangular field CD = 50 cm and breadth of the rectangular field BC = 40 m
Area of the rectangular field ABCD = 50 m x 40 m = 2000 m2
Area of the road KLMN = 40 m x 2.5 m = 100 m2
Area of the road PQRS = 50 m x 1.8 m = 90 m2
Clearly area of EFGH is common to the two roads.
Thus, Area of EFGH = 2.5 m x 1.8 m = 4.5 m2
Hence, Area of the roads = Area (KLMN) + Area (PQRS) – Area (EFGH)
= (100 m2 + 90 m2) – 4.5 m2
= 185.5 m2
Area of the remaining portion of the field = Area of the rectangular field ABCD – Area of the roads
= (2000 – 185.5) m2
= 1814.5 m2
### Question: 12
There is a rectangular field of size 94 m x 32 m. Three roads each of 2 m width pass through the field such that two roads are parallel to the breadth of the field and the third is parallel to the length. Calculate: (i) area of the field covered by the three roads (ii) area of the field not covered by the roads.
### Solution:
Let ABCD be the rectangular field.
Here, Two roads which are parallel to the breadth of the field KLMN and EFGH with width 2 m each. One road which is parallel to the length of the field PQRS with width 2 m.
Length of the rectangular field AB = 94 m and breadth of the rectangular field BC = 32 m
Area of the rectangular field = Length x Breadth = 94 m x 32 m = 3008 m2
Area of the road KLMN = 32 m x 2 m = 64 m2
Area of the road EFGH = 32 m x 2 m = 64 m2
Area of the road PQRS = 94 m x 2 m = 188 m2
Clearly area of TUVI and WXYZ is common to these three roads.
Thus, Area of TUV1 = 2 m x 2 m = 4 m2
Area of WXYZ = 2 m x 2 m = 4 m2
Hence,
(i) Area of the field covered by the three roads: = Area (KLMN) + Area (EFGH) + Area (PQRS) – {Area (TUVI) + Area (WXYZ)}
= [ 64+ 64 + 188 – (4 + 4 )] m2
= 316 m2 – 8 m2
= 308 m2
(ii) Area of the field not covered by the roads: = Area of the rectangular field ABCD – Area of the field covered by the three roads
= 3008 m2 – 308 m2
= 2700 m2
### Question: 13
A school has a hall which is 22 m long and 15.5 m broad. A carpet is laid inside the hall leaving all around a margin of 75 cm from the walls. Find the area of the carpet and the area of the strip left uncovered. If the width of the carpet is 82 cm, find the cost at the rate of Rs 18 per metre.
### Solution:
We have,
Length of hall PQ = 22 m and breadth of hall QR = 15.5 m
Area of the school hall PQRS = 22 m x 15.5 m = 341 m2
Length of the carpet AB = 22 m – ( 0.75 m + 0.75 m) = 20.5 m [ Since 100 cm = 1 m]
Breadth of the carpet BC = 15.5 m – ( 0.75 m + 0.75 m) = 14 m
Area of the carpet ABCD = 20.5 m x 14 m = 287 m2
Area of the strip = Area of the school hall PQRS – Area of the carpet ABCD
= 341 m2 – 287 m2 = 54 m2
Again, Area of the 1 m length of carpet = 1 m x 0.82 m = 0.82 m2
Thus, Length of the carpet whose area is 287 m2 = 287 m+ 0.82 m2 = 350 m
Cost of the 350 m long carpet = Rs. 18 x 350 = Rs. 6300
### Question: 14
Two cross roads, each of width 5 m, run at right angles through the centre of a rectangular park of length 70 m and breadth 45 m parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of Rs 105 per m2 .
### Solution:
Let ABCD be the rectangular park then EFGH and IJKL the two rectangular roads with width 5 m.
Length of the rectangular park AD = 70 cm
Breadth of the rectangular park CD = 45 m
Area of the rectangular park = Length x Breadth = 70 m x 45 m = 3150 m2
Area of the road EFGH = 70 m x 5 m = 350 m2
Area of the road JKIL = 45 m x 5 m = 225 m2
Clearly area of MNOP is common to the two roads.
Thus, Area of MNOP = 5 m x 5 m = 25 m2
Hence,
Area of the roads = Area (EFGH) + Area (JKIL) – Area (MNOP)
= (350 + 225) m2– 25 m2 = 550 m2
Again, it is given that the cost of constructing the roads = Rs. 105 per m2
Therefore,
Cost of constructing 550 m2 area of the roads = Rs. (105 x 550)
= Rs. 57750.
### Question: 15
The length and breadth of a rectangular park are in the ratio 5: 2. A 2.5 m wide path running all around the outside the park has an area 305 m2 . Find the dimensions of the park.
### Solution:
We have,
Area of path = 305 m2
Let the length of the park be 5x m and the breadth of the park be 2x m
Thus,
Area of the rectangular park = (5x) x (2x) = 10x2 m2
Width of the path = 2.5 m
Outer length PQ = 5x m + 2.5 m + 2.5 m = (5x + 5) m
Outer breadth QR = 2x + 2.5 m + 2.5 m = (2x + 5) m
Area of PQRS = (5x + 5) m x (2x + 5) m = (10x2 + 25x + 10x + 25) m2= (10x2 + 35x + 25) m2
Area of the path = [(10x2 + 35x + 25) – 10x2] m2
→ 305 = 35x + 25
→ 305 – 25 = 35x
→ 280 = 35x
→ x = 280 + 35 = 8
Therefore,
Length of the park = 5x = 5 x 8 = 40 m
Breadth of the park = 2x = 2 x 8 = 16 m
### Question: 16
A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m2 , find the area of the lawn.
### Solution:
Let the side of the lawn be x m.
Given that width of the path = 2.5 m
Side of the lawn including the path = (x + 2.5 + 2.5) m = (x + 5 ) m
So, area of lawn = (Area of the lawn including the path) – (Area of the path)
We know that the area of a square = (Side)2
Area of lawn (x2) = (x + 5)2 – 165
→ x2 = (X2 + 10X + 25) – 165
→ 165 = 10x + 25
→ 165 – 25 =10x
→ 140 = 10x
Therefore x = 140 / 10 = 14
Thus the side of the lawn = 14 m
Hence,
The area of the lawn = (14 m) 2 = 196 m2
All Chapter RD Sharma Solutions For Class 7 Maths
I think you got complete solutions for this chapter. If You have any queries regarding this chapter, please comment on the below section our subject teacher will answer you. We tried our best to give complete solutions so you got good | 4,891 | 14,339 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.78125 | 5 | CC-MAIN-2023-14 | longest | en | 0.91216 |
https://psichologyanswers.com/library/lecture/read/140589-what-is-difference-between-stochastic-and-deterministic | 1,656,993,438,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656104512702.80/warc/CC-MAIN-20220705022909-20220705052909-00339.warc.gz | 544,382,988 | 7,728 | # What is difference between stochastic and deterministic?
## What is difference between stochastic and deterministic?
In deterministic models, the output of the model is fully determined by the parameter values and the initial conditions initial conditions. Stochastic models possess some inherent randomness. The same set of parameter values and initial conditions will lead to an ensemble of different outputs.
## Why is Monte Carlo simulation used?
Monte Carlo simulations are used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables. ... A Monte Carlo simulation can be used to tackle a range of problems in virtually every field such as finance, engineering, supply chain, and science.27 dic. 2020
## What is stochastic event?
Stochastic social science theory is similar to systems theory in that events are interactions of systems, although with a marked emphasis on unconscious processes. The event creates its own conditions of possibility, rendering it unpredictable if simply for the number of variables involved.
## What are the applications of stochastic process?
The focus will especially be on applications of stochastic processes as key technologies in various research areas, such as Markov chains, renewal theory, control theory, nonlinear theory, queuing theory, risk theory, communication theory engineering and traffic engineering.
## Where is stochastic processes used?
Some examples of stochastic processes used in Machine Learning are: Poisson processes: for dealing with waiting times and queues. Random Walk and Brownian motion processes: used in algorithmic trading. Markov decision processes: commonly used in Computational Biology and Reinforcement Learning.
## What is the difference between time series and stochastic process?
A time series is a sequence of actual, fixed, values, like: 61, 63, 58, 64, 56, 48, 39, 42, ... A stochastic process is a sequence of random variables that have some kind of specified correlation or other distributional relationship between them.
## Is Evolution a stochastic?
Reason: Evolution is a stochastic process based on chance events in nature and chance mutation in the organisms.
## Why do we need stochastic process?
In medical statistics, you need stochastic processes to calculate how to adjust significance levels when stopping a clinical trial early. In fact, the whole area of monitoring clinical trials as emerging evidence points to one hypothesis or another, is based on the theory of stochastic processes.3 nov. 2010
## What is the difference between random variable and random process?
A random process is a collection of random variables usually indexed by time. ... Note that for any time t1, the random variable N(t1) is a discrete random variable. Thus, N(t) is a discrete-valued random process. However, since t can take any real value between 9 and 16, N(t) is a continuous-time random process.
## What is stochastic signals?
Stochastic signal is used to describe a non deterministic signal, i.e. a signal with some kind of uncertainity. A random signal is, by definition, a stochastic signal with whole uncertainty, i.e. with autocorrelation function with an impulse at the origin and power spectrum completely flat.1 dic. 2013
## What is a stochastic process in time series?
The stochastic process is a model for the analysis of time series. ... The stochastic process is considered to generate the infinite collection (called the ensemble) of all possible time series that might have been observed. Every member of the ensemble is a possible realization of the stochastic process.
## What is the difference between probabilistic and stochastic?
As adjectives the difference between probabilistic and stochastic. is that probabilistic is (mathematics) of, pertaining to or derived using probability while stochastic is random, randomly determined, relating to stochastics.
## What is deterministic time series?
The distinction between a deterministic and stochastic trend has important implications for the long-term behavior of a process: Time series with a deterministic trend always revert to the trend in the long run (the effects of shocks are eventually eliminated). Forecast intervals have constant width.
## What is meant by random process?
A random process is a time-varying function that assigns the outcome of a random experiment to each time instant: X(t). ... If one scans all possible outcomes of the underlying random experiment, we shall get an ensemble of signals.
## What are the two types of random variable?
A random variable, usually written X, is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types of random variables, discrete and continuous.
## How many classifications of random processes are there?
Next, the four basic types of random processes are summarized, depending on whether and the random variables are continuous or discrete.
## When can a random process is said to be an ergodic process?
A random process is said to be ergodic if the time averages of the process tend to the appropriate ensemble averages. This definition implies that with probability 1, any ensemble average of {X(t)} can be determined from a single sample function of {X(t)}. | 1,013 | 5,335 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2022-27 | latest | en | 0.905697 |
https://www.varsitytutors.com/psat_math-help/plane-geometry/geometry/pentagons | 1,582,784,750,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875146647.82/warc/CC-MAIN-20200227033058-20200227063058-00116.warc.gz | 896,411,209 | 45,555 | # PSAT Math : Pentagons
## Example Questions
### Example Question #1 : Pentagons
What is the measure, in degrees, of one interior angle of a regular pentagon?
108
180
72
120
144
108
Explanation:
The formula for the sum of the interior angles of any regular polygon is as follows:
where is equal to the number of sides of the regular polygon.
Therefore, the sum of the interior angles for a regular pentagon is:
To find the measure of one interior angle of a regular pentagon, simply divide by the number of sides (or number of interior angles):
The measure of one interior angle of a regular pentagon is 108 degrees.
### Example Question #2 : Pentagons
Refer to the above figure, which shows Square and regular Pentagon .
Evaluate .
Explanation:
is one of two acute angles of isosceles right triangle , so .
To find we examine .
is an angle of a regular pentagon and has measure .
Also, since, in , sides , by the Isosceles Triangle Theorem,
Since the angles of a triangle must total in measure, | 249 | 1,024 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.953125 | 4 | CC-MAIN-2020-10 | latest | en | 0.820991 |
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## Question 837
### Question
MCQ▾
The figure is ACDF made up of three rectangles. The area of each rectangles is given here. The length of DF is 14 cm. find the length of EF.
### Choices
Choice (4)Response
a.
9.50 cm
b.
9.52 cm
c.
9.00 cm
d.
9.34 cm
## Question 838
MCQ▾
### Choices
Choice (4)Response
a.
8
b.
7
c.
3
d.
None of the above
## Question 839
Appeared in Year: 2019
### Question
MCQ▾
Which of the following Venn diagrams best represents the relationship amongst, “Birds, Cats and Pigeons” ?
### Choices
Choice (4)Response
a.
b.
c.
d.
## Question 840
Appeared in Year: 2019
### Question
MCQ▾
Find the weight of
### Choices
Choice (4)Response
a.
480 g
b.
700 g
c.
500 g
d.
420 g
## Question 841
Appeared in Year: 2019
### Question
MCQ▾
Which of the following alphabet is fourth to the right of ninth element from the right end in the given arrangement?
### Choices
Choice (4)Response
a.
R
b.
L
c.
X
d.
I
## Question 842
Appeared in Year: 2019
### Question
MCQ▾
n a garden, there are 403354 plants in 329 rows. If each row has the same number of plants then how many plants are there in 115 rows?
### Choices
Choice (4)Response
a.
104099
b.
140990
c.
149090
d.
149900 | 495 | 1,692 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.015625 | 3 | CC-MAIN-2021-17 | latest | en | 0.743969 |
https://wwaf.ca/personal-values-oyuyw/f71395-what-is-set-in-math | 1,624,526,556,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488552937.93/warc/CC-MAIN-20210624075940-20210624105940-00553.warc.gz | 546,986,789 | 16,384 | First we specify a common property among \"things\" (we define this word later) and then we gather up all the \"things\" that have this common property. And we have checked every element of both sets, so: Yes, they are equal! We can also define a set by its properties, such as {x|x>0} which means "the set of all x's, such that x is greater than 0", see Set-Builder Notation to learn more. {{courseNav.course.topics.length}} chapters | {1, 2, 3} is a proper subset of {1, 2, 3, 4} because the element 4 is not in the first set. Well, that part comes next. Finite sets are also known as countable sets as they can be counted. Those books could be a set written as: Since all items in set B are also in another set, set B is called a subset. - Lesson for Kids, The Algebra of Sets: Properties & Laws of Set Theory, Complement of a Set in Math: Definition & Examples, Venn Diagrams: Subset, Disjoint, Overlap, Intersection & Union, What is a Text Feature? Find the intersection of the sets C and D. What does the intersection represent? A is the set whose members are the first four positive whole numbers, B = {..., â8, â6, â4, â2, 0, 2, 4, 6, 8, ...}. The language of set theory can be used to … What does the intersection represent? c. Set-builder notation: Set 1 and set 4 can be written as { x / x is a letter of the modern English alphabet} and { x / x is a type of sausage} { x / x is a letter of the modern English alphabet} is read, " The set of all x such that x is a letter in the modern English alphabet. Some other examples of the empty set are the set of countries south of the south pole. first two years of college and save thousands off your degree. If so, then you are going to enjoy working with sets! This little piece at the end is there to make sure that A is not a proper subset of itself: we say that B must have at least one extra element. They are inside the green circle. Just remember how Billy wanted the entire Mysteries of Michael series next time you're having trouble with sets! Billy has a friend named Sue who likes Mysteries of Michael, too. For the three sets A, B, and C, of pets owned by three people, find the following: The union represents the sports that either Aaron or Bryce plays (or both). Its notation is ∅ or { }. credit-by-exam regardless of age or education level. Finite sets are the sets having a finite/countable number of members. Elements are the objects contained in a set. This is known as a set. Don’t worry, we won’t do a lot of maths here as we will focus on practical aspects that we will use when writing T-SQL queries. "But wait!" - Definition & Examples, Over 83,000 lessons in all major subjects, {{courseNav.course.mDynamicIntFields.lessonCount}}, What is a Carroll Diagram? Two sets are equal if and only if they have precisely the same elements. A finite set has finite order (or cardinality). Notice how the first example has the "..." (three dots together). But remember, that doesn't matter, we only look at the elements in A. 1. Select a subject to preview related courses: If you put her books together with Billy's books, that would be called a union. In the diagram, you can see how to write that B is a subset of A using the subset symbol. Sometimes a collection … You don't write anything twice if it's in both sets, just one time. In math, the letters R, Q, N, and Z refer, respectively, to real numbers, rational numbers, natural numbers, and integers. We can come up with all different types of sets. At the start we used the word "things" in quotes. These objects are sometimes called elements or members of the set. . 1 is in A, and 1 is in B as well. You can test out of the To reduce a fracture, that is, to bring the bones back into a normal position or alignment. The union represents the courses that either Cynthia or Damon (or both) plan to take. shown and explained . Another subset is {3, 4} or even another is {1}, etc. But what is a set? For finite sets the order (or cardinality) is the number of elements. Or we can say that A is not a subset of B by A B ("A is not a subset of B"). But sometimes the "..." can be used in the middle to save writing long lists: In this case it is a finite set (there are only 26 letters, right?). A non-e… Why or why not? There are sets of clothes, sets of baseball cards, sets of dishes, sets of numbers and many other kinds of sets. Then the union of A with the intersection of B and C is the set of elements in set A or in the intersection of B and C: Did you know… We have over 220 college What is a set? The process will run out of elements to list if the elements of this set have a finite number of members. This symbol looks like an upside-down U! Her set would be written like this: Get access risk-free for 30 days, Find {R}'. - Definition & Examples, Basic Algebra: Rules, Equations & Examples, What are Natural Numbers? A union contains all items in either set. No, not the order of the elements. Graph Theory, Abstract Algebra, Real Analysis, Complex Analysis, Linear Algebra, Number Theory, and the list goes on. Sets may be thought of as a mathematical way to represent collections or groups of objects. Visit the Math for Kids page to learn more. An infinite set has infinite order (or cardinality). The empty set is a subset of every set, including the empty set itself. . Prove E_1 \cup (E_2 \cup E_3) = E_2 \cup (E_1 \cup E_3) b. And 3, And 4. Example. How many boxes are empty?? Human visual inspection of solder joints on printed circuit boards can be very subjective. Who says we can't do so with numbers? A set is flashcard set{{course.flashcardSetCoun > 1 ? Example: {1,2,3,4} is the same set as {3,1,4,2}. Going back to our definition of subsets, if every element in the empty set is also in A, then the empty set is a subset of A. Find the intersection of the sets A and B. Already registered? A set is defined as an unordered collection of distinct elements of the same type where type is defined by the writer of the set. Prove (E_1 \cup E_2) = (E_2 \cup E_1) b. In the diagram, you can see how to write the intersection of A and B using the intersections symbol. All correct mathematics can be spoken in English. A Set is an unordered collection of objects, known as elements or members of the set. Billy happens to have Cow, Key, and Fish. Show that if absolute value of A = absolute value of S, then both A and S are infinite. Instead of math with numbers, we will now think about math with "things". For example, thenatural numbers are identified with the finite ordinals, soN=ω. So, where two sets cross each other, there is also an intersection! Aaron plays the sports in the set A = { football, baseball, tennis } and Bryce plays the sports in the set B = { basketball, football, soccer, rugby }. Note that 2 is in B, but 2 is not in A. Find the union of the sets C and D. What does the union represent? In the following examples, students will apply their knowledge on sets, unions, and intersections to answer the questions and describe the meaning of the results. The order of the items does NOT matter. - Definition & Example, What is a Column Graph? Should I Major in Math? 's' : ''}}. {{courseNav.course.mDynamicIntFields.lessonCount}} lessons It is a subset of itself! Well, we can't check every element in these sets, because they have an infinite number of elements. So, Hound is not in the intersection since only Sue owns it. Zero. The elementary set is the empty set. The three dots ... are called an ellipsis, and mean "continue on". - Definition & Examples, What is a Class Interval? Also, notice curly brackets at each end. But what is a set? succeed. A set may be defined by a membership rule (formula) or by listing its members within braces. Study.com has thousands of articles about every The integers are the set of whole numbers, both pos- In fact, forget you even know what a number is. As an example, think of the set of piano keys on a guitar. Now as a word of warning, sets, by themselves, seem pretty pointless. If possible, identify the great bound (GLB) and the least upper bound (LUB). What does the union represent? To learn more, visit our Earning Credit Page. When a set is part of another set it is called a subset. Now, at first glance they may not seem equal, so we may have to examine them closely! - Definition & Example, Frequency Histogram: Definition & Examples, Definition of an Ogive Graph in Statistics, Ratios Lesson for Kids: Definition & Examples, Biological and Biomedical This is the notation for the two previous examples: {socks, shoes, watches, shirts, ...} Aaron and Bryce were discussing the sports that they play. We write B ⊆ A By definition, the empty set( { } or ∅ ) is a subset of every set… The concept of sets is used for the foundation of various topics in mathematics. It takes an introduction to logic to understand this, but this statement is one that is "vacuously" or "trivially" true. Synonyms for Set (math) in Free Thesaurus. Set definition In mathematics, we define set theory is a branch of mathematics and more particularly mathematical logic that studies collections of objects we refer to as sets. It is a set with no elements. It is written like this: You can remember union because the symbol for union is a U, the first letter of union. As a member, you'll also get unlimited access to over 83,000 What is a set? Let A be a set. We simply list each element (or "member") separated by a comma, and then put some curly brackets around the whole thing: The curly brackets { } are sometimes called "set brackets" or "braces". Lets get started! So the answer to the posed question is a resounding yes. 2. For example: Are all sets that I just randomly banged on my keyboard to produce. lessons in math, English, science, history, and more. Is the empty set a subset of A? So what does this have to do with mathematics? This set includes index, middle, ring, and pinky. © copyright 2003-2021 Study.com. What Is a Data Set? set: a collection of elements: A = {3,7,9,14}, B = {9,14,28} A ∩ B: intersection: objects that belong to set A and set B: A ∩ B = {9,14} A ∪ B: union: objects that belong to set A or set B: A ∪ B = {3,7,9,14,28} A ⊆ B: subset: A is a subset of B. set A is included in set B. The union of set A with the intersection of B and C. The union of A, B, and C is all the elements which appear in at least one of the sets. Alright, let's review what we've learned. 3 common methods used for representing set: 1. Set (mathematics) From Wikipedia, the free encyclopedia A set in mathematics is a collection of well defined and distinct objects, considered as an object in its own right. When we define a set, all we have to specify is a common characteristic. First we specify a common property among "things" (we define this word later) and then we gather up all the "things" that have this common property. To learn sets we often talk about the collection of objects, such as a set of vowels, set of negative numbers, a group of friends, a list of fruits, a bunch of keys, etc. . Enrolling in a course lets you earn progress by passing quizzes and exams. We can list each element (or "member") of a … What is Bar Notation in Math? Two sets are equal if they have precisely the same members. We start with the closed interval [0, 1] and remove the open interval (\frac{1}{3}, \frac{2}{3. (Cantor's naive definition) • Examples: – Vowels in the English alphabet V = { a, e, i, o, u } – First seven prime numbers. They both contain 2. A set is a collection of things, usually numbers. Sets are one of the most fundamental concepts in mathematics. Set-builder is an important concept in set notation. . Every object in a set is unique. It doesn't matter where each member appears, so long as it is there. Prove (E_1 \cap E_2) = (E_2 \cap E_1) Problem 2 a. In mathematics, a set is a well-defined collection of distinct elements or members. If U=\left \{ ...,-3,-2,-1,0,1,2,3,.. \right \} is the universal set and R=\left \{ ...,-3,-1,1,3,... \right \}. Identify all the sets to which 3.1214122144 belongs. Is every element of A in A? Examples of finite sets: Set symbols of set theory and probability with name and definition: set, subset, union, intersection, element, cardinality, empty set, natural/real/complex number set A readiness to perceive or respond in some way; an attitude that facilitates or predetermines an outcome, for example, prejudice or bigotry as a set to respond negatively, independently of the merits of the stimulus. When we talk about proper subsets, we take out the line underneath and so it becomes A B or if we want to say the opposite, A B. When talking about sets, it is fairly standard to use Capital Letters to represent the set, and lowercase letters to represent an element in that set. If the sum of 3 non-zero distinct real numbers a, b and c is 2 , and the two sets {a, b, c} and {1/a, 1/b, 1/c} are the same, what is the value of a^2 +b^2 +c^2 ? Antonyms for Set (math). A subset of this is {1, 2, 3}. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The concept of sets is an essential foundation for various other topics in mathematics. So it is just things grouped together with a certain property in common. When we define a set, if we take pieces of that set, we can form what is called a subset. So that means the first example continues on ... for infinity. There were 5 books in the set: Michael and the Lost Key, Michael and the Hound, Michael and the Big Fish, Michael's Lost Cow and Michael's Bike. The set of integers Z may be definedas the set of equivalence classes of pairs of natural numbers underthe equivalence relation (n,m)≡(n′,m′) if and only ifn+m′=m+n′. They are all in set A. Try refreshing the page, or contact customer support. All rights reserved. There are sets of clothes, sets of baseball cards, sets of dishes, sets of numbers, and many other kinds of sets. That's all the elements of A, and every single one is in B, so we're done. A set may be defined by a common property amongst the objects. By pairing off members of the two sets, we can see that every member of A is also a member of B, but not every member of B is a member of A: A is a subset of B, but B is not a subset of A. Prove E_1 \cap (E_2 \cap E_3) =. {x: x^2 greaterthan 4} b) Assume the following sequenc, The Cantor set, named after the German mathematician Georg Cantor (1845-1918), is constructed as follows. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal numberof a set. So let's go back to our definition of subsets. - Definition & Examples, What are Whole Numbers? - Definition & Example, How to Make a Frequency Distribution Table, What is a Frequency Distribution Table? Everything that is relevant to our question. To unlock this lesson you must be a Study.com Member. Not one. To write the set in math terms you would write: A set is usually named with a capital letter. Get the unbiased info you need to find the right school. Create your account. credit by exam that is accepted by over 1,500 colleges and universities. Let's check. Oddly enough, we can say with sets that some infinities are larger than others, but this is a more advanced topic in sets. Services. List all of the elements of each set using the listing method. Example: {10, 20, 30, 40} has an order of 4. A is a subset of B if and only if every element of A is in B. But it's only when we apply sets in different situations do they become the powerful building block of mathematics that they are. And the equals sign (=) is used to show equality, so we write: They both contain exactly the members 1, 2 and 3. The whole set of The Mysteries of Michael contains Key, Hound, Fish, Cow, and Bike. She has 3 books also. So let's use this definition in some examples. When we say order in sets we mean the size of the set. If 250 of them play in the jazz band, and 130 play in both, how many of the. The only problem with this definition is that we do not yet have a formal definition of the integers. In this case, the set is named A. Notice that when A is a proper subset of B then it is also a subset of B. you say, "There are no piano keys on a guitar!". 3. An empty set or null set or void sethas no elements. Math Symbols: Specialized Set Notations (N, Z, Q, R) . But what if we have no elements? I'm sure you could come up with at least a hundred. Of 375 musicians at a high school, some play only in the jazz band, some play only for the marching band, and some do both. But there is one thing that all of these share in common: Sets. Plus, get practice tests, quizzes, and personalized coaching to help you In naive set theory, a set is a collection of objects (called members or elements) that is regarded as being a single object. Cynthia and Damon are planning their class schedules. We can see that 1 A, but 5 A. You never know when set notation is going to pop up. {1, 2, 3} is a subset of {1, 2, 3}, but is not a proper subset of {1, 2, 3}. These unique features make Virtual Nerd a viable alternative to private tutoring. (OK, there isn't really an infinite amount of things you could wear, but I'm not entirely sure about that! If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button. The set containing no elements is called the empty set (or null set) and is denoted by { } or ∅. imaginable degree, area of {index, middle, ring, pinky}. An introduction of sets and its definition in mathematics. Well, simply put, it's a collection. Every mathematical object may be viewed as a set. An error occurred trying to load this video. Set of even numbers: {..., â4, â2, 0, 2, 4, ...}, And in complex analysis, you guessed it, the universal set is the. She has over 10 years of teaching experience at high school and university level. Equal Sets. Kathryn earned her Ph.D. in Mathematics from UW-Milwaukee in 2019. I'm sure you could come up with at least a hundred. 3. Note the commas separates each item in the set. For example, the set E E of positive even integers is the set Let A be a set and S a proper subset of A. If we look at the defintion of subsets and let our mind wander a bit, we come to a weird conclusion. The intersection of A and C are the elements which appear in both A and C. We may describe a set by a defining … A data set is a collection of numbers or values that relate to a particular subject. The objects in the set are called its elements. This doesn't seem very proper, does it? Forget everything you know about numbers. By identifying every natural number n with theequivalence class of the pair (n,0), one may extend naturally theoperations of sum and product of natural numbers to Z (seeEnderton (1977) for details, and Levy (1979) for a differ… Not sure what college you want to attend yet? Usually, you'll see it when you learn about solving inequalities, because for some reason saying "x < 3" isn't good enough, so instead they'll want you to phrase the answer as "the solution set is { x | x is a real number and x < 3 }".How this adds anything to the student's understanding, I don't know. Summary: A set is a collection of objects that have something in common or follow a rule. So that means that A is a subset of A. just create an account. 2. For example, the items you wear: hat, shirt, jacket, pants, and so on. Show Video Lesson Try the free Mathway calculator and problem solver below to practice various math topics. As we learn all about sets, we'll look for things in common and sometimes things that are different. Thus, the set A ∪ B—read “A union B” or “the union of A and B”—is defined as the set that consists of all elements belonging to either set A or set B (or both). But {1, 6} is not a subset, since it has an element (6) which is not in the parent set. They all have the same thing in common, Michael has a mystery to solve in all of them! Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. And if something is not in a set use . A set is a collection of items that have something in common. X … Earn Transferable Credit & Get your Degree, Universal Set in Math: Definition, Example & Symbol, The Empty Set in Math: Definition & Symbol, What is a Venn Diagram? The union of A and B is the set of elements in either set A or set B or both. And we can have sets of numbers that have no common property, they are just defined that way. He only owns 3 of the 5, but he wants all 5. - Definition & Examples, Common Core Math Grade 8 - Functions: Standards, High School Algebra II: Tutoring Solution, Contemporary Math Syllabus Resource & Lesson Plans, College Algebra Syllabus Resource & Lesson Plans, College Mathematics Syllabus Resource & Lesson Plans, College Precalculus Syllabus Resource & Lesson Plans, Calculus Syllabus Resource & Lesson Plans, Business Math Curriculum Resource & Lesson Plans, Algebra I Curriculum Resource & Lesson Plans, Algebra II Curriculum Resource & Lesson Plans, Common Core Math Grade 7 - Ratios & Proportional Relationships: Standards, Common Core Math Grade 6 - Ratios & Proportional Relationships: Standards, MEGA Middle School Mathematics: Practice & Study Guide, MEGA Elementary Education Mathematics Subtest: Practice & Study Guide. Find the union of the sets A and B. For infinite sets, all we can say is that the order is infinite. Anyone can earn So we need to get an idea of what the elements look like in each, and then compare them. Math can get amazingly complicated quite fast. Let’s just review some fundamentals of this theory: 1. They are Cow, Bike, and Hound. Elements of a set are either in a set or not in a set. So let's just say it is infinite for this example.). Definition: Set B is a subset of a set A if and only if every object of B is also an object of A. Billy wanted the whole set of The Mysteries of Michael. Do you like solving puzzles and gathering information? All other trademarks and copyrights are the property of their respective owners. When two roads cross each other, there is an intersection. To indicate that an object x is a member of a set A one writes x ∊ A, while x ∉ A indicates that x is not a member of A. Also, when we say an element a is in a set A, we use the symbol to show it. Set theory not only is involved in many areas of mathematics but has important applications in other fields as well, e.g., computer technology and atomic and nuclear physics. - Quiz & Self-Assessment Test, Universities with Master's Degrees in Math: How to Choose, Learn Math in the Blogosphere: 10 Top Math Blogs, White House Announces New Math and Science Achievement Campaign, Register for the 2010 American Math Challenge, Tau Day Generates Controversy Among Math Scholars, Power Systems Engineer: Job Description & Salary, SAP Project Manager: Job Description, Salary & Responsibilities, Be a Military Communications Analyst Education and Career Roadmap, Become a Personal Image Consultant Career Roadmap, Working with Numbers for Elementary School, Representing Numbers for Elementary School, Fraction Operations for Elementary School, GED Math: Quantitative, Arithmetic & Algebraic Problem Solving, Prentice Hall Algebra 2: Online Textbook Help, NY Regents Exam - Integrated Algebra: Tutoring Solution, Increasing Function: Definition & Example, Aphorism in Literature: Definition & Examples, Quiz & Worksheet - Factoring a Perfect Cube, Quiz & Worksheet - Inverse Tangent Function, Quiz & Worksheet - Working with Exponent Properties, High School Algebra - Decimals and Fractions: Help and Review, High School Algebra - Percent Notation: Help and Review, High School Algebra - Real Numbers: Help and Review, High School Algebra - Exponential Expressions & Exponents: Help & Review, High School Algebra - Radical Expressions: Help and Review, California Sexual Harassment Refresher Course: Supervisors, California Sexual Harassment Refresher Course: Employees. 2. Do you think he will get the other 2 books? A good way to think about it is: we can't find any elements in the empty set that aren't in A, so it must be that all elements in the empty set are in A. We have a set A. set (set), 1. set, in mathematics, collection of entities, called elements of the set, that may be real objects or conceptual entities. The only book that both Billy and Sue own is Cow. We call this the universal set. The set definition above is spoken “The set of twice n where n is an integer”. So far so good. To make it easy, how about calling the books: Key, Hound, Fish, Cow, and Bike. The intersection is empty and represents the fact that Cynthia and Damon have no common courses. and career path that can help you find the school that's right for you. But in Calculus (also known as real analysis), the universal set is almost always the real numbers. Since only Sue owns it elements are in a collection of numbers have... How about calling the books: Key, Hound is not in the intersection of a and B using intersections. ( E_2 \cap E_1 ) problem 2 a the listing method enrolling in a set a can... Show that if absolute value of a using the subset symbol serves their needs ) problem 2.. Words 2 ) listing ( roster ) method 3 ) Set-builder notation either or., over 83,000 lessons in all of these share in common, how about calling books. System, users are free to take just one time ) is the same elements keys on a.! Seem pretty pointless 20, 30, 40 } has an order of.! Same elements for infinity billy happens to have Cow, Key,,! Cs M. Hauskrecht set • Definition: a set we say that a is a collection well-defined! Of two sets are one of the integers non-linear system, users are free to take at first glance what is set in math. Empty and represents the sports that they play glance they may not equal. You earn progress by passing quizzes and exams set has finite order ( or ). Of Ten boxes, five contain pencils, four contain pens, so. Absolute value of a set is a well-defined collection of numbers or values relate... Over 83,000 lessons in all major subjects, { { courseNav.course.mDynamicIntFields.lessonCount } }, What is called subset. Or alignment representing set: 1 we only look at the elements of using... Know when set notation is going to enjoy working with sets Sue likes. And only if every element of a = absolute value of s, both... And pinky Damon have no common courses not change from person to person n't define it any than. Think about math with things '': you can see how to write intersection. Of Designating sets example 1 ) a description in words 2 ) listing ( roster ) method 3 ) notation... Try the free Mathway calculator and problem solver below to practice various math.... See that 1 a, we 'll look for things in common has a mystery to solve all. ( or cardinality ) is the number of members and pinky contained in a set be!, shirt, jacket, pants, and Bike 's a collection of items that something... Easy, how many of the integers circuit boards can be represented by various methods { { }... Of thinking of different things, I 'm still not sure What college you want to yet! Formula ) or by listing its members within braces proper subset of a set is named a as number is. To specify is a Class Interval employed to denote the union of the he wanted the whole of. We mean the size of the integers are the elements of each set using the listing method,. A Class Interval mystery to solve in all of them play in the definition. What the elements of a set may be defined by a common property, they are equal if have... On a guitar! { 3,1,4,2 } experience at high school and university level elements to list if elements. You will find in some Examples is going to enjoy working with!... Are n't any elements in a, and the list goes on so weird about the empty?... Test scores of each set using the subset symbol put, it 's in both a and B we done... If you like this: you can see how to write the of. The powerful building block of mathematics that they play if every element of both sets, so long as is! Change from person to person billy has a friend named Sue who likes Mysteries of Michael next! ( LUB ) commas separates each item in the jazz band, and Bike may be viewed as collection. One of the Mysteries of Michael equal if and only if every of. 'M not entirely sure about that every single one is in a set days, one... Rules, Equations & Examples, Basic Algebra: Rules, Equations & Examples, over 83,000 lessons all. Theory the universal set is a subset of B what is set in math idea of What elements..., at first glance they may not seem equal, so we need to an! Back to our Definition of subsets be very subjective 2, 3.!, forget you even know What a number is used to indicate that objects. To the posed question is a subset of B then it is infinite resounding yes, just football •:! The answer to the posed question is a Data set is a branch mathematical. The three dots... are called curly brackets owns 3 of the set in terms. Certain property in common then compare them this: what is set in math can remember union the! Theory: 1 in the diagram, you can see that 1 a, and 130 play in both.. The material best serves their needs one thing that all of these share in common, Michael a. Change from person to person items you wear: hat, shirt, jacket pants! The universal set is a subset of a and C are the elements are in book that both aaron Bryce! - Definition & Examples, What is a subset of a = absolute value of a and are. Theory - Operations on sets: What is a subset of every set including! Elements are the objects in the intersection represent just review some fundamentals of set! And many other kinds of sets this Definition in some references, it could be any.... Have to specify is a Column graph are one of the empty set are called its.... By passing quizzes and exams not seem equal, so we 're done we define a,. Ordinals, soN=ω up with all different types of sets lesson Try the free Mathway calculator problem. Just create an account E_3 ) = ( E_2 \cup E_3 ) = E_2 E_3! What a number is 3 } to do with mathematics other kinds of sets s proper. We may have to specify is a subset of every set, if take. For the foundation of various topics in mathematics whole set of twice n where n is an unordered of! Amount of things, usually numbers we apply sets in different situations do they become powerful. Of that set, all we can have sets of baseball cards, sets of or... Elements are the set are the objects contained in a to list the. Mystery to solve in all of them, 40 } has an order 4... Button, too each, and Fish we 're done also an intersection is empty and represents the that... Groups of objects, known as real Analysis ), 1 hat, shirt, jacket, what is set in math! N, Z, Q, R ) of s, then you are going to pop up about! E_2 ) = E_2 \cup ( E_1 \cup ( E_1 \cap ( E_2 \cup ( E_2 \cup E_3 B. Symbol ∪ is employed to denote the union of the Mysteries of Michael, too of... '' ( three dots... are called curly brackets, all we have checked every element of sets. 20, 30, 40 } has an order of 4 to a particular subject in each and... Free to take whatever path through the material best serves their needs } or even another is { }. X … a set is all the elements of the Mysteries of Michael between them belong to a Course..., ring, and Bike 1 is in B as well to with. Written between them belong to a particular subject a capital letter a Interval... Of clothes, sets of baseball cards, sets of numbers and many other of. The commas separates each item in the diagram, you can see how to a! Methods used for the foundation of various topics in mathematics, a set is part of another it! Thought of as a word of warning, sets of numbers and many other kinds sets... You are going to enjoy working with sets your degree for Kids Page to more! The books: Key, Hound, Fish, Cow, and pinky a capital letter the real numbers in! Set theory is simply the study of integers to add this lesson you must be Study.com! Note that 2 is in B as well mean continue on '' Basic Algebra Rules!, then both a and B weird about the empty set are the set of the sets and! Enrolling in a pencils, four contain pens, and the list on... ) is the same thing in common: sets as elements or members of what is set in math sets C D.! Out of the 5, but 5 a visit the math for Kids to. Their respective owners notice that when a set is a subset of B then it is.! Tests, quizzes, and pinky, but I 'm sure you could wear, but I sure. Another is { 1, 2, 3 } that when a set is named a all sets... Union because the symbol to show it, where two sets cross each other, there one... Unique features make Virtual Nerd a viable alternative to private tutoring subset is { 1,! What are whole numbers, we will now think about math with things '' in quotes an!
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The ring signature used in cryptonote https://cryptonote.org/whitepaper.pdf looks like:
KEYGEN: $P_i=x_i*G, I_i=x_i*H(P_i)$
SIGN: as signer $j$; random $s_i, w_i$
(I relabeled $q_i$ as $s_i$ to be more standard, and relabeled the signer s as signer $j$)
IF $i=j$ THEN $L_i=s_i*G$ ELSE $L_i=s_i*G+w_i*P_i$
IF $i=j$ THEN $R_i=s_i*H(P_i)$ ELSE $R_i=s_i*H(P_i)+w_i*I_j$
$c=h(m,L_1,...,L_n,R_1,...,R_n)$
IF $i=j$ THEN $c_i=c-sum_{i!=j}(c_i)$ ELSE $c_i=w_i$
IF $i=j$ THEN $r_i=w_i-c_i*x_i$ ELSE $r_i=w_i$
$\sigma = (m,I_j,c_1,...,c_n,r_1,...,r_n)$
VERIFY:
$$L_i'=r_i*G+c_i*P_i R_i'=r_i*H(P_i)+c_i*I_j sum_{1..n}( c_j ) =? h(m,L_1',...,L_n',R_1',...,R_n')$$
LINK: reject duplicate $I_j$ values.
where $H(.)$ is a hash2curve function (taking a value in Zn and deterministically mapping it to a curve point), and $h(.)$ is a hash function with a hash output size very close to n the order of the curve, ie $h(.)=SHA256(.) mod n$.
Towards finding a more compact ring signature I'd been trying to find a way to make c_i into a CPRNG generated sequence as they are basically arbitrary, though they must be bound to the rest of the signature (non-malleable) so that you can compute at most n-1 existential signature forgeries without knowing any private keys.
I found this paper "1-out-of-n Signatures from a Variety of Keys" by Abe, Ohkubo and Suzuki http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.363.3431&rep=rep1&type=pdf section 5.1 shows a way to do it. I show here how that is compatible with crypto note:
KEYGEN: $P_i=x_i*G, I_i=x_i*H(P_i)$
SIGN: as signer $j$; $\alpha = random, \forall_{i!=j} s_i = random$
$$c_{j+1} = h(P_1,...,P_n,\alpha*G,\alpha*H(P_j)) c_{j+2} = h(P_1,...,P_n,s_{j+1}*G+c_{j+1}*P_{j+1},s_{j+1}*H(P_{j+1})+c_{j+1}*I_j) ... c_j = h(P_1,...,P_n,s_{j-1}*G+c_{j-1}*P_{j-1},s_{j-1}*H(P_{j-1})+c_{j-1}*I_j)$$
so that defines $c_1,...,c_n$ with $j$ values taken mod $l$ some number of signers. Next find the $s_j$ value:
Now $\alpha*G = s_j*G+c_j*P_j so \alpha = s_j+c_j*x_j so s_j = \alpha - c_j*x_j mod n$.
Similarly $\alpha*H(P_j) = s_j*H(P_j)+c_j*I_j$ so $\alpha$ works there too.
$\sigma = (m,I_j,c_1,s_1,...,s_n)$
VERIFY:
$$\forall_{i=1..n} compute e_i=s_i*G+c_i*P_i and E_i=s_i*H(P_i)+c_i*I_j and c_{i+1}=h(P_1,...,P_n,e_i,E_i) check c_{n+1}=c_1$$
LINK: reject duplicate $I_j$ values.
This alternate linkable ring signature tends to 1/2 the size of the crypto note ring signature as the signature is 3+n values vs 2+2n values. | 957 | 2,489 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.109375 | 3 | CC-MAIN-2018-51 | latest | en | 0.644204 |
https://www.thestudentroom.co.uk/showthread.php?t=7457194 | 1,716,445,166,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058611.55/warc/CC-MAIN-20240523050122-20240523080122-00419.warc.gz | 900,755,353 | 45,961 | # Isaac Physics Working with Terms-HELP ME
Yh I cant do this q for some reason, i have the correct answer but it wants it in a special form.
Q:
https://isaacphysics.org/questions/binomial_series5?board=192ea231-defd-4eda-ba8f-1dffb3abccdb&stage=a_level
Just search Working with Terms Isaac Physics if u cant use the link.
I got (n-r)/(r+1) * (x^(r+1)/(2*x^r)). However, when you submit this you get this message:
This is the correct answer for the ratio of the (r+1)th power of x to the rth power of x in the expansion, however what is the power of x in the first term of the expansion?
Original post by Hihobyu
Yh I cant do this q for some reason, i have the correct answer but it wants it in a special form.
Q:
https://isaacphysics.org/questions/binomial_series5?board=192ea231-defd-4eda-ba8f-1dffb3abccdb&stage=a_level
Just search Working with Terms Isaac Physics if u cant use the link.
I got (n-r)/(r+1) * (x^(r+1)/(2*x^r)). However, when you submit this you get this message:
This is the correct answer for the ratio of the (r+1)th power of x to the rth power of x in the expansion, however what is the power of x in the first term of the expansion?
Looks like a simple indexing problem (though your x's could be simplified).
First term is 1
Second term is nx/2
....
so just be clear about which terms the r+1th and rth terms refer to.
(edited 2 months ago)
Original post by mqb2766
Looks like a simple indexing problem (though your x's could be simplified).
First term is 1
Second term is nx/2
....
so just be clear about which terms the r+1th and rth terms refer to.
sorry i dont understnad what your saying - i used binomial expansion to get the first term? why is it 1. and for the second, it isnt nx/2, as it is from one to another, x, increases in quantities of 1 from one term to another
Original post by Hihobyu
sorry i dont understnad what your saying - i used binomial expansion to get the first term? why is it 1. and for the second, it isnt nx/2, as it is from one to another, x, increases in quantities of 1 from one term to another
Edited - Probably best to consider the case for (1+x)^2 = 1+2x+x^2 and consider the ratio of the first to zeroth term so r=0. We know the ans is 2x/1=2x, so using your expression
(n-r)/(r+1) x = (2-0)/(1) x = 2x
so correct. They want an offset of 1 in r so it would be considering the r to the r-1 where r starts from 0 or if you assume the first term is (r=) 1, then it gives the same result. However, its not the usual definition/consistent with nCr.
(edited 1 month ago)
Original post by mqb2766
Edited - Probably best to consider the case for (1+x)^2 = 1+2x+x^2 and consider the ratio of the first to zeroth term so r=0. We know the ans is 2x/1=2x, so using your expression
(n-r)/(r+1) x = (2-0)/(1) x = 2x
so correct. They want an offset of 1 in r so it would be considering the r to the r-1 where r starts from 0 or if you assume the first term is (r=) 1, then it gives the same result. However, its not the usual definition/consistent with nCr.
so i use r-1/r ? sorry i dont underdstnad what your saying
Original post by Hihobyu
so i use r-1/r ? sorry i dont underdstnad what your saying
The error message in the OP is that theyre making a distinction between the index associated with the power of x, so
1*x^0 + n*x^1 + n(n-1)/2*x^2 + ...
and the index of the term in the series expansion. The first term (r=1) has zeroth power. The second term (r=2) has power 1. The third term (r=3) has power 2, .... So the rth term in the series is
nC(r-1) x^(r-1)
(edited 1 month ago)
Original post by mqb2766
The error message in the OP is that theyre making a distinction between the index associated with the power of x, so
1*x^0 + n*x^1 + n(n-1)/2*x^2 + ...
and the index of the term in the series expansion. The first term (r=1) has zeroth power. The second term (r=2) has power 1. The third term (r=3) has power 2, .... So the rth term in the series is
nC(r-1) x^(r-1)
Sorry I’m still confused. So the Rth term is in fact the r-1th term?
Original post by Hihobyu
Sorry I’m still confused. So the Rth term is in fact the r-1th term?
Pretty much - imho a dodgy question. So just adjust the terms of the numerator and denominator in the OP to account for an offset by 1. Not sure what youve typed in here.
Note as in #1, the x terms simplify.
(edited 1 month ago)
Original post by mqb2766
Pretty much - imho a dodgy question. So just adjust the terms of the numerator and denominator in the OP to account for an offset by 1. Not sure what youve typed in here.
Note as in #1, the x terms simplify.
Like this?
Original post by Hihobyu
Like this?
You may be guessing? You want to consider ratio of the pair of terms r-1 and r (using the x power indices), rather than r and r+1 as in the OP. You should be able to work how the numerator and denominator are adjusted, so are the terms larger or smaller?
Also, last time, what is x^(r+1)/x^r (simplified)?
(edited 1 month ago) | 1,447 | 4,935 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.09375 | 3 | CC-MAIN-2024-22 | latest | en | 0.928613 |
https://www.coursehero.com/file/5941805/Class-Notes-11-x-12/ | 1,513,180,814,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948527279.33/warc/CC-MAIN-20171213143307-20171213163307-00019.warc.gz | 727,262,371 | 73,233 | Class_Notes_1.1_x_1.2
# Class_Notes_1.1_x_1.2 - squares so that they exactly fill...
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Guiding Problem #1 Plot the 3 points A(-2, 1), B(2, 3), and C(3, 1). (a) Draw the triangle ABC. (b) Find the length of each side of the triangle. (c) Verify that the triangle is a right triangle. (d) Find the perimeter of the triangle. (e) Find the area of the triangle. (f) Find the midpoints of the three sides. Reflective Questions What does the Pythagorean Theorem say? How does this relate to the distance formula? Why is it true? “Understanding Why” Activity Do paper and scissors “proofs” of the Pythagorean Theorem. Use scissors to cut out and rearrange the small
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Unformatted text preview: squares so that they exactly fill the big square in each figure. Guiding Problem #2 Use the following information to draw a graph of a geometric figure. (a) In quadrant 1, the points satisfy the equation y = -3 x + 3. (b) The graph is symmetric with respect to the x-axis, the y-axis, and the origin. List all x-intercepts and all y-intercepts on the graph. What shape did you draw? Follow-up Practice Look at the graphs of y = x 4- 1 x = y 2- 4 x 2 + y 2 = 25 (a) Find the intercepts from the graph and from the equation. (b) Test each equation for symmetry....
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Ask a homework question - tutors are online | 472 | 1,753 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.0625 | 4 | CC-MAIN-2017-51 | latest | en | 0.84604 |
http://mathhelpforum.com/calculus/130225-horizontal-asymptote-problem-print.html | 1,508,767,200,000,000,000 | text/html | crawl-data/CC-MAIN-2017-43/segments/1508187826049.46/warc/CC-MAIN-20171023130351-20171023150351-00408.warc.gz | 221,262,060 | 3,179 | # Horizontal Asymptote Problem
• Feb 22nd 2010, 06:26 PM
bobsanchez
Horizontal Asymptote Problem
I understand fairly well how to find horizontal asymptotes, but this function is really messing with me. I don't think it has any, but I want to be sure. If it does have some, I'm sure I'm missing some basic step. Anyways, here it is:
f(x) = 3x^3 - x +1 / x+3
What would be the horizontal asymptote(s) if they even exist for this function?
• Feb 22nd 2010, 06:39 PM
drumist
Is this the correct function?
$f(x) = \frac{3x^3-x+1}{x+3}$
To determine the end-behavior (i.e., what happens at the extreme "left" and extreme "right" of the graph), you can take the largest power term from each the numerator and denominator, and calculate the limit like this:
$\lim_{x\to+\infty} \frac{3x^3-x+1}{x+3} = \lim_{x\to+\infty} \frac{3x^3}{x} = \lim_{x\to+\infty} 3x^2 = +\infty$
You should also check the left side if it's not a simple rational function. In this case it's not necessary, but just to be thorough:
$\lim_{x\to-\infty} \frac{3x^3-x+1}{x+3} = \lim_{x\to-\infty} \frac{3x^3}{x} = \lim_{x\to-\infty} 3x^2 = +\infty$
Since the end-behavior goes to infinity on both sides, there aren't any horizontal asymptotes.
• Feb 22nd 2010, 06:42 PM
bobsanchez
Quote:
Originally Posted by drumist
Is this the correct function?
$f(x) = \frac{3x^3-x+1}{x+3}$
To determine the end-behavior (i.e., what happens at the extreme "left" and extreme "right" of the graph), you can take the largest power term from each the numerator and denominator, and calculate the limit like this:
$\lim_{x\to+\infty} \frac{3x^3-x+1}{x+3} = \lim_{x\to+\infty} \frac{3x^3}{x} = \lim_{x\to+\infty} 3x^2 = +\infty$
You should also check the left side if it's not a simple rational function. In this case it's not necessary, but just to be thorough:
$\lim_{x\to-\infty} \frac{3x^3-x+1}{x+3} = \lim_{x\to-\infty} \frac{3x^3}{x} = \lim_{x\to-\infty} 3x^2 = +\infty$
Since the end-behavior goes to infinity on both sides, there aren't any horizontal asymptotes.
Okay, I thought so, just wanted to make sure I wasn't missing something obvious.
Thanks for the help, I appreciate it. :) | 728 | 2,155 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.21875 | 4 | CC-MAIN-2017-43 | longest | en | 0.784958 |
https://www.ukessays.com/essays/biology/solve-the-system-of-non-linear-equations-biology-essay.php | 1,493,613,749,000,000,000 | text/html | crawl-data/CC-MAIN-2017-17/segments/1492917127681.50/warc/CC-MAIN-20170423031207-00465-ip-10-145-167-34.ec2.internal.warc.gz | 1,007,091,352 | 13,759 | # Solve The System Of Non Linear Equations Biology Essay
Published: Last Edited:
This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.
In numerical analysis, Newtons method also known as the Newton-Raphson method, named after Isaac Newton and Joseph Raphson, is perhaps the best known method for finding successively better approximations to the zeroes (or roots) of a real-valued function. Newton's method can often converge remarkably quickly, especially if the iteration begins "sufficiently near" the desired root. Just how near "sufficiently near" needs to be, and just how quickly "remarkably quickly" can be, depends on the problem (detailed below). Unfortunately, when iteration begins far from the desired root, Newton's method can fail to converge with little warning; thus, implementations often include a routine that attempts to detect and overcome possible convergence failures.
Given a function Æ’(x) and its derivative Æ’ '(x), we begin with a first guess x0. Provided the function is reasonably well-behaved a better approximation x1 is
The process is repeated until a sufficiently accurate value is reached:
An important and somewhat surprising application is Newton-Raphson division, which can be used to quickly find the reciprocal of a number using only multiplication and subtraction.
## Description
The function Æ’ is shown in blue and the tangent line is in red. We see that xn+1 is a better approximation than xn for the root x of the function f.
The idea of the method is as follows: one starts with an initial guess which is reasonably close to the true root, then the function is approximated by its tangent line (which can be computed using the tools of calculus), and one computes the x-intercept of this tangent line (which is easily done with elementary algebra). This x-intercept will typically be a better approximation to the function's root than the original guess, and the method can be iterated.
Suppose ƒ : [a, b] → R is a differentiable function defined on the interval [a, b] with values in the real numbers R. The formula for converging on the root can be easily derived. Suppose we have some current approximation xn. Then we can derive the formula for a better approximation, xn+1 by referring to the diagram on the right. We know from the definition of the derivative at a given point that it is the slope of a tangent at that point.
That is
Here, f ' denotes the derivative of the function f. Then by simple algebra we can derive
We start the process off with some arbitrary initial value x0. (The closer to the zero, the better. But, in the absence of any intuition about where the zero might lie, a "guess and check" method might narrow the possibilities to a reasonably small interval by appealing to the intermediate value theorem.) The method will usually converge, provided this initial guess is close enough to the unknown zero, and that ƒ'(x0) ≠0. Furthermore, for a zero of multiplicity 1, the convergence is at least quadratic (see rate of convergence) in a neighbourhood of the zero, which intuitively means that the number of correct digits roughly at least doubles in every step. More details can be found in the analysis section below.
## Application to minimization and maximization problems
Newton's method can also be used to find a minimum or maximum of a function. The derivative is zero at a minimum or maximum, so minima and maxima can be found by applying Newton's method to the derivative. The iteration becomes:
## SOLUTION OF THE EQUATIONS IS AS FOLLOWS-
Given:
x²+y=11….(1), y²+x=7….(2)
Rewriting the given equation as follows
x²+y-11=0 and x+y²-7=0
let f(x,y) = x²+y-11 and g(x,y)= x+y²-7
so fx=2x, fy=1, gx=1 and gy=2y
Let the initial approximation to a root of given system be (2.9, 1.9) i.e.
x0=2.9 and y0=1.9 (Clearly x=3 & y=2 satisfies the given non-linear system)
from (1) y = 11- x²
put value of y in (2)
(11-x²)² + x = 7
121-(x²)²-22x² +x =7
(x²)²-22x²+x = -114
By hit and trial method
Put x=3
81-198+3 = -114
84 - 198 = -114
-114 = -114
So x=3
Put value of x=3 in (1)
9+y = 11
Y = 2
ITERATION 1:
Since x0=2.9 y=1.9
f(x0,y0) = (2.9)² + 1.9 -11
= 8.41 +1.9 -11
= 10.31 - 11
f(x0,y0) = -0.69
g(x0,y0) = 2.9 + (1.9)²-7
= 2.9 + 3.61 -7
= 6.51 - 7
g(x0,y0) = -0.49
fx(x0,y0) = 2*x0
= 2*2.9
= 5.8
fy = 1
gx = 1
gy = 2*y
= 2*1.9
= 3.8
D = fx(x0,y0)* gy(x0,y0) - fy(x0,y0)* gx(x0,y0)
= 5.8*3.8 - 1*1
= 22.04 - 1
= 21.04
Now find the values of h and k
h = 1 -f(x0,y0) fy(x0,y0)
D -g(x0,y0) gy(x0,y0)
= 1 -(-0.69) 1
21.04 -(-0.49) 3.8
= 1/21.04 (0.69* 3.8 - 0.49)
= (2.622-0.49)/21.04
= 2.312/21.04
= 0.101
K = 1 -fx(x0,y0) -f(x0,y0)
D -gx(x0,y0) -g(x0,y0)
= 1 5.8 -(-0.69)
D 1 -(-0.49)
= 1/21.04 (5.8 *0.49 - 0.69)
= 1/21.04 (2.842 - 0.69)
= 2.152/21.04
= 0.102
So the first approximation as a root is given by
x1 = x0 + h
= 2.9 + 0.101
= 3.001
Y1 = y0 + k
= 1.9 + 0.102
= 2.002
ITERATION 2
Since x1 = 3.001
And y1 = 2.002
f(x1,y1) = (3.001)² + 2.002 -11
= 9.006 +2.002 -11
= 11.008-11
= 0.008
g(x1,y1) = 3.001 + (2.002)² - 7
= 3.001 + 4.008 -7
= 7.009 - 7
= 0.009
fx(x1,y1) = 2*x1 = 2*3.001
= 6.002
fy(x1,y1) = 1
gx(x1,y1) = 1
gy(x1,y1) = 2*y1 = 2*2.002
= 4.004
D = fx(x1,y1)* gy(x1,y1) - fy(x1,y1)* gx(x1,y1)
= 6.002*4.004 - 1*1
= 24.032 - 1
= 23.032
h = 1 -f(x1,y1) fy(x1,y1)
D -g(x1,y1) gy(x1,y1)
= 1 -0.008 1
23.032 -0.009 4.004
= 1/23.032 (-0.008*4.004-(-0.009))
= 1/23.032(-0.032+0.009)
= -0.023/23.032
= -0.000998
K = 1 -fx(x1,y1) -f(x1,y1)
D -gx(x1,y1) -g(x1,y1)
= 1 6.002 -0.008
23.032 1 -0.009
= 1/23.032(6.002*(-0.009) - (-0.008))
= 1/23.032(-0.054+0.008)
= -0.046/23.032
= -0.00199
So the second approximation as a root is given by
x2 = x1 + h = 3.001+ (-0.000998)
= 3.00002
y2 = y1 + k = 2.002 + (-0.00199)
= 2.00001
From 1a nd 2nd iteration it is clear that there is no change in the successive approximation to the root upto first two decimal places. So the root of given system is given by
X = 3.00
And y = 2.00(upto two decimal places)
Hence equation is solved.
## Analysis
Suppose that the function ƒ has a zero at α, i.e., ƒ(α) = 0.
If f is continuously differentiable and its derivative is nonzero at α, then there exists a neighborhood of α such that for all starting values x0 in that neighborhood, the sequence {xn} will converge to α.
If the function is continuously differentiable and its derivative is not 0 at α and it has a second derivative at α then the convergence is quadratic or faster. If the second derivative is not 0 at α then the convergence is merely quadratic. If the third derivative exists and is bounded in a neighborhood of α, then:
where
If the derivative is 0 at α, then the convergence is usually only linear. Specifically, if Æ’ is twice continuously differentiable, Æ’ '(α) = 0 and Æ’ ''(α) ≠0, then there exists a neighborhood of α such that for all starting values x0 in that neighborhood, the sequence of iterates converges linearly, with rate log10 2 (Süli & Mayers, Exercise 1.6). Alternatively if Æ’ '(α) = 0 and Æ’ '(x) ≠0 for x ≠0, x in a neighborhood U of α, α being a zero of multiplicity r, and if Æ’ ∈ Cr(U) then there exists a neighborhood of α such that for all starting values x0 in that neighborhood, the sequence of iterates converges linearly.
However, even linear convergence is not guaranteed in pathological situations.
In practice these results are local and the neighborhood of convergence are not known a priori, but there are also some results on global convergence, for instance, given a right neighborhood U+ of α, if f is twice differentiable in U+ and if , in U+, then, for each x0 in U+ the sequence xk is monotonically decreasing to α.
## Proof of quadratic convergence for Newton's iterative method
According to TaylorHYPERLINK "http://en.wikipedia.org/wiki/Taylor's_theorem"'HYPERLINK "http://en.wikipedia.org/wiki/Taylor's_theorem"sHYPERLINK "http://en.wikipedia.org/wiki/Taylor's_theorem" theorem, any function f(x) which has a continuous second derivative can be represented by an expansion about a point that is close to a root of f(x). Suppose this root is Then the expansion of f(α) about xn is:
## (1)
where the Lagrange form of the Taylor series expansion remainder is
where ξn is in between xn and
Since is the root, (1) becomes:
## (2)
Dividing equation (2) by and rearranging gives
## (3)
Remembering that xn+1 is defined by
one finds that
That is,
## (5)
Taking absolute value of both sides gives
## (6)
Equation (6) shows that the rate of convergence is quadratic if following conditions are satisfied:
sufficiently close to the root
The term sufficiently close in this context means the following:
(a) Taylor approximation is accurate enough such that we can ignore higher order terms,
(b)
(c)
Finally, (7) can be expressed in the following way:
where M is the supremum of the variable coefficient of on the interval defined in the condition 1, that is:
The initial point has to be chosen such that conditions 1 through 3 are satisfied, where the third condition requires that
## Nonlinear systems of equations
One may use Newton's method also to solve systems of k (non-linear) equations, which amounts to finding the zeroes of continuously differentiable functions F : Rk → Rk. In the formulation given above, one then has to left multiply with the inverse of the k-by-k Jacobian matrix JF(xn) instead of dividing by f '(xn). Rather than actually computing the inverse of this matrix, one can save time by solving the system of linear equations
for the unknown xn+1 − xn. Again, this method only works if the initial value x0 is close enough to the true zero. Typically, a well-behaved region is located first with some other method and Newton's method is then used to "polish" a root which is already known approximately.
## Nonlinear equations in a Banach space
Another generalization is the Newton's method to find a root of a function F defined in a Banach space. In this case the formulation is
where is the Fréchet derivative applied at the point Xn. One needs the Fréchet derivative to be boundedly invertible at each Xn in order for the method to be applicable. A condition for existence of and convergence to a root is given by the Newton-Kantorovich theorem. | 3,199 | 10,426 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2017-17 | latest | en | 0.94848 |
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1 Statistical Maps: Best Practice Why draw a map? Maps are an excellent means of presenting statistical information. Not only are they visually attractive, they also: make it easier for users to relate data to location; and help users to identify geographic trends in the data, in a way which would be difficult using a chart or a table. When a map is less suitable Maps are for demonstration (i.e. display) purposes rather than as a source of reference material. They are excellent for showing geographic patterns but are poor for providing precise values with which users can do their own calculations. Such reference material is much better presented in a table (although you could do both a map and a table if required). Types of statistical map There are three main types of statistical map: Choropleth (colour shaded) maps. This is the most common type, and is especially appropriate for showing standardised data such as rates, densities or percentages. A different colour is used for each of a number of bands, allowing users to identify which areas have high, low or middling values. Proportional symbol maps. These use symbols that are proportional in size to the values they represent, such that the biggest symbol will fall in the area with the highest value. Symbols can include circles, bars, or objects indicating what is being measured. This type of map is better for count data. Dot maps. Individual events or groups of events are marked with a dot, allowing users to geographic patterns such as clusters. The most famous use of this technique was by Dr John Snow, who mapped cholera deaths in an outbreak in London in 1854 and was able to show that they were concentrated around a particular water pump.* * Note that dot maps are not generally suitable for Neighbourhood Statistics data see note later. 1
2 This document considers some general good practice in mapping, and some particulars relating to each of the main types of map. Design principles for all maps Clear title (supported by relevant footnotes if appropriate). Indicate the geographic areas used. Indicate the time period(s) both of the data and of the currency of the geographic boundaries (eg 1990 data presented to 2005 boundaries). Include a key to explain what is meant by the colours on the map, the different sizes of symbol etc. Ensure the ranges on the key do not overlap (So don t use 0-5 and 5-10, for example. Otherwise, how would you show an area with value 5? Better ranges would be 0-4 and 5-9). Indicate data source. Textual summary. The key message(s) of your map should also be summarised in words. Your map should be as large as is necessary to show everything clearly. If you are showing data for smaller areas (such as local authorities) you will probably need a larger map than if you were showing region-level data. You may not wish to label each of the areas shown on the map as this might make the page too cluttered and obscure the statistics. However, as an alternative, you may wish to consider publishing a separate reference map containing just area names and boundaries. Choropleth (colour shaded) maps Choose an appropriate number of classes for your data, and also how to divide them. There are a number of possibilities here. For example: o Equal ranges eg classes take values 0-9, etc. o Percentiles. For example, you could use quintiles whereby the bottom 20% of values fall into one class, the next 20% into another etc. o Polarised ranges, whereby categories cluster towards one (or both) ends of the range of values. For example, if you were highlighting deprivation you might decide that the most prosperous 80% of areas are one shade, but the most deprived areas are highlighted by having different shades for the worst 20%, 10% and 5% of areas. o Natural breaks in the data. If data values tend to cluster into distinct groups, you may wish to adjust the ranges such that all those areas falling into a particular group are shaded in the same colour. Most Geographic Information Systems (GIS) offer a range of ways of doing this. Make sure that the one you choose is appropriate to the data you are showing. Note that having too many classes is bad practice as it makes the map too complicated and colours harder to pick out. Five or six classes is usually ample. Appropriate choice of colours. There are a number of aspects to this too: o It is best to have a gradation of colour along a range, rather than having completely unrelated colours for each category. Note however that it is not 2
3 easy for readers to distinguish more than four shades of one colour. o In general, use light colours for low values and darker ones for high values. Also be aware that in some cases certain colours may have natural associations - for example, red and debt. o White is generally used to indicate areas where data are missing or unavailable. It is therefore inadvisable to use white to represent any part of your range of actual values. Proportional symbol maps This sort of map is good for showing big and small, and giving an idea of where events are concentrated, but is less effective for comparison across a range. This is because it is very difficult for the human eye to interpret the relative size of two-dimensional objects (although a good key will help here). It is important that the symbols you use are genuinely proportional to the value being mapped. A value twice as high needs a symbol with double the surface area, not a doubling of each dimension. Consider that if you double both the height and width of anything, the area becomes four times larger, which would give a very misleading visual impression. Dot maps Geographic Information Systems (GIS) offer aggregated dot maps, which take the aggregate statistic for a given area and randomly scatter an appropriate number of dots across it. It would be possible to do this with Neighbourhood Statistics data, but you should not do so. Such maps are misleading and are not true dot maps. A true dot map will only mark data at the exact location of occurrence. Neighbourhood Statistics datasets do not generally provide locations of individual data events, but instead aggregate them into standard areas (such as Super Output Areas and local authorities). This means that you will not be able to produce dot maps of Neighbourhood Statistics data. You may, however, produce dot maps based on the datasets containing grid references for the location of services such as doctors, dentists and schools. Map dangers Although maps are a valuable means of data presentation, there are some pitfalls in the way they may be interpreted: They may exaggerate the difference between areas. Suppose the dividing line between two classes on a choropleth map is 20%. Then suppose, for the variable in question, that area A has a rate of 19.95% and B has one of 20.05%. This is very little difference in reality, but their different colouring on the map might be interpreted otherwise. This is a reason why it is often useful to make the data available in a table too. As different geographic areas vary greatly in both size and population, presenting maps of count data (either choropleth or graduated symbol) can be misleading. The human mind will often associate dark colours or large symbols with a high likelihood of the variable in question, but they may have more to do with the simple 3
4 fact that the area has a large overall population. For this reason it is often more appropriate to map using standardised data such as rates or percentages. The Tyne & Wear example on page 7 is a good example. The fact that some geographic units are much larger than others means their colours can dominate a choropleth map. For example, rural local authorities are often large, whereas urban authorities tend to have a much smaller area. This means that if one end of a range of values is common in rural areas, and the other in urban, the colour of the typically rural characteristic might misleadingly dominate the map. Although this is inevitable you can reduce the effect by choosing nondominant colours, and your textual summary might usefully highlight the urbanrural distinction. Be aware of how the areas you use can substantially alter the visual impact of a map. For example, a neighbourhood with a particularly high crime rate might really stand out on a map if the boundaries approximate to those of the neighbourhood. However, if the boundaries used happened to combine the neighbourhood with an adjacent area of particularly low crime, the presence of the hotspot could be lost. Don t assume that the default values suggested by your GIS (for choropleth map ranges, for example) are necessarily the best. Always examine the data and its context to see if it could be presented in a better way, and adjust the settings on your GIS accordingly. Mapping Examples Choropleth map Source: Regional Trends 2004, Office for National Statistics 4
5 Population mapping using proportional symbols Source: Extract from an Office for National Statistics map Presenting count data: Choropleth vs proportional symbol The map extracts overleaf show the amount of spending by overseas residents in The graduated symbol map is preferable as it overcomes the distortion caused by large blocks of colour (eg Northern Ireland, and the Highland area of Scotland). Note too that the first map has a geographically incorrect title (Northern Ireland and the Isle of Man are not part of Great Britain). In addition the note below the key is poorly worded - how should the user interpret the shading on Shetland and Eilean Siar (Western Isles)? 5
6 Choropleth Proportional symbol 6
7 Choropleth maps: comparison of count data vs rate data: Tyne & Wear, Population by Ward, 2001 Source: Office for National Statistics The left hand map uses count data i.e. the number of people in each ward. However, the wards with larger populations are often larger in extent so no settlement pattern is obvious. Much better is the right hand map showing population density from this the settlement pattern is obvious, with towns such as Newcastle, Gateshead, South Shields and Sunderland clearly visible. Selective use of naming on a choropleth map Source: Jason Dykes, 2005 (gicentre, City University, London), with kind permission. 7
8 You wouldn t normally provide labels for areas on a choropleth map they generally add clutter and make the map harder to read. In this case, however, appropriate use of selected labels (and values) provides useful extra information drawing the reader s attention to those wards with a particular crime problem. 8
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More information | 8,422 | 39,617 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3 | 3 | CC-MAIN-2018-47 | latest | en | 0.945972 |
http://slideplayer.com/slide/4159803/ | 1,524,470,846,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945855.61/warc/CC-MAIN-20180423070455-20180423090455-00622.warc.gz | 293,658,780 | 18,546 | # Simulation Software Integration Connect Velocity and Acceleration to Mathematical Models.
## Presentation on theme: "Simulation Software Integration Connect Velocity and Acceleration to Mathematical Models."— Presentation transcript:
Simulation Software Integration Connect Velocity and Acceleration to Mathematical Models
Graphing Motion Introduce Linear Functions Unit with Linear Regression activity collecting walking distance data. Review this with students using Moving Man Applet with velocity only. http://phet.colorado.edu/en/simu lation/moving-man
Student Review What equation can you write to model a man starting a 0 with a velocity of 2m/s? – Let’s use x to represent time and y to represent his position. – Based on this equation, how long should it take for him to hit the wall? – Verify this with the simulation software. What is the equation if he is at 6 feet and walks at speed of.25m/s? – How long should it take him to hit the wall? – Were you correct? What if he is at -4 feet and walks at a speed of.25m/s. Create your own example. – How long do you expect it to take him? Were you correct?
Add Acceleration So far we have been walking at a constant rate with a straight line graph or linear function. What do you predict the line will look like if the walker accelerates as he is walking. (Gets consistently faster) Lets try, position the walker at -10, with velocity of 1 m/s and acceleration of 1m/s2. Review the playback. What was happening to his speed during over time? What did the graph of velocity vs time look line? How did his speed increase? After 2 seconds, what was his speed? Is the velocity curve linear?
Compare Distance over time Linear and with Acceleration Now look at the graph of distance vs time. – Is this still linear? – Can you use your equation to calculate distance like you did before? – Why or Why not? Looking for students to recognize that the since the rate is changing that the line is no longer linear.
Download ppt "Simulation Software Integration Connect Velocity and Acceleration to Mathematical Models."
Similar presentations | 436 | 2,097 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2018-17 | latest | en | 0.943642 |
https://tbc-python.fossee.in/convert-notebook/A_textbook_of_Internal_Combustion_Engines_by_R._K._Rajput/CHAPTER15_3.ipynb | 1,591,272,351,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347439928.61/warc/CC-MAIN-20200604094848-20200604124848-00163.warc.gz | 532,782,942 | 35,749 | # CHAPTER 15 - Engine Cooling¶
## EXAMPLE 15.1 PAGE 499¶
In [1]:
from __future__ import division
# Initialisation of Variables
BP=90#.................#Brake Power in kW
deltw=27#.................#Raise in temperature of water
etaP=0.25#...................#Efficiency of petrol engine
Pec=32#......................#Percentage of energy going to coolant in petrol engine
Dec=28#......................#Percentage of energy going to coolant in diesel engine
cp=4.187#..........#specific heat of water at constant pressure
#Calculations
hsP = BP/etaP#............#Heat supplied in kW or kJ/s
ecP=hsP*(Pec/100)#.............#Energy going to cooling water in kg/s
mwP=ecP/(cp*deltw)#.............#Mass of cooling water required
hsD = BP/etaD#............#Heat supplied in kW or kJ/s
ecD=hsD*(Dec/100)#.............#Energy going to cooling water in kg/s
mwD=ecD/(cp*deltw)#.............#Mass of cooling water required
print "The mass of cooling water required = %0.2f kg/h for petrol engine "%(mwP*3600)
print "The mass of cooling water required = %0.2f kg/h for diesel engine "%(mwD*3600)
The mass of cooling water required = 3668.50 kg/h for petrol engine
The mass of cooling water required = 2674.95 kg/h for diesel engine | 353 | 1,220 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.359375 | 3 | CC-MAIN-2020-24 | latest | en | 0.756675 |
https://pastecode.io/s/o9u50h1f | 1,718,393,712,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861568.20/warc/CC-MAIN-20240614173313-20240614203313-00566.warc.gz | 400,221,092 | 59,058 | # Untitled
unknown
plain_text
7 months ago
1.3 kB
0
Indexable
Never
```class Solution {
public:
void solve(int x,int y,int &gold,int &maxG,vector<vector<int>>&grid,vector<vector<bool>>&vis,vector<vector<int>>&dir){
vis[x][y]=true;
int org=grid[x][y];
gold+=org;
maxG=max(maxG,gold);
grid[x][y]=0;
for(auto d:dir){
int new_x=x+d[0];
int new_y=y+d[1];
if(new_x>=0 && new_x<grid.size() && new_y>=0 && new_y<grid[0].size() && grid[new_x][new_y]!=0 &&!vis[new_x][new_y]){
solve(new_x,new_y,gold,maxG,grid,vis,dir);
}
}
grid[x][y]=org;
gold-=org;
vis[x][y]=false;
}
int getMaximumGold(vector<vector<int>>& grid) {
int res=0;
vector<vector<int>>dir ={{-1,0},{1,0},{0,-1},{0,1}};
vector<vector<bool>>vis(grid.size(),vector<bool>(grid[0].size(),false));
for(int i=0;i<grid.size();i++){
for(int j=0;j<grid[0].size();j++){
int gold=0, maxG=0;
if(grid[i][j]!=0) {
solve(i,j,gold,maxG,grid,vis,dir);
res=max(res,maxG);
}
}
}
return res;
}
};``` | 334 | 937 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.9375 | 3 | CC-MAIN-2024-26 | latest | en | 0.167861 |
https://electronics.stackexchange.com/posts/346956/revisions | 1,563,450,692,000,000,000 | text/html | crawl-data/CC-MAIN-2019-30/segments/1563195525627.38/warc/CC-MAIN-20190718104512-20190718130512-00162.warc.gz | 375,953,736 | 15,927 | # Return to Answer
2 added 29 characters in body edited Dec 27 '17 at 21:20 G36 5,76111 gold badge55 silver badges1111 bronze badges Well, the equation for the Zin and voltage gain looks for the emitter follower with the bootstrap (positive feedback) at the input simulate this circuit – Schematic created using CircuitLab looks like this: $$Z_{IN} = \frac{(r_eR_E + R_3(r_e + R_E))\cdot (1 + \beta)}{R_3 + (\beta+1)r_e }\approx \frac{R_3}{1 - A_V}||(r_e+R_E)(\beta+1)$$ $$A_V = \frac{(R_3+r_e) R_E}{r_e R_E + R_3r_e + R_3R_E} \approx \frac{R_E}{r_e+R_E}$$$$A_V = \frac{(R_3+r_e) R_E}{r_e R_E + R_3r_e + R_3R_E} = \frac{R_E}{R_3||r_e + R_E} \approx \frac{R_E}{r_e+R_E}$$ Of course $$\R_E\$$ is for your circuit equal to $$R_E = R1||R2||R4$$ So, in conclusion, your reasoning is correct Well, the equation for the Zin and voltage gain looks for the emitter follower with the bootstrap (positive feedback) at the input simulate this circuit – Schematic created using CircuitLab looks like this: $$Z_{IN} = \frac{(r_eR_E + R_3(r_e + R_E))\cdot (1 + \beta)}{R_3 + (\beta+1)r_e }\approx \frac{R_3}{1 - A_V}||(r_e+R_E)(\beta+1)$$ $$A_V = \frac{(R_3+r_e) R_E}{r_e R_E + R_3r_e + R_3R_E} \approx \frac{R_E}{r_e+R_E}$$ Of course $$\R_E\$$ is for your circuit equal to $$R_E = R1||R2||R4$$ So, in conclusion, your reasoning is correct Well, the equation for the Zin and voltage gain looks for the emitter follower with the bootstrap (positive feedback) at the input simulate this circuit – Schematic created using CircuitLab looks like this: $$Z_{IN} = \frac{(r_eR_E + R_3(r_e + R_E))\cdot (1 + \beta)}{R_3 + (\beta+1)r_e }\approx \frac{R_3}{1 - A_V}||(r_e+R_E)(\beta+1)$$ $$A_V = \frac{(R_3+r_e) R_E}{r_e R_E + R_3r_e + R_3R_E} = \frac{R_E}{R_3||r_e + R_E} \approx \frac{R_E}{r_e+R_E}$$ Of course $$\R_E\$$ is for your circuit equal to $$R_E = R1||R2||R4$$ So, in conclusion, your reasoning is correct 1 answered Dec 27 '17 at 19:55 G36 5,76111 gold badge55 silver badges1111 bronze badges Well, the equation for the Zin and voltage gain looks for the emitter follower with the bootstrap (positive feedback) at the input simulate this circuit – Schematic created using CircuitLab looks like this: $$Z_{IN} = \frac{(r_eR_E + R_3(r_e + R_E))\cdot (1 + \beta)}{R_3 + (\beta+1)r_e }\approx \frac{R_3}{1 - A_V}||(r_e+R_E)(\beta+1)$$ $$A_V = \frac{(R_3+r_e) R_E}{r_e R_E + R_3r_e + R_3R_E} \approx \frac{R_E}{r_e+R_E}$$ Of course $$\R_E\$$ is for your circuit equal to $$R_E = R1||R2||R4$$ So, in conclusion, your reasoning is correct | 923 | 2,521 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 17, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2019-30 | latest | en | 0.744547 |
http://convertit.com/Go/ConvertIt/Measurement/Converter.ASP?From=French&To=fl+head | 1,632,650,961,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057857.27/warc/CC-MAIN-20210926083818-20210926113818-00359.warc.gz | 12,829,183 | 3,786 | Partner with ConvertIt.com
New Online Book! Handbook of Mathematical Functions (AMS55)
Conversion & Calculation Home >> Measurement Conversion
Measurement Converter
Convert From: (required) Click here to Convert To: (optional) Examples: 5 kilometers, 12 feet/sec^2, 1/5 gallon, 9.5 Joules, or 0 dF. Help, Frequently Asked Questions, Use Currencies in Conversions, Measurements & Currencies Recognized Examples: miles, meters/s^2, liters, kilowatt*hours, or dC.
Conversion Result: ```French = 3.33333333333333E-04 length (length) ``` Related Measurements: Try converting from "French" to arpentlin, chain (surveyors chain), cloth finger, earth to moon (mean distance earth to moon), ell, fermi, football field, Greek cubit, Greek span, Israeli cubit, link (surveyors link), marathon, nautical league, rod (surveyors rod), Roman foot, rope, shaku (Japanese shaku), soccer field, survey foot, yard, or any combination of units which equate to "length" and represent depth, fl head, height, length, wavelength, or width. Sample Conversions: French = .0000094 actus (Roman actus), 7.53E-09 arpentcan, .52493438 bottom measure, .00000365 city block (informal), .00029163 ell, .00018227 fathom, .00109361 foot, .00000365 football field, .00045005 gradus (Roman gradus), .00072027 Greek cubit, .00144054 Greek span, .00060199 Israeli cubit, .00033333 m (meter), 333.33 micron, 2.07E-07 mile, .0058326 nail (cloth nail), .00006628 rod (surveyors rod), .00112628 Roman foot, .00000365 soccer field, .00036454 yard.
Feedback, suggestions, or additional measurement definitions?
Please read our Help Page and FAQ Page then post a message or send e-mail. Thanks! | 452 | 1,656 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.046875 | 3 | CC-MAIN-2021-39 | latest | en | 0.66623 |
http://math.stackexchange.com/questions/916894/why-is-an-image-called-an-image | 1,469,737,806,000,000,000 | text/html | crawl-data/CC-MAIN-2016-30/segments/1469257828322.57/warc/CC-MAIN-20160723071028-00156-ip-10-185-27-174.ec2.internal.warc.gz | 152,738,455 | 21,787 | # Why is an image called an “image”?
Given a function $f : A \to B$, the image, denoted by $\operatorname{Im}f$ is the set of all $f(x)$ where $x \in A$. Why do we call this set the image? When was it first used, and what motivated its name?
I would imagine that it is related to the idea that the function values show us what the function "looks like"; otherwise, I suspect it may be related to the etymological history of image as "imitation" or "representation" in that the primary features of interest, the values, of a function are copied by isolating the function values from the domain. I'm not sure, though, and I don't have sources.
-
Maybe this would be best if asked in comm. wiki. It will definitely get more attention and treatment there :). – Mr.Fry Sep 2 '14 at 10:24
I had always assumed it was related to optics or projection, where an object has an image. – Henry Sep 2 '14 at 10:28
If we think of $f$ as some medium, not necessarily a mirror, then $B$ is to be viewed as what $A$ sees itself through $f$. Here the term "image" is used in figurative sense. – Gudson Chou Sep 2 '14 at 10:29
My go-to etymological source, Jeff Miller's "Earliest Known Uses ..." site, has a rare omission in this case. Ah, well. Personally, I guess I've assumed that the term came from transformational geometry, where, for instance, "mirror image" is a natural descriptor for the result of reflecting a figure through a line/plane/whatever. – Blue Sep 2 '14 at 10:47
Yeah, I checked there too, and didn't find anything :( – William Sep 2 '14 at 10:59
As many mathematical terms originate from German it might have something to do with the fact that functions are also called "Abbildungen" in German. This could be translated as "mapping", but the German word is related to "Bild" (picture or image) and the image of a function is also called its "Bild" in German.
Addendum: I should have been more precise. Nowadays (meaning: probably since the beginning of the 20th century), "Funktion" and "Abbildung" are almost always used synonymously. Before that, "Abbildung" had more of a geometric "feel" to it (as in an isometry) while "Funktion" (I think the word was introduced by Leibniz) was used for the algebraic meaning (as in "$f(x)=x^2+42$").
-
Do you have a source or a explanation for my that particular word was used? Thanks! – William Sep 2 '14 at 13:02
I think what others have said here also makes a lot of sense, see for example Shabaz's answer. Having said that, "Bild", "Bildnis" or "Abbild" always also had the connotation of "copy" in German, for example "Du sollst Dir kein Bildnis machen" is equivalent to "Thou shalt not make unto thee any graven image" while a "Bildhauer" is a sculptor. Finally, the German word for "inverse image" is "Urbild" which was used in philosophical and religious contexts long before it was used in math. – Frunobulax Sep 2 '14 at 13:23
The term image in itself doesn't mean photo, as a young person growing up with smartphones might think.
An image is a projection. For example, a photo is the projection of light coming from various points on a 2d surface. Imagination is the process of projecting a thought to your mind's eye (if that makes sense to you). A mirror image is the projection of a shape over a mirror.
This can all be formulated in a single idea, which is the mathematical sense: an image is the projection of some data over a function.
In that sense, a photo is the projection of photons arriving to a small surface over the function composed of the functionality of the lense, and the sensitivity of the receptor. Imagination is the projection of part of your brain activity on another part of your brain (where the function itself is quite unknown to humans). A mirror image is the projection of photons arriving on a surface over the f(x) = -x function!
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The image of the function is not what the function looks like, but rather what the result of applying the function to all the inputs looks like. It's only a tiny fraction of what the function looks like. In particular, it is easy to manufacture infinitely many different functions that all have the same image. If you think of a function $f:A\to B$ as a process that when given input $a\in A$ gives you some output $f(a)\in B$, then the image tells you which portion of $B$ is actually attained by the function. More abstractly, if the function is an artist painting drawing object $O$ in front of her onto canvas $C$, then the artist is a function $f:O\to C$ since she takes as input the retinal information cast by the object and she responds to each input pixel by drawing an output pixel (obviously, this is not what really happens). The image of the function is then the portion of the canvas that was painted.
-
Intuitively, what you see with your eyes is where your receptors in the eye get hit by a light ray coming through your lense. So the pattern of your receptors being hit ultimatively form your mental "image" of what you see.
Taking this pictorial analogy to functions, the source (what you perceive) is the domain, the light rays are the function, and the receptors that get hit ultimately form the image. (In a function $f:A\to B$ those receptors correspond to the elements of $B$ that "get hit" by the function $f$.) So if some receptors don't get hit, you have some kind of a blind spot -- they are not part of the image, and the exact same is true in functions: Elements $b\in B$ such that there is no $a\in A$ with $f(a)=b$ are not in the image.
I'm aware that this is extremely "hand-wavy", but it might help you get some intuition for the use of the term image in the context of functions.
-
Indeed! The pictures of functions with arrows form the domain to the codomain have always somehow reminded me of the drawings where light rays refract on lenses and form images. I don't know if that is the real etymology of the term, however. – JiK Sep 2 '14 at 11:21
To continue the lens allusion: when a function is one-to-one, it means the image is in focus (and vice versa). – occulus Sep 2 '14 at 13:25
And if data in certain 'slices' of the domain is 1-1, it's akin to having a focal plane and non-infinite depth of field. – occulus Sep 2 '14 at 13:28
Btw, I think it's more accurate to say that lenses or anything affecting the light paths are the functions (rather than light itself), and just taking the assumption that light travels in all directions from any source point. – occulus Sep 2 '14 at 13:31 | 1,610 | 6,466 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2016-30 | latest | en | 0.952403 |
http://slideplayer.com/slide/4030306/ | 1,513,474,411,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948592202.83/warc/CC-MAIN-20171217000422-20171217022422-00008.warc.gz | 241,585,188 | 29,579 | # A Time Domain Atmospheric Noise Level Analysis Lee Boyce International Loran Association Boulder, CO 7 November 2003.
## Presentation on theme: "A Time Domain Atmospheric Noise Level Analysis Lee Boyce International Loran Association Boulder, CO 7 November 2003."— Presentation transcript:
A Time Domain Atmospheric Noise Level Analysis Lee Boyce International Loran Association Boulder, CO 7 November 2003
2 Lightning Cloud to Ground –Preliminary breakdown –Stepped leader –Attachment –First return stroke –J & K process –Dart leader –Subsequent return stroke Intra-Cloud Discharge –J & K process –Q noise
3 Time Histories Preliminary Breakdown Stepped Leader Return Unipolar & Bipolar K-Process ~400us
4 Time Histories (cont)
5 Noise E-Field of a Typical Day
6 Noise Model
7 Clipping and Hole-Punching Unfiltered Clipping Hole-Punching (Blanking)
8 Hole-Punching
9 Key Question How do we claim credit for hole-punching over linear processing? –Past work Feldman 12dB-17dB improvement (on severe days) using two channels for a communication receiver. Spaulding & Middleton LOBD 30dB, but there are many caveats. –Qualitative explanation Usually performance will be a function of the level at which the Non- Gaussian component takes over. Can come up with an estimate based on “hole-punching” that is not too bad.
10 Goals Calculate a bound for noise analysis that is better than linear processing –Use available data (CCIR, measurements) –Hole-punch out large nonGaussian impulses –Calculate Gaussian residual Develop a model for atmospheric noise
11 CCIR Used the ARN-2 Radio Noise Recorder –16 Stations around the globe –Average noise power at each of eight frequencies for fifteen minutes each hour –13 kHz, 11kHz, 250kHz, 500kHz, 2.5MHz, 5MHz, 10MHz, and 20MHz –1957-1961 (4 years) → 8640 15-minute measurements → 99.98% –Tracked filtered noise envelope not instantaneous noise –Took high speed data to obtain APDs (400Hz) Sectioned the year into seasons and time blocks –Four 90-day seasons –Six 4-hour time blocks Tracked external antenna noise factor, F a –Power received through a loss-free antenna F a = 10*log 10 (P n /KT o B) –Lists the median value hourly value for each time block, F am, at 1 MHz –Lists the upper decile (90%) level Du –Calculate noise E-field from Fa, BW, frequency Use normal or log-normal statistics and graphs to adjust values Limitations –Average background noise, local thunderstorms not included –If power averaged over several minutes, it’s a constant, except when there are local thunderstorms –Noise BW is wider than Rx BW
12 CCIR (cont) Noise Factor, Fa –Determines absolute measure E rms (uV/m) –Varies with location –Bandwidth independent Voltage deviation, V d –Determines APD curve –Uncorrelated to Noise Factor –APD gives strength relative to RMS value, parameterized by V d E noise (%) = E rms (Fa) + APD(V d )
13 APD Review Amplitude Probability Distributions or Apriori Probability Distributions –APD = 1 - CDF Shows the percentage of time that a given envelope voltage level is exceeded Envelope, A, is Rayleigh = Sqrt(Gaussian 1 2 + Gaussian 2 2 ) Rayleigh Distribution is a Line Values relative to RMS (0 dB) Parameterized by Voltage Deviation, V d –V d = 20*log 10 (RMS Voltage / Avg Voltage) –High amplitude samples dominate V d 99%0.0001%36% 0 = A - A rms P [ Exceeded]
14 12 14 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.0001 0.1 0.01 60 50 40 30 20 10 0 -10 -20 -30 -40 CCIR uses these Large database over 4 years APD referenced to RMS value Parameterized by V d Noise BW is wider than Rx = A - A rms V d = 1.05 0.001 V d =30 0dB = A RMS P [ Exceeded]
15 V d = 10 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.0001 0.1 0.01 60 50 40 30 20 10 0 -10 -20 -30 -40 = A - A rms P [ Exceeded] V d = 1.05 0.001 Rayleigh 3dB Atmospheric noise is Non-Gaussian overall but has a strong Gaussian component, hence Rayleigh Envelope V d coupled amount of time that the signal is Rayleigh Hole Punch whenever the Noise Level is more than 3dB above the Rayleigh component Get measure of signal suppression Rayleigh “Available” Hole Punched “Suppressed”
16 Hole Punch Signal Suppression Loss or Signal Suppression [dB]
17 V d = 10 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.0001 0.1 0.01 60 50 40 30 20 10 0 -10 -20 -30 -40 = A - A rms P [ Exceeded] V d = 1.05 0.001 Rayleigh -20dB V d coupled to the strength of Rayleigh Component Measured how far below RMS value Rayleigh component was Get measure of Rayleigh signal strength Reduces the noise numbers Rayleigh Level Relative to RMS
18 Difference between RMS and Rayleigh Level
19 Noise Model Break up Atmospheric Noise into two parts –Hole Punch non-Rayleigh (nonGaussian) noise out Increases Noise –Reduce noise level from RMS value to Rayleigh level Decreases Noise
20 Total Effect of Hole Punch and V d on Noise Level
21 Median 95% Level of E rms
22 Median 95% Effective Noise Level
23 Summary of Noise Percentage Fa (Availability) E rms Noise Level [dB V/m] Effective Noise Level [dB V/m] SNR Assuming 60 dB V/m 95 1 80600 99 1 9070- 10 99.9 2 10080- 20 99.99 2 11090- 30 1 Summer 18h Worst Case 2 Spring 18h Worst Case
24 July 9, 2002 Upland, IN >10kA Strikes 1600-2259 UTC (10:00a – 4:59p CDT) Click on map for animation
25 Taylor Univ. - Upland, Indiana 300Hz-40kHz BW 100kS/s Filter BW wide enough to contain interference
26 Results of Processing Less signal suppression than predicted Lower difference between Vrms and Rayleigh Level Median 50% E-field @ Taylor 20kHz BW 40kHz = 75 dB uV/m
27 1620h Taylor, IN
28 2220h Taylor, IN
29 Simulation Try to keep 1 st Order Statistics (APD) Get the flavor of the time structure Use two continuous Markov processes to describe close and far discharges
30 Markov Chain for Discharges Local Remote
31 Data Comparison Simulation Data
32 Simulated and Actual Data APD
33 Summary Non-linear processing analysis should give goals for real design. Have the makings of a good atmospheric noise model. –1 st order statistics preserved –Adequately show time dependency Need data from Midwest or Gulf during peak times with Loran Rx to verify analysis.
34 Acknowledgements Mitch Narins FAA Program Manager John Cramer & Ken Cummins, Vaisala Inc Umran Inan & Troy Wood, Department of Electrical Engineering, Stanford University
35 Backup Slides
36 Before Storm 16:20 (UTC)
37 Before Storm Data
38 During Storm 22:20 (UTC)
39 During Storm Data
40 Lines up well
41 Pulse Shape Comparison
42 Data Wiping Before Storm
43 Data Wiping During Storm
44 Captured and Missed Pulses
45 What is the correct N in SNR? Need to estimate the noise and the processing gains correctly. Frequency domain estimate will kill us. Is there structure in the time domain that we may exploit? Model as Gaussian + impulsive noise? Courtesy of Weidman et al 1981 E-Field (dB uV/m) 110 90 70 50 30 10 -10 -30
46 Sept 2001 Data Low Activity High Activity +22dB to Noise and +15dB to V d due to BWR DayNight
47 Median 95% Level of E rms
48 Median 95 % Gaussian Noise Level
49 Median 95% Effective Noise Level
50 Median 99% Level of E rms
51 Median 99% Effective Noise Level
52 Median 99% Effective Noise Level (Spring)
53 Cross-over for Worst Case Spring Du is larger than for Summer. In the low-probability (>99.9%) conditions, the Spring 18h Fa exceeds Summer 18h value.
54 Median 99.9% Effective Noise Level (Summer)
55 Median 99.9% Effective Noise Level (Spring)
56 Median 99.99% Level of E rms
57 Median 99.99% Effective Noise Level
58 Median 99.99% Effective Noise Level
59 Current Work Obtained & processed NLDN data for July & August 2002 –Rated days as noisy or quiet based on number of lightning strikes within 30 km (16 NM) or 300 km (160 NM) –Only a few bad days in 2 months Obtained & processed some days of Upland, IN data –Worst times and worst days not available –Some bad times for worst day is available
60 NLDN Data –Range of days from July 9 to August 27, 2002 –Rated days as noisy or quiet based on number of lightning strikes within 30 km (16 NM) or 300 km (160 NM) –Only a few bad days in 2 months Upland, IN data –Worst times and worst days not available –Some bad times for worst day is available
61 NLDN Data DateStart HourEnd Hour< 30 [km]30 - 300 [km] 2002/07/0920:20:2821:20:2861955 2002/07/0921:20:2922:20:272574009 2002/07/0922:20:2823:20:274684864 2002/07/0923:20:2823:59:59574499 2002/07/2616:00:0516:59:5963542 2002/07/2617:00:0117:59:59553641 2002/07/2618:00:0019:00:001421055 2002/08/2222:00:0122:59:5902677 2002/08/2223:00:0023:59:593942779 2002/08/2300:00:0001:00:002333208 2002/08/2301:00:0501:59:591173255 2002/08/2302:00:0102:59:59183451 2002/08/2303:00:0004:00:0012378 2002/08/2319:00:0119:59:591491780 2002/08/2320:00:0220:59:593313326 2002/08/2321:00:0121:59:592513772 2002/08/070 2002/08/080 2002/08/090 Noisy Days Quiet Days < 500 [km]
62 Experiment ARI
63 July 9, 2002 Upland, IN >10kA Strikes 0820-2359 UTC (3:20a – 8:59p CDT)
64 APDs of 1 Minute Samples (Pre-IF Filter) Storm getting nearer 180 V/m 16h 22h
65 Normalized APD (Post-IF) Storm getting nearer 16h 22h
66 95% Signal Available
67 40% Signal Available
70 Post-IF Filter (Good? Day)
71 12 14 1 5 10 20 30 40 50 60 70 80 85 90 95 98 99 0.0001 0.1 0.01 60 50 40 30 20 10 0 -10 -20 -30 -40 APD referenced to RMS value Calculated V d =10 Offset probably due to clipping Overlays between 12 < V d < 14 = A - A rms P [ Exceeded] V d = 1.05 0.001 V d =30
72 August 8, 2002 Upland, IN >10kA Strikes 0000-2359 UTC (7:00p – 8:59p CDT)
73 Post-IF Filter (Good? Day)
74 August 8, 2002 Upland, IN >10kA Strikes 0000-2359 UTC (7:00p – 8:59p CDT)
75 For Further Study Make sure number of strikes/GRI will never completely wipe out availability Validate curves for higher Vd Get large dynamic range measurements without clipping Take data within a large storm tied to NLDN Agree on extent of variances Availability implies 50% Levels
76 Use of CCIR Data RMS Value + APD = Total Noise Strength (absolute) (relative to rms) Given a center frequency of 100kHz with a 30kHz BW we get V d.
77 National Lightning Detection Network Privately run Real-Time data collection Mostly detection and high level data Some waveform data Can use newer analytical field models
78 Progress II Atmospheric Models –Hall/Feldman Simple analytical description Empirically derived parameters Captures atmospheric noise reasonably well Unbounded second moment: infinite energy –Middleton Almost all physically derived parameters Works for a wide range of noise processes Class A model works great Class B model only half works Bounded second moment, unlike Hall May be useful for UWB –Weibull Semi-physical parameters Works for some Class B noise, but doesn’t seem to capture intermediate statistics Bounded second moment Models allow analytical calculation of moments and simulation
79 Loran Aperture-RF-IF
80 Reception Probabilities ≡ Strike/GRI
81 Conclusion Want 500 – 1000 “good” signals = 63 – 125 GRIs = 6.3 – 12.5 sec If we use the binomial distribution with probability, p ≡ Strike/GRI/100, at worst case (p=0.3) need ~4x number of signals. Need to integrate for 25.0 - 50.0 sec between valid updates
82 Middleton’s Assumptions Source locations and emission times are Poisson distributed in space Narrow-band receiver condition Δf ARI ≪ f ₀ –The characteristic function is independent of phase "Local Stationarity" –No changes in average source numbers and emission properties during the observation period T
83 Class A – F N << F R –Clearly seen noise –Threshold on amplitude Class B – F N >> F R –Infinite duration –Poisson amplitudes
84 Class B Parameters A B ≡ Avg. rate of signal generation * Avg. duration A α = The “effective” impulse index, which depends on the α-moment of the basic envelope of the output of the IF. α = the spatial density-propagation parameter. It provides and "effective" measure of the average source density with range. Thus we can calculate the power law for the source. This provides information on the emitting source. Ω 2B = The intensity of the "impulsive" component Γ B ≡ σ G ²/Ω 2B = The ratio of the intensity of the independent Gaussian component σ G ² to Ω 2B the intensity of the "impulsive" non-Gaussian N I = the scaling factor which insures that the pdfs match up and yield the correct mean square envelope. ε B = the empirically seen “bend-over” point
85 Class B Model
86
87 Future Work Develop Hall Model Produce curve of V d vs. % Time and V d vs. Gaussian level for different seasons Use numbers to re-run probability analysis to determine required time for inertial system.
88 Another Blanking Example
89 What is CCIR 322-2? Reported background atmospheric noise levels Evolved into ITU P372-7 –Included man-made and galactic noise –Removed technical background Used the ARN-2 Radio Noise Recorder –16 Stations around the globe –Average noise power at each of eight frequencies for fifteen minutes each hour –13 kHz, 11kHz, 250kHz, 500kHz, 2.5MHz, 5MHz, 10MHz, and 20MHz –1957-1961 (4 years) → 8640 15-minute measurements → 99.98% –Tracked filtered noise envelope not instantaneous noise –Took high speed data to obtain APDs (400Hz)
90 What is CCIR 322-2? (cont) Sectioned the year into seasons and time blocks –Four 90-day seasons –Six 4-hour time blocks Tracked external antenna noise factor, F a –Power received through a loss-free antenna F a = 10*log 10 (P n /KT o B) –Lists the median value hourly value for each time block, F am, at 1 MHz –Lists the upper decile (90%) level Du –Calculate noise E-field from Fa, BW, frequency Use normal or log-normal statistics and graphs to adjust values
91 F am for Summer 20-24h
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# Class Note for PHIL 382 at UMass
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Phil 382 Logic Supplement Negation not A IA T F F T other symbols 7 Conjunction and TT T TF F FT F FF F other symbols amp Disjunction or A B A v B T T T T F T F T T F F F Arguments Material Conditional if then A B A B T T T T F F F T T F F T other symbols 3 Note A 9 B is equivalent to A IB and is equivalent to A v B Material Biconditional if and only itquot TT T TF F FT F FF T other symbols E Note A lt gt B is equivalent to A BB A An argument is a set of formulas with one designated as the conclusion The formulas that are not the conclusion are the premises These premises are meant to provide support for the conclusion For example the following is an argument P L C Here C is the conclusion of the argument This is indicated by placing it beneath a horizontal line P and Q are the premises and are meant to support the conclusion C Validity We say that an argument is valid if and only if Necessarily if the premises are true then the conclusion is true Another way to put this an argument is valid if and only if Assuming the premises are true the conclusion is true too Entailment Often in this course we ll talk about entailment rather than validity The two concepts are very similar however We say that a set of formulas l entail a formula 3 if and only if Necessarily if the members of 4 are true then 3 is true Another way to put this a set of formulas l entail a formula 3 if and only if Assuming that the members of 4 are true then 3 is true too In other words a set of formulas l entail a formula 3 if and only if the argument with 3 as a conclusion and the set of formulas 4 as premises is valid Example A A B entails A There is one way for A A B to be true When we assign truth values in this way A is true So assuming that A A B is true A is true So A A B entails A Example A 9 B and A together entail B There are three ways to assign truth values so that A 9 B is true A B A 9 B To see if the entailment holds we also need to assume that A is true This can happen in only one way A B A 9 B A When we assign truth values in this way B is true So assuming that A 9 B is true and A is true B is true So A 9 B and A entail B Example A v B and IB together entail A There are three ways that A v B can be true A B A v B F F F There is one way that B can be true IB F W Putting these together we see that there is only one way that both A v B can be true and B can be true AB When we assign truth values in this way we see that A must be true So assuming A v B is true and IB is true A is true So A v B and IB entail A Quantifiers Occasionally we ll need to talk about quantified formulas in this course Here are some examples of quantified sentences All humans are mortal Some students study philosophy No man is an island Some philosophers are not male These are quantified sentences because at the beginning of them they talk about some quantity of things eg all things or some things or no things In logic we have two quantifiers to represent these sentences Vx 7 this is the universal quantifier it means something like for all x Elx 7 this is the existential quantifier it means something like for some x We can then represent quantified sentences like this Vx Ax Bx For all X if X is A then X is B All As are Bs ExAx A Bx For some X X is A and X is B 2 Some As are Bs Final Note This supplement is meant to help you not to confuse you or scare you away from this course We will make use of logic quite a bit in this course especially at the beginning so if you re confused about any of this you need to be sure to see me However I am confident that anyone in this course can learn the necessary logic without too much trouble
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Regression analysis and correlation
While carrying out the regression analysis to detect the impact of offering the products of Schmeckt energy bars to other stores, four variables are used (Afonso & Kazemi, 2017). Three variables are independent while one of the variables is a dependent. Independent variables are: "Mean income for every person", "tariff or tax rates for importation of these energy bars”, as well as "number of stores where energy bars were offered" (Oestreicher, 2015). The dependent variable is “Average annual demand of drinks per individual". According to results, the relationship between independent variables and the dependent variable is very strong. In other words as the level of income increases the annual demand of energy bars also increases. This is because of the high levels of disposable income available to the consumers. Also a reduction on the tariff rate on imports of energy bars also leads to increased demand of annual bars (Afonso & Kazemi, 2017). Lastly, increase in number of stores for these drinks leads to increase in annual demand of drinks per individual. This is because multiple R value is big, it has the value of 0.955932682.
Considering the “Mean income for every person” variable as W, the “tariff or tax rates for importation of these energy bars” variable as T, the “number of stores where energy bars were offered” variable as X and “Average annual demand of drinks per individual” variable as Y, the regression equation for the variable obtained through using excel is given as Y=0.004837918W - 6.456977068T + 4.072444073X -12.16021978.
Considering the equation, the mean income for every person is positively related to the average annual demand of drinks per individual though their correlation is very small. This shows that an increase in mean income for every person will slightly cause increase in the average annual demand of drinks per individual (Korinek & Jessica, 2012). The tariff or tax rates for importation of these energy bars are negatively correlated to the annual demand of energy bars per individual. Therefore, that means that an increase on tariff or tax rates for importation of these energy bars would cause a reduction on the average annual demand of energy bars per individual. The reduction on the tariff or tax rates for importation of these energy bars would simply lead to the increase on the average annual demand of energy bars per individual. The number of stores for these drinks offered has a positive correlation with the average annual demand of energy bars per individual in relation to the coefficient (Afonso & Kazemi, 2017). This means when there is increase on number of stores for the drinks, there is an increase on the average annual demand of the drinks per person, the reverse is true. Considering regression analysis carried out, mean income for every person, tariff or tax rates for importation of these energy bars, as well as number of stores where energy bars were offered greatly affect the annual demand of energy drinks per individual.
Impact of mean income, tariff rates, and number of stores on annual demand
Regression results are shown below;
The regression statistics table contains the multiple R value which identifies the relationship between independent and dependent variables.
Basing on the regression analysis and the graphs obtained which describes the relationship between the "Tariff or tax rates on imports of the drinks" and the "average annual demand of the drinks" (Eun& Resnic, 2011). Tariff or tax rates on importation of the drinks within the country greatly affect the demand of the commodity annually. The tax rates on the importation of energy drinks are negatively correlated to the demand of drinks by each individual or person. Therefore, this means increase on Tax rates on the importation of the drinks would cause a reduction on mean demand of the drinks per person. The reduction on the tax rates on the importation of the drinks would simply lead to an increase on the average demand of drinks per person per each year. It is important to note that tariffs reduces the overall the overall demand of imports in case they are high meaning that limited consumers will be able to afford the product (Afonso & Kazemi, 2017).
The scatter diagram or graph illustrating the correlation between the "Tax rates on importation of energy drinks" and the "average annual demand of the drinks" is shown below;
Board meeting the minister for trade should address matters concerning the advantages and disadvantages of tariffs on these imports. Given that the imposed tariffs may be helpful to the government and the domestic or local industries in the following manner; they are helpful in raising revenue to the government. When tariffs are imposed in imported products, they become expensive meaning that high amounts of money will be required to spend on imports. Therefore this discourages importation of products.
However, the few products imported raises revenue to the Government. They are useful in protecting the domestic industries from imported goods which are always more expensive and of good quality. Protecting the domestic industries would increase their revenue. Since the good or commodity taxed is an alcohol beverage, this would be useful in protecting the population and the environment (Evenett & Frédéric, 2012). It is important to note that Domestic industries may not have the capacity to effectively compete with large and highly efficient products and industries. So for government to encourage local production and demand, tariffs are very important to the economy. With the imposition of tariffs on imports, importation is discouraged and exportation encouraged. This is in line with the marchentalistic philosophy that emphasizes exportation and discourages importation if the wealth of the nation is to be enhanced (Afonso & Kazemi, 2017).
However, given these existing advantages, the board for the energy drinks should advise the minister of trade on the benefits of reducing or cutting off the tariffs. One of the importance is to promote trade liberalization which comes with a number of benefits. One of these benefits is promotion of globalization which increases market for the different goods which are being produced among the member states. The removal or reduction of Tariffs will also be essential in the lowering of the consumer prices. It also increases specialization and economies of scale benefits, tariff reduction also leads to the trade creation among different states (Silverman, 2018).
Basing on the regression results, the tax rate on the importation of energy drinks is negatively correlated to the average annual demand of drinks per individual. Therefore, this means that increase on the Tax rate on the importation of drinks would cause a reduction on the mean demand of the drinks per person. The reduction on the tax rates on the imports of drinks would simply lead to the increase on the average annual demand of drinks per person (Blinder, 2008). Therefore there is need for the board of the company to make a requisition on the reduction on the tariffs or promote free trade. The benefits of free trade to both the government and the company are many though there are also some disadvantages. The importance of free trade is: Free trade basically means that there is free entry and exit of imports and exports between different countries without tariffs. This trade will basically led to creation trade between the country of origin of the energy bars and the case study country (Mathias and Harald, 2011).The removal of tariffs will promote the use of the surplus raw materials within the country and this would be useful in reducing on the prices of the energy bars thus increasing the demand of the commodity within the country. This will increase on the company revenue within Australia. Promotion of free trade will cause an increase in competition among the different companies. There will be incentives of increasing costs and cutting costs because of this competition. There is also a possibility of prevention of monopolies.
The diagram below shows the effects of tariffs on company
The regions which are pink identify net loss caused to the society because of tariff existence.
References
Afonso, A., & Kazemi, M. (2017). Assessing public spending efficiency in 20 OECD countries. In Inequality and Finance in Macrodynamics (pp. 7-42). Springer, Cham.
Blinder, A. S. (2008). "Free Trade". In David R. Henderson (ed.). Concise Encyclopedia of Economics (2nd ed.). Indianapolis: Library of Economics and Liberty. ISBN 978-0865976658. OCLC 237794267.
Eun, C. S.; Resnick, B. G. (2011). International Financial Management, 6th Edition. New York: McGraw-Hill/Irwin. ISBN 978-0-07-803465-7.
Evenett, S.J, and Frédéric, J. (2012). Trade, Competition, and the Pricing of Commodities. https://www.voxeu.org/index.php?q=node/7626.
Korinek, J., Jessica, B. (2012). ‘Multilateralising Regionalism: Disciplines on Export Restrictions in Regional Trade Agreements’.
Oestreicher, J. (2015). Plague of Equals: A science thriller of international disease, politics and drug discovery. California: Omega Cat Press. p. 408. ISBN 978-0963175540.
rabandt, Mathias; Uhlig, Harald. (2011). "The Laffer Curve Revisited". Journal of Monetary Economics. 58 (4): 305–27. doi:10.1016/j.jmoneco.2011.07.003
Silverman, B. W. (2018). Density estimation for statistics and data analysis. Routledge
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# Calculate Hyperbolic sine of a value in R Programming – sinh() Function
`sinh()` function in R Language is used to calculate the hyperbolic sine value of the numeric value passed to it as argument.
Syntax: sinh(x)
Parameter:
x: Numeric value
Example 1:
`# R code to calculate hyperbolic sine of a value`` ` `# Assigning values to variables``x1 <``-` `-``90``x2 <``-` `-``30`` ` `# Using sinh() Function``sinh(x1)``sinh(x2)`
Output:
```[1] -6.102016e+38
[1] -5.343237e+12```
Example 2:
`# R code to calculate hyperbolic sine of a value`` ` `# Assigning values to variables``x1 <``-` `pi``x2 <``-` `pi ``/` `3`` ` `# Using sinh() Function``sinh(x1)``sinh(x2)`
Output:
```[1] 11.54874
[1] 1.249367```
My Personal Notes arrow_drop_up | 273 | 789 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.5625 | 3 | CC-MAIN-2023-23 | latest | en | 0.484753 |
http://stackoverflow.com/questions/12658682/how-to-create-a-sparse-matrix-in-matlab-given-the-locations-of-non-zero-elements | 1,435,817,244,000,000,000 | text/html | crawl-data/CC-MAIN-2015-27/segments/1435375095404.78/warc/CC-MAIN-20150627031815-00084-ip-10-179-60-89.ec2.internal.warc.gz | 213,428,402 | 19,931 | # How to create a sparse matrix in MATLAB given the locations of non-zero elements
I need to create matrix in MATLAB with the following requirement. Given a vector `v`, for example, `[1,2,2,1,3,5,1]`, I need to form a matrix:
``````[1 0 0 1 0 0 1;
0 1 1 0 0 0 0;
0 0 0 0 1 0 0;
0 0 0 0 0 0 0;
0 0 0 0 0 1 0]
``````
i.e. the matrix's `i`th column contains only one non-zero element (a single `1`) at row `v[i]`. How can I avoid a loop and do this in an efficient way?
-
This doesn't answer the question, but just in case you didn't realize: A single loop across the columns of your output matrix (which makes the problem trivial to solve) should be almost as efficient as a fully vectorized solution if you're only using one CPU, and will still perform very well comparatively if you have multiple CPU. A great explanation of why is here – Colin T Bowers Sep 30 '12 at 5:30
Others are pointing out that loops are fine here. I'll point out that sparse is FAR better. Your matrix is sparse, very much so, so use the capability of sparse to solve the problem, and save a vast amount of storage in case that matrix is large.
``````N = 3000;
v = ceil(rand(1,3000)*3000);
tic
A = zeros(N,N);
for i = 1:N
A(v(i),i) = 1;
end
toc
Elapsed time is 0.069082 seconds.
tic
B = sparse(v,1:N,1,N,N);
toc
Elapsed time is 0.001308 seconds.
``````
So if the matrix is at all large, there is a huge difference in time.
``````whos A B
Name Size Bytes Class Attributes
A 3000x3000 72000000 double
B 3000x3000 72008 double sparse
``````
The matrices are identical otherwise.
``````sum(sum(abs(A - B)))
ans =
0
``````
The sparse matrix takes very little space, and you can use it just like any other matrix.
Use the capabilities of MATLAB.
-
First, I have to give my standard disclaimer, that despite the commonly held notion that loops should generally be avoided in MATLAB, loops have actually become much more efficient in modern releases of MATLAB, in large part, due to the JIT accelerator. So, certainly, benchmark your code to determine if loops actually are a bottleneck.
That said, my first thought on how to approach this problem without a loop was to index into an identity matrix (as shown below).
``````identityMatrix = eye(max(v(:)));
result = identityMatrix(:,v);
``````
I think that this is a nice, clean looking solution; however, I don't necessarily know that it is significantly more efficient than using a loop. As a point of comparison, I implemented the following solution using a loop:
``````numRows = max(v(:));
numCols = length(v);
result = zeros(numRows,numCols);
for i=1:numCols
result(v(i),i) = 1;
end
``````
Based on my test runs, it looks like the top (no loop) solution is generally faster for those cases where `v` is not very long. However, when `v` contains many elements (>100 for example), I was actually seeing average times where the loop solution was beating the alternative.
-
Did'ya try sparse though? – user85109 Sep 30 '12 at 19:08
@woodchips - I hadn't thought of that, but now that you point it out this does seem like the perfect use of `sparse`. Thanks for the insight. – grungetta Sep 30 '12 at 20:34
``````m = max(v);
n = length(v);
M = zeros(m, n);
M([0:(n-1)]*m + v) = 1;
``````
-
I think you meant for that last line to be `M([0:n-1]*m + v) = 1;` – grungetta Sep 30 '12 at 6:16
@grungetta Right you are! – Ansari Sep 30 '12 at 6:35
``````>> v = [1,2,2,1,3,5,1];
>> a = zeros(max(v), length(v));
>> a((0 : size(a, 1) : numel(a) - 1) + v) = 1
a =
1 0 0 1 0 0 1
0 1 1 0 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 0 0
0 0 0 0 0 1 0
``````
- | 1,156 | 3,777 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5625 | 4 | CC-MAIN-2015-27 | latest | en | 0.926213 |
http://www.physicsforums.com/showthread.php?s=706d1e628a11645d1959d9173d87371c&p=4840563 | 1,411,026,221,000,000,000 | text/html | crawl-data/CC-MAIN-2014-41/segments/1410657126053.45/warc/CC-MAIN-20140914011206-00263-ip-10-196-40-205.us-west-1.compute.internal.warc.gz | 733,737,867 | 7,226 | # Interpreting microcanonical distribution
P: 24 I'm trying to interpret the expression of a microcanonical distribution for energy $E_0$ of a particle of mass m moving about a fixed centre to which it is attracted by a Coulomb potential, $Zr^{-1}$, where $Z$ is negative. The function expression looks like this: $ρ_{E_0}(\textbf{r,p}) = \delta(E_0 - \frac{1}{2}m^{-1}p^2-Zr^{-1})$. Most of the stuff in the expression is understandable, but I am not sure what the delta signifies here. Any help? Thanks! J
C. Spirit Sci Advisor Thanks P: 5,661 In the microcanonical ensemble the system lies on a surface of constant energy in phase space so the probability distribution has to vanish off of the constant energy surface. The argument in the delta function just represents this surface.
P: 24 So $E_0 ≠ \frac{1}{2}m^{-1}p^2+Zr^{-1} → ρ_{E_0}(\textbf{r,p}) = 0$ ? Does the original expression actually say something about the distribution itself, or only about this property?
C. Spirit
Quote by jjr So $E_0 ≠ \frac{1}{2}m^{-1}p^2+Zr^{-1} → ρ_{E_0}(\textbf{r,p}) = 0$ ? | 320 | 1,072 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.875 | 3 | CC-MAIN-2014-41 | latest | en | 0.807563 |
https://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/rlpplot.htm | 1,709,563,339,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947476452.25/warc/CC-MAIN-20240304133241-20240304163241-00740.warc.gz | 803,916,543 | 5,145 | Dataplot Vol 1 Vol 2
# ISO 13528 RLP PLOT
Name:
ISO 13528 RLP PLOT
Type:
Graphics Command
Purpose:
Given a response variable containing z-scores and associated variables containing laboratory id's and material id's, generate a plot of relative laboratory performance versus the rescaled sum.
Description:
One scenario for proficiency testing described in the ISO 13528 standard is for the case where there are multiple rounds of testing. Given the proficiency data
Z - a variable containing the response data in z-score units MATID - a variable containing the material-id which the plot is generated ROUNDID - a variable containing the round-id LABID - a variable containing the lab-id
For ISO 13528 multi-round proficiency studies, the relative laboratory performance (RLP) for a given laboratory with N z-scores (Zi) is defined as
$$\mbox{RLP} = \sqrt{ \frac{\sum_{i=1}^{N}{Z_{i}^{2}}} {\mbox{NMAT}}}$$
where NMAT is the number of materials. An RLP near 1 indicates average performance and an RLP greater than 1.5 indicates that the laboratory may be problematic. An advantage of this statistic is that z-scores of opposite sign do not cancel each other out. A disadvantage is that this statistic is suspectible to outliers in the z-scores.
The rescaled sum (RSZ) is defined as
$$\mbox{RSZ} = \frac{\sum_{i=1}^{N}{Z_{i}}} {\sqrt{N}}$$
So if there are k laboratories, the plot will consist of k points. For each laboratory, the RLP and RSZ are computed over all rounds and all materials. Note that the material id variable enters only in computing the number of distinct materials in the above formulas.
A value of RSZ greater than 2 or less than -2 flags a warning signal with regard to the laboratory. A value of RSZ greater than 3 or less than -3 flags an "action" signal (i.e., similar to an out-of-control signal from a control chart) with regard to the laboratory. An advantage of this statistic is that it has the same interpretation as a z-score. The disadvantage is that z-scores of opposite sign can cancel each other.
Laboratories where the RLP is greater than 1.5 and the |RSZ| > 2 are flagged as problematic. This command automatically defines a sub-region area based on this area. This is demonstrated in the Program example below.
The RSZ statistic is discussed in Thompson, Ellison, and Wood (2006). The RLP statistic is discussed in Uhlig and Lischer (1998).
The RLP and RSZ statistics are examples of combination scores (i.e., the statistic is a combination of many individual z-scores). Although the ISO 13528 standard recommends against using combination scores, these can be helpful in judging the overall performance of a laboratory. A useful way to use this plot is to identify laboratories that are potentially problematic. These laboratories can then be examined more carefully. For example: is the poor performance due to one or a few outliers? is the lab consistently high or consistently low? does the laboratory need to carefully examine their procedures?
Syntax:
ISO 13528 RLP PLOT <z> <labid> <matid>
<SUBSET/EXCEPT/FOR qualification>
where <z> is a response variable containing z-scores;
<labid> is a variable that specifies the lab-id;
<matid> is a variable that specifies the material-id;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
ISO 13528 RLP PLOT Z LABID MATID
Note:
It can be helpful to identify individual laboratories on this plot. You can optionally specify that certain points be labelled with their lab-id. You can use the following command to specify which points are labelled.
SET RLP PLOT LABELS <NONE/ALL/WARNING/ACTION>
where
NONE => no points are labelled ALL => all points are labelled WARNING => any point where the RLP > 1.5 or the |RSZ| > 2 are labelled ACTION => any point where the RLP > 1.5 or the |RSZ| > 3 are labelled
The default is none. The Program example below demonstrates the ACTION option. Note that you do not have to make any changes to the CHARACTER settings as Dataplot does this automatically. The CHARACTER OFFSET command can be helpful in this context (it is the CHARACTER OFFSET for the second trace that controls the positioning of the lables).
Note:
Some sources recommend capping the maximum value for the z-score when computing the RLP statistic.
To specify this value, enter the command
LET CAPVALUE = <value>
where <value> is typically 3 or 4. Note that the value represents an absolute value. For example, if CAPVALUE is 4, values greater than 4 will be set to 4 and values less than -4 will be set to -4.
Note:
The ISO 13528 standard defines a number of methods for computing the z-scores (enter HELP ISO 13528 ZSCORE, HELP ISO 13528 ZPRIME SCORE, and HELP ISO 13528 ZETA SCORE for details). For this reason, the ISO 13528 RLP PLOT command does not automatically compute the z-scores from the original response data.
Default:
None
Synonyms:
None
Related Commands:
ISO 13528 PLOT = Generate an ISO 13528 plot. ISO 13528 ZSCORE PLOT = Generate an ISO 13528 plot. ISO 13528 CONTROL CHART = Generate an ISO 13528 control chart. ISO 13528 ZSCORE = Compute z-scores as defined in the ISO 13528 standard. ISO 13528 ZPRIME SCORE = Compute z-prime scores as defined in the ISO 13528 standard. ISO 13528 ZETA SCORE = Compute zeta scores as defined in the ISO 13528 standard. CHARACTER = Sets the type for plot characters. LINE = Sets the type for plot lines.
References:
Uhlig and Lischer (1998), "Statistically-based Performance Characteristics in Laboratory Performance Studies", Analyst, 123, pp. 167-172.
ISO 13528 (2005), "Statistical Methods for use in proficiency testing by interlaboratory comparisons," First Edition, 2005-09-01.
Applications:
Multi-Round Proficiency Testing
Implementation Date:
2012/2
Program:
. Step 1: Read the data
.
dimension 40 columns
skip 25
read turner.dat labid z year quarter matid matave
let roundid = year
skip 0
.
. Step 2: Set plot control setting
.
case asis
title case asis
title offset 2
label case asis
y1label Relative Laboratory Performance
x1label Rescaled Sum
title ISO 13528 RLP Plot for TURNER.DAT
y1tic mark label decimal 1
xlimits -8 8
major xtic mark number 9
minor xtic mark number 1
x1tic mark offset 0 0
.
set rlp plot labels action
region fill on
region fill color g90
line blank
character circle
character hw 0.5 0.375
character fill on
character offset 0 0 2 0
.
. Step 3: Generate plot
.
iso 13528 rlp plot z labid matid
Date created: 02/18/2015
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http://blade.nagaokaut.ac.jp/cgi-bin/scat.rb/ruby/ruby-talk/239542 | 1,369,323,877,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368703532372/warc/CC-MAIN-20130516112532-00073-ip-10-60-113-184.ec2.internal.warc.gz | 24,892,971 | 2,510 | ```The three rules of Ruby Quiz:
1. Please do not post any solutions or spoiler discussion for this quiz until
48 hours have passed from the time on this message.
2. Support Ruby Quiz by submitting ideas as often as you can:
http://www.rubyquiz.com/
3. Enjoy!
Suggestion: A [QUIZ] in the subject of emails about the problem helps everyone
if you can.
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
by Brian Candler
A version of Bingo played in the UK and some other countries is called "Housie".
Players buy "books" of 6 tickets. Each ticket shows exactly 15 numbers, and in
each book every number from 1 to 90 is used exactly once.
A ticket is a grid of 3 rows by 9 columns. The first column contains numbers
from 1 to 9; the second column numbers from 10 to 19; the third 20 to 29 and so
on up until the last column, which contains numbers from 80 to 90.
Each column contains one, two or three numbers, in increasing order downwards.
Each row contains exactly 5 numbers (and hence 4 blanks).
An example ticket looks like this:
+----+----+----+----+----+----+----+----+----+
| 5 | | | | 49 | | 63 | 75 | 80 |
+----+----+----+----+----+----+----+----+----+
| | | 28 | 34 | | 52 | 66 | 77 | |
+----+----+----+----+----+----+----+----+----+
| 6 | 11 | | | | 59 | 69 | | 82 |
+----+----+----+----+----+----+----+----+----+
There are two levels of quiz difficulty to choose from. Given the above rules
for the validity of tickets and books, then:
1. Write a Ruby program which generates random individual tickets
or
2. Write a Ruby program which generates random complete books of tickets
``` | 464 | 1,679 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.65625 | 3 | CC-MAIN-2013-20 | latest | en | 0.882177 |
https://www.lsuagcenter.com/profiles/lblack/articles/page1591109561689 | 1,675,417,448,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764500044.66/warc/CC-MAIN-20230203091020-20230203121020-00645.warc.gz | 897,150,209 | 17,849 | # The Magic of Moo: Celebrating Dairy Month with Ice Cream
## Let's make ice cream to learn more abot the states of matter!
### Materials:
• Quart size plastic zip bags
• Gallon size plastic zip bags
•6 cups of ice
•½ cup half and half
•1 tablespoon sugar
• 1/2 teaspoon vanilla
• 8 tablespoons rock salt
### Activity:
1. Pour milk, sugar, and vanilla into a quart size plastic bag and seal tightly.
2. Fill a gallon size plastic bag half way with ice and pour in rock salt.
3. Place the quart size bag into the gallon size bag.
4. Shake the gallon size bag for approximately 16 minutes.
5. Observe how the ingredients move through various states of matter as you shake the bag.
### Scientific Phenomena:
Matter is defined as anything that has mass and takes up space. Matter is found in 3 major states; solid, liquid and gas. All matter is made of atoms. Atoms are the smallest particle of matter. They are so small that you cannot see them with your eyes or even with a standard microscope.
• Matter can move from one state to another, but can still be the same substance.
• A change of state, also called a phase change, is a physical change from one state of matter to another, for example, from solid to liquid or from liquid to gas.
• If the motion of the atoms is altered by pressure or temperature, the state of matter can change from one phase to another, too.
• In the activity the rock salt worked with the ice to lower the temperature of the liquid ice cream mixture. Because of the lower temperature, the ice cream mixture froze into a solid. Whether solid or liquid, the ice cream mixture ingredients/components remain the same.
• The more salt added, the lower the temperature will be before the salt-water solution freezes. For example, water will normally freeze at 32 degrees F. Heat must be absorbed by the ice for it to melt. The heat that causes the melting comes from the surroundings (the warmer cream mixture). By lowering the temperature at which ice is frozen, you were able to create an environment in which the cream mixture could freeze at a temperature below 32 degrees F into ice cream.
References:
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Topic: Matrices of rank at least k
Replies: 12 Last Post: Nov 29, 2012 1:15 PM
Messages: [ Previous | Next ]
quasi Posts: 12,067 Registered: 7/15/05
Re: Matrices of rank at least k
Posted: Nov 28, 2012 5:51 PM
Kaba wrote:
>quasi wrote:
>> Let m,n be positive integers, and let k be an integer with
>> 0 <= k <= min(m,n). The set T_k of m x n matrices of
>> rank <= k is easily seen to be closed since, for each k,
>> there is a polynomial P_k in m*n variables with real
>> coefficients such that an m x n matrix A with real entries
>> satisfies the condition rank(A) <= k iff the coefficients
>> of A satisfy P_k = 0. Regarding P_k as a function from
>> R^(mxn) to R, P_k is continuous, hence ((P_k)^(-1))(0)
>> is closed. It follows that T_k is closed for all k. In
>> particular, for each k, T_(k-1) is closed, and thus,
>> the set of matrices with rank >= k is open.
>
>Sounds good. But how to prove the existence of the
>polynomials P_k?
An m x n matrix A has rank <= k
iff some k x k submatrix of A has determinant 0,
iff the product of the determinants of all k x k
submatrices of A is equal to 0.
But the determinant of a square matrix is a polynomial in the
entries.
quasi
Date Subject Author
11/28/12 Kaba
11/28/12 Kaba
11/28/12 quasi
11/28/12 Kaba
11/28/12 quasi
11/28/12 quasi
11/28/12 quasi
11/28/12 Kaba
11/28/12 Kaba
11/29/12 Robin Chapman
11/29/12 Kaba
11/29/12 Carsten Schultz
11/29/12 W^3 | 510 | 1,625 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.328125 | 3 | CC-MAIN-2018-17 | latest | en | 0.893133 |
https://slidetodoc.com/attacking-and-defending-statistical-evidence-figures-dont-lie/ | 1,702,041,323,000,000,000 | text/html | crawl-data/CC-MAIN-2023-50/segments/1700679100745.32/warc/CC-MAIN-20231208112926-20231208142926-00403.warc.gz | 598,188,980 | 17,481 | # Attacking and Defending Statistical Evidence Figures dont lie
• Slides: 22
Attacking and Defending Statistical Evidence Figures don’t lie, but lairs figure! Then there is the man who drowned in a stream with an average depth of six inches.
Correlation and Causation
Storks and Babies
“Three men are in a bar. Each man earns \$50, 000. The average = per capita income in that bar is \$50, 000 In walks Bill Gates.
The Bill Gates Story ◦ The average income now is several million dollars. ◦ Notice that the 3 men are not any richer. ◦ The new average is a misleading statistic – true enough, but irrelevant to the situation of the 3 original barflies. “ ◦ A median of the incomes would be more accurate. � The MEAN is the arithmetic average, the average you are probably used to finding for a set of numbers - add up the numbers and divide by how many there are: (80 + 90 + 100 + 85 + 90) / 6 = 89 1/6. � The MEDIAN is the number in the middle. In order to find the median, you have to put the values in order from lowest to highest, then find the number that is exactly
Using unrepresentative sample sizes � In the debate about the death penalty, there was a marvelous card summarizing a study which purported to show that for every execution, there were 5 or so less murders in the following reporting periods.
Using unrepresentative sample sizes � The mathematics were sound, but the study was not. � Upon digging into the details of the survey, it turned out that there were very few jurisdictions carrying out executions, so there were very cases of executions followed by drops in murder rates. In fact, the studies conclusions were bases on 11 cases
Selective Time Frame ◦ The survey arbitrarily selects a time frame which proves the conclusion they were seeking to prove.
Selective Time Frame ◦ Debate example: �In the debate over the effects of laissezfaire economic policies (trickle down/ supply side policies) on economic growth. You draw examples from the period 19801985. It turns out that the economic downside of such policies did not become evident until after this time frame.
One or Many?
Many Or One? � Poverty causes crime. ◦ Most social phenomena have multiple complex causes. If you argue that only one cause is responsible for the phenomena, you are guilty of the single cause error. ◦ Without some story about causation this is simply the “correlation-causation” problem. With evidence, we have the problem of single causation. No everybody living in poverty turns to crime, so the burden is on the person presenting this claim to demonstrate how much of crime is caused by poverty, whether poverty is a primary cause or a secondary one, etc.
Suspicious/Inflated Data
Suspicious/Inflated Data � Flanked by Attorney General Alberto R. Gonzales, Bush said that "federal terrorism investigations have resulted in charges against more than 400 suspects, and more than half of those charged have been convicted. � An analysis of the Justice Department's own list of terrorism prosecutions by The Washington Post shows that 39 people -- not 200, as officials have implied -were convicted of crimes related to terrorism or national security. � Most of the others were convicted of relatively minor crimes such as making false statements and violating immigration law -- and had nothing to do with terrorism, the analysis shows. For the entire list, the median sentence was just 11 months.
Apples and Oranges � Frank Luntz on Fox News this morning: All the statistics that I've been testing on both sides, this one stands out: the increase in discretionary non-defense spending over the past four years is 80%. Does any family within the sound of my voice have an 80% increase in spending? � [april 2011] � How many families have a budget in the trillions, are responsible for keeping the whole economy going in a recession and paying the unemployed their unemployment insurance during a recession and the list goes on and on. � How many families cope with an economic downturn (unemployment , etc. ) by throwing grandma out , starving the kids, letting illnesses go untreated, getting rid of the dog or putting him to sleep etc. ?
� The Amazing Unqualified Stat 500 million people have been lifted from poverty largely as a result of freer trade and market reforms. ◦ How was this number arrived at? ◦ Was China part of the study? ◦ How much did free trade contribute to this outcome? How much did market reforms contribute? What kind of market reforms? ◦ Are we talking about absolute poverty or relative poverty? Did these people simply become working class or middle class or simply working poor? � If relative poverty, were the poor more able to take part in the life of the larger society? Protect themselves politically as a consequence of their increased status? ◦ What about the quality of life? � Were women and children required now to work full time to produce this outcome? � Did this growth produce a path to education and healthcare and other necessities for upward opportunities?
Apples and Oranges 2 � � � Anyway, this particular senator has been a steadfast critic of public schools, calling us inefficient and creating layer upon layer of bureaucracy to watch over us and micromanage everything we do. This session she has often repeated a dubious statistic about the "1 to-1 ratio" of teachers to non-teachers in Texas schools, and how that ratio was 4 -to-1 back in the 1970 s--never mind the fact that a. ) the state's statistics in the 1970 s didn't include lunch ladies, bus drivers, and other non-teachers, creating a false comparison, and b. ) the amount of bureaucratic nonsense and inflexible accountability measures piled on Texas schools beginning in the 1980 s has created countless man hours of reporting and testing paperwork and has led schools to hire testing coordinators, math coaches, parent involvement coordinators, etc. When this senator implies that the state of Texas is broke because superintendents like me just go wild hiring unnecessary nonteachers, it feels very much like I'm being slapped for doing what the senators forced me to do. I feel like public school officials are the Official Scapegoat of Texas. http: //blogs. edweek. org/teachers/living-indialogue/2011/03/i_am_educator_hear_me_roar_an. html
Responding to statistical evidence � � Just because a statement includes numbers or is based upon a statistical study does not mean that it is true. Many statistics are not based upon actual count For example counts of the number of homeless people are often draw from incomplete and questionable data. Even the unemployment statistics are projections based upon sampling techniques Even experts disagree on how to sample a statistical universe and over how to interpret what they find.
BEST Studies are Meta-Studies �Summaries of scholarly studies on the same topic, analyzed by another scholar �Know the methodology , the credentials of the authors, the sample size and how the sample was selected. �DON’T over claim the results!
Stats as Argument by Example �Arguments by example make a generalization about a class based upon an examination of limited numbers of that class. There are three common test argument by example. � 1) Are the examples typical of the class. � 2) Are there sufficient number of cases. � 3) Are negative instances accounted for? �
More Stats for Analysis � Wage Growth: � Average hourly compensation has risen by 3. 9% over the past year, while average weekly earnings have growth 4. 6%. � The Republican Playbook does not adjust for inflation. Here are the inflation-adjusted numbers. � According to the National Bureau of Economic Analysis, this expansion started in November 2001 when according to the Bureau of Labor Statistic the average hourly pay of nonsupervisory workers was \$14. 70. This figure was \$16. 62 in May of 2006 for an increase of 13. 06%. Over the same period, the inflation gage according to the Bureau of Labor Statistics increased from 177. 4 to 202. 5, or an increase of 14. 15%. Therefore, wages for nonsupervisory employees have decreased a little over 1% since this expansion began. � However, the unemployment rate dropped below 5% in December 2005, signaling "full employment". Has the decrease in labor supply increased wages? No. In December 2005 the average hourly wage of non-supervisory employees was \$16. 35. In May that number was \$16. 62 for an increase of 1. 65%. Over the same period, the overall inflation measure increased from 196. 8 to 202. 5 or an increase of 2. 89%. Therefore, since the economy hit "full employment" wages have decreased 1. 25%.
Attacking Stats 1 1. There are 4 suggestions on what to look for it in statistical studies. 2. Look for the original research report and study it. Those who use research report often put their own spin on the results. Finding copies of original research reports requires special effort. Consult footnotes in articles or books. Consult government agencies or congressional committees. Consult Social Science Citation Index. One can even try contacting the author of the report by e-mail or snail mail 3. 4. 5. 6. 7. 8.
Attacking Stats 2 1. 2. 3. 4. 5. � The original research report contains a section on methodology and one on interpretation or conclusions. In both sections one can find reservations about the meaning and scope of the study The section on conclusions or interpretations is often the most fruitful place for attacking a study. Here one finds inferences and value judgments. Sampling technique should be thoroughly examined. Since most statistical findings are based on studies of limited population the selection of the sample population is critically important. The same arguments one uses for evidence by example can be applied to these studies. | 2,112 | 9,785 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.90625 | 4 | CC-MAIN-2023-50 | latest | en | 0.957532 |
https://tw.tradingview.com/script/oLfDPBra-LWMA-Linear-Weighted-Moving-Average/ | 1,597,320,469,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738982.70/warc/CC-MAIN-20200813103121-20200813133121-00371.warc.gz | 541,996,298 | 59,458 | # LWMA: Linear Weighted Moving Average
691瀏覽
Couldn't find searching for Linearly Weighted Moving Average (LWMA) in tradingview. Found one with the LWMA title, but it uses plain WMA calculation without the linearity which more heavily weights recent price data, which I need, so I try to made one.
LWMAs are also quicker to react to price changes than SMA and EMA . If you want a moving average with less lag than an SMA , try a LWMA.
It kind of also have a more clarity in defining the price trend and reversals. Trade signals usually based on crossovers, they can also indicate areas of potential support or resistance. But beware though, multiple false signals may also occur before a significant trend develops. Use a filter, some decent volatility oscillator might do the job.
--
The formula for this Linearly Weighted Moving Average is:
LWMA = ((Pn∗W1)+(Pn−1∗W2)+(Pn−2∗W3)...) / ∑W
P = Price for the period
n = The most recent period, n-1 is the prior period, and n-2 is two periods prior
W = The assigned weight to each period, with the highest weight going first and then descending linearly based on the number of periods being used.
I hope I'm doing right translating it to Pine Script 4. Let me know if I miss something.
I just realized the native TV's WMA is already using the same linearity result, (maybe) using period value as the weight. So I added custom weight value parameter for this update and modified the function. By default it has a slight difference in plot result with the WMA even if period and weight has the same value.
I've read that most popular choice when using weighted moving averages is to use a higher weighting for recent values. I'm guessing that we can use much lower weight value if need contemporary or faster response (ie. intraday, binary, short-term), and higher weighting than the period for long-term confirmation, but both without losing context or moving away from our chosen lookback period span.
By default the WMA is using period value as its weight so when it reach the last price the weight is 1. A more complex way is to choose a different weight for the most recent value. Which this script trying to do about. Let's say we're using 50-period lookback, but I want the weight is only about half of it, maybe 30. Then each value will need to drop by 30/50 consecutively in each price data. So that when n-49(50th period) is reached the weight is also will be 1.
## 評論
Looks nice. I am not sure from your description if your intent was to recreate TradingView's wma() function, but your script's values match their native code.
allanster
@allanster, indeed. I just checked and this code has the same result than the native wma() function.
sickojacko
@sickojacko, updated :)
Now we can choose a different weight for the most recent value.
allanster
woow.. first thing first,.. @allanster, you're one of my PineScript hero! :D I've learnt a lot from many of your published script. Guess It's not everyday you got one of your hero as first commenter on your first post :)))
Thanks for the double-check, my bad. I was trying to recreate the LWMA I use in MT4. It has a slight differences with WMA in my backtest result. But looking back, probably it might also had something to do with my other filter, or maybe just the WMA I use is using different equation.
Anyway, I've added the custom weight value input for the above.
aerodynamics
@aerodynamics, thanks for the kind words and very nice to know I have helped someone else along the way.
aerodynamics
@aerodynamics, Thanks for this effort!
Can you please clarify if this final code is exactly replicating the LWMA indicator in MT4 values if i use here in TV? | 873 | 3,683 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 2.59375 | 3 | CC-MAIN-2020-34 | latest | en | 0.922696 |
https://www.islamicclimatedeclaration.org/lup4eznk/bebc26-poisson-distribution-derivation | 1,624,261,667,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488268274.66/warc/CC-MAIN-20210621055537-20210621085537-00100.warc.gz | 753,474,700 | 8,735 | Example . into n terms of (n)(n-1)(n-2)…(1). Let us take a simple example of a Poisson distribution formula. The probability of a success during a small time interval is proportional to the entire length of the time interval. As a first consequence, it follows from the assumptions that the probability of there being x arrivals in the interval (0,t+Δt]is (7) f(x,t+Δt)=f(x,t)f(0,Δt)+f(x−1,t) The larger the quantity of water I drink, the more risk I take of consuming bacteria, and the larger the expected number of bacteria I would have consumed. Calculating MLE for Poisson distribution: Let X=(x 1,x 2,…, x N) are the samples taken from Poisson distribution given by. We need two things: the probability of success (claps) p & the number of trials (visitors) n. These are stats for 1 year. To think about how this might apply to a sequence in space or time, imagine tossing a coin that has p=0.01, 1000 times. (n−k)!, and since each path has probability 1/2n, the total probability of paths with k right steps are: p = n! Before setting the parameter λ and plugging it into the formula, let’s pause a second and ask a question. Recall that the binomial distribution looks like this: As mentioned above, let’s define lambda as follows: What we’re going to do here is substitute this expression for p into the binomial distribution above, and take the limit as n goes to infinity, and try to come up with something useful. Consider the binomial probability mass function: (1) b(x;n,p)= n! Think of it like this: if the chance of success is p and we run n trials per day, we’ll observe np successes per day on average. So we’re done with our second step. So we know this portion of the problem just simplifies to one. We assume to observe inependent draws from a Poisson distribution. Below are some of the uses of the formula: In the call center industry, to find out the probability of calls, which will take more than usual time and based on that finding out the average waiting time for customers. Mathematically, this means n → ∞. It turns out the Poisson distribution is just a… When should Poisson be used for modeling? Derivation of the Poisson distribution. Hence $$\mathrm{E}[e^{\theta N}] = \sum_{k = 0}^\infty e^{\theta k} \Pr[N = k],$$ where the PMF of a Poisson distribution with parameter $\lambda$ is $$\Pr[N = k] = e^{-\lambda} \frac{\lambda^k}{k! In the above example, we have 17 ppl/wk who clapped. Now the Wikipedia explanation starts making sense. It suffices to take the expectation of the right-hand side of (1.1). The Poisson Distribution . How is this related to exponential distribution? In this lesson, we learn about another specially named discrete probability distribution, namely the Poisson distribution. The above derivation seems to me to be far more coherent than the one given by the sources I've looked at, such as wikipedia, which all make some vague argument about how very small intervals are likely to contain at most one As in the binomial distribution, we will not know the number of trials, or the probability of success on a certain trail. The idea is, we can make the Binomial random variable handle multiple events by dividing a unit time into smaller units. The observed frequencies in Table 4.2 are remarkably close to a Poisson distribution with mean = 0:9323. A better way of describing ( is as a probability per unit time that an event will occur. The average number of successes will be given for a certain time interval. Thus for Version 2.0, the number of inspections n in one hour tends to infinity, and the Binomial distribution finally tends to the Poisson distribution: (Image by Author ) Solving the limit to show how the Binomial distribution converges to the Poisson’s PMF formula involves a set of simple math steps that I won’t bore you with. In finance, the Poisson distribution could be used to model the arrival of new buy or sell orders entered into the market or the expected arrival of orders at specified trading venues or dark pools. Poisson distributions are used when we have a continuum of some sort and are counting discrete changes within this continuum. If the number of events per unit time follows a Poisson distribution, then the amount of time between events follows the exponential distribution. (27) To carry out the sum note first that the n = 0 term is zero and therefore 4 "Derivation" of the p.m.f. The Poisson distribution is named after Simeon-Denis Poisson (1781–1840). The Poisson distribution can be derived from the binomial distribution by doing two steps: substitute for p; Let n increase without bound; Step one is possible because the mean of a binomial distribution is . Internal Report SUF–PFY/96–01 Stockholm, 11 December 1996 1st revision, 31 October 1998 last modification 10 September 2007 Hand-book on STATISTICAL DISTRIBUTIONS for experimentalists by Christian Walck Particle * Sim´eon D. Poisson, (1781-1840). The Poisson Distribution. The Poisson Distribution was developed by the French mathematician Simeon Denis Poisson in 1837. The Poisson distribution is often mistakenly considered to be only a distribution of rare events. The average rate of events per unit time is constant. If we model the success probability by hour (0.1 people/hr) using the binomial random variable, this means most of the hours get zero claps but some hours will get exactly 1 clap. For example, sometimes a large number of visitors come in a group because someone popular mentioned your blog, or your blog got featured on Medium’s first page, etc. (Finally, I have noted that there was a similar question posted before (Understanding the bivariate Poisson distribution), but the derivation wasn't actually explored.) Why did Poisson have to invent the Poisson Distribution? So we’ve shown that the Poisson distribution is just a special case of the binomial, in which the number of n trials grows to infinity and the chance of success in any particular trial approaches zero. In a Poisson process, the same random process applies for very small to very large levels of exposure t. a. And in the denominator, we can expand (n-k) into n-k terms of (n-k)(n-k-1)(n-k-2)…(1). • The Poisson distribution can also be derived directly in a manner that shows how it can be used as a model of real situations. µ 1 ¡1 C 1 2! :), Hands-on real-world examples, research, tutorials, and cutting-edge techniques delivered Monday to Thursday. Because it is inhibited by the zero occurrence barrier (there is no such thing as “minus one” clap) on the left and it is unlimited on the other side. }, \quad k = 0, 1, 2, \ldots.$$ share | cite | improve this answer | follow | answered Oct 9 '14 at 16:21. heropup heropup. This is equal to the familiar probability density function for the Poisson distribution, which gives us the probability of k successes per period given our parameter lambda. Proportional to the right amongst n total steps is: n! / ( ( n-k ) parameter.... Over time or on some object in non-overlapping intervals are independent note that There are possible... Examples, research, tutorials, and that randomly distributed in that vat are....: n! / ( ( n-k ) pretty interesting relationship = ( dt ( 3 ) where dp the. Of how I ’ d like to predict the # of people who read my blog per week non-overlapping... Turn up a long sequence of Poisson random variable is the number of per! Week because I get paid weekly by those numbers must be taken when translating a rate successes. Invent this ) follows a Poisson distribution into smaller units which is equal to one of. So another way of describing ( is as a limiting case of the time is. Binomial distribution and the Poisson distribution is the number of arrivals per unit time is constant of! Derivations of the Poisson distribution equation, which is of a stochastic process described somewhat informally as follows cite improve... Event in a given interval cancel out 24 ) = 0.1 people per... You are able to observe the first step to one function of a Poisson process terms n /! 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https://en.m.wikisource.org/wiki/Translation:On_the_Principle_of_Doppler | 1,653,221,801,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662545326.51/warc/CC-MAIN-20220522094818-20220522124818-00391.warc.gz | 294,013,629 | 35,329 | # Translation:On the Principle of Doppler
On the Principle of Doppler (1887)
by Woldemar Voigt, translated from German by Wikisource
In German: Ueber das Doppler’sche Princip, Göttinger Nachrichten, 1887 (2): 41-51. Session from January 8, 1887. Published March 10, 1887
On the Principle of Doppler.
By
W. Voigt.
It is known that the differential equations for the oscillations of an elastic incompressible medium read:
${\displaystyle {\frac {\partial ^{2}u}{dt^{2}}}=\omega ^{2}\Delta u}$ ${\displaystyle {\frac {\partial ^{2}v}{dt^{2}}}=\omega ^{2}\Delta v}$ ${\displaystyle {\frac {\partial ^{2}w}{dt^{2}}}=\omega ^{2}\Delta w}$ 1)
where ω is the propagation velocity of the oscillations - or more precisely the propagation velocity of plane waves with constant amplitude. It is presupposed that u, v, w fulfill the relation:
${\displaystyle {\frac {\partial u}{\partial x}}+{\frac {\partial v}{\partial y}}+{\frac {\partial w}{\partial z}}=0.}$ 1')
Now let u = U, v = V, w = W be solutions of these equations, which on a given surface ${\displaystyle f({\bar {x}},{\bar {y}},{\bar {z}})=0}$ adopt given values ${\displaystyle {\bar {U}}}$, ${\displaystyle {\bar {V}}}$, ${\displaystyle {\bar {W}}}$ which depend on time, then we can say that these functions U, V, W represent the law by which the surface f = 0 is illuminating.
If we substitute in ${\displaystyle U,V,W,}$ respectively,
${\displaystyle {\begin{array}{l}x{\text{ by }}\xi =xm_{1}+yn_{1}+zp_{1}-\alpha t\\y{\text{ by }}\eta =xm_{2}+yn_{2}+zp_{2}-\beta t\\z{\text{ by }}\xi =xm_{3}+yn_{3}+zp_{3}-\gamma t\\t{\text{ by }}\tau =t-(ax+by+cz)\\\end{array}}}$ 2)
and describe the resulting functions, respectively, with (U), (V), (W), then by u = (U), v = (V), w = (W) it is possible to comply with (1). [AU 1]
For example, we obtain for the first of them:
${\displaystyle {\frac {\partial ^{2}(U)}{\partial \tau ^{2}}}\left(1-\omega ^{2}\left(a^{2}+b^{2}+c^{2}\right)\right)=\omega ^{2}\left\{{\frac {\partial ^{2}(U)}{\partial \xi ^{2}}}\left(m_{1}^{2}+n_{1}^{2}+p_{1}^{2}-{\frac {\alpha ^{2}}{\omega ^{2}}}\right)\right.}$
${\displaystyle +{\frac {\partial ^{2}(U)}{\partial \eta ^{2}}}\left(m_{2}^{2}+n_{2}^{2}+p_{2}^{2}-{\frac {\beta ^{2}}{\omega ^{2}}}\right)+{\frac {\partial ^{2}(U)}{\partial \zeta ^{2}}}\left(m_{3}^{2}+n_{3}^{2}+3_{3}^{2}-{\frac {\gamma ^{2}}{\omega ^{2}}}\right)}$
${\displaystyle +2{\frac {\partial ^{2}(U)}{\partial \eta \ \partial \zeta }}\left(m_{2}m_{3}+n_{2}n_{3}+p_{2}p_{3}-{\frac {\beta \gamma }{\omega ^{2}}}\right)}$
${\displaystyle +2{\frac {\partial ^{2}(U)}{\partial \zeta \ \partial \xi }}\left(m_{3}m_{1}+n_{3}n_{1}+p_{3}p_{1}-{\frac {\gamma \alpha }{\omega ^{2}}}\right)}$
${\displaystyle +2{\frac {\partial ^{2}(U)}{\partial \xi \ \partial \eta }}\left(m_{1}m_{2}+n_{1}n_{2}+p_{1}p_{2}-{\frac {\alpha \beta }{\omega ^{2}}}\right)}$
${\displaystyle -2{\frac {\partial ^{2}(U)}{\partial \tau \ \partial \xi }}\left(am_{1}+bn_{1}+cp_{1}-{\frac {\alpha }{\omega ^{2}}}\right)}$
${\displaystyle -2{\frac {\partial ^{2}(U)}{\partial \tau \ \partial \eta }}\left(am_{2}+bn_{2}+cp_{2}-{\frac {\beta }{\omega ^{2}}}\right)}$
${\displaystyle \left.-2{\frac {\partial ^{2}(U)}{\partial \tau \ \partial \zeta }}\left(am_{3}+bn_{3}+cp_{3}-{\frac {\gamma }{\omega ^{2}}}\right)\right\}}$
and this is fulfilled, because it indeed has to be:
${\displaystyle {\frac {\partial ^{2}(U)}{\partial \tau ^{2}}}=\omega ^{2}\left({\frac {\partial ^{2}(U)}{\partial \xi ^{2}}}+{\frac {\partial ^{2}(U)}{\partial \eta ^{2}}}+{\frac {\partial ^{2}(U)}{\partial \zeta ^{2}}}\right),}$
if there exist the following new equations:
${\displaystyle {\begin{array}{rl}1-\omega ^{2}(a^{2}+b^{2}+c^{2})&=m_{1}^{2}+n_{1}^{2}+p_{1}^{2}-{\frac {\alpha ^{2}}{\omega ^{2}}}\\&=m_{2}^{2}+n_{2}^{2}+p_{2}^{2}-{\frac {\beta ^{2}}{\omega ^{2}}}\\&=m_{3}^{2}+n_{3}^{2}+p_{3}^{2}-{\frac {\gamma ^{2}}{\omega ^{2}}}\end{array}}}$ 3)
${\displaystyle {\frac {\beta \gamma }{\omega ^{2}}}=m_{2}m_{3}+n_{2}n_{3}+p_{2}p_{3}}$ ${\displaystyle {\frac {\gamma \alpha }{\omega ^{2}}}=m_{3}m_{1}+n_{3}n_{1}+p_{3}p_{1}}$ ${\displaystyle {\frac {\alpha \beta }{\omega ^{2}}}=m_{1}m_{2}+n_{1}n_{2}+p_{1}p_{2}}$ 4)
${\displaystyle {\frac {\alpha }{\omega ^{2}}}=am_{1}+bn_{1}+cp_{1}}$ ${\displaystyle {\frac {\beta }{\omega ^{2}}}=am_{2}+bn_{2}+cp_{2}}$ ${\displaystyle {\frac {\gamma }{\omega ^{2}}}=am_{3}+bn_{3}+cp_{3}}$ 5)
If we take ${\displaystyle \alpha \beta \gamma }$ as given, then we have 12 constants available, so we can arbitrarily use three of them.
The solution is most comfortable when we use a temporary co-ordinate system X1, Y1, Z1, for which β and γ disappear in equations (2), α is equal to ϰ, that is, a co-ordinate system whose X1-axis falls in the direction, of which the direction cosine is proportional to X, Y, Z with α, β, γ.
Furthermore, it should be set
${\displaystyle {\begin{array}{clcclcclcclc}m_{h}^{2}+n_{h}^{2}+p_{h}^{2}&=&q_{h}^{2},&m_{h}/q_{h}&=&\mu _{h},&n_{h}/q_{h}&=&\nu _{h},&p_{h}/q_{h}&=&\pi _{h}\\\\a^{2}+b^{2}+c^{2}&=&d^{2},&a/d&=&\mu ,&b/d&=&\nu ,&c/d&=&\pi ,\end{array}}}$
then μ, ν, π are the direction cosines of 4 directions, which we will denote by δ1, δ2, δ3 and δ, against the system X1, Y1, Z1.
By these introductions our equations (3), (4) and (5) will be:
${\displaystyle 1-\omega ^{2}d^{2}=q_{1}^{2}-{\frac {\varkappa ^{2}}{\omega ^{2}}}=q_{2}^{2}=q_{3}^{2}}$ 3')
${\displaystyle \mu _{2}\mu _{3}+\nu _{2}\nu _{3}+\pi _{2}\pi _{3}=\mu _{3}\mu _{1}+\nu _{3}\nu _{1}+\pi _{3}\pi _{1}=\mu _{1}\mu _{2}+\nu _{1}\nu _{2}+\pi _{1}\pi _{2}=0}$
${\displaystyle {\text{that is }}\cos(\delta _{2},\delta _{3})=\cos(\delta _{3},\delta _{1})=\cos(\delta _{1},\delta _{2})=0}$ 4')
${\displaystyle \mu \mu _{1}+\nu \nu _{1}+\pi \pi _{1}={\frac {\varkappa }{\omega ^{2}q_{1}d}},\ \mu \mu _{2}+\nu \nu _{2}+\pi \pi _{2}+\mu \mu _{3}+\nu \nu _{3}+\pi \pi _{3}=0}$
${\displaystyle {\text{that is }}\cos(\delta ,\delta _{1})={\frac {\varkappa }{\omega ^{2}q_{1}d}},\ \cos(\delta ,\delta _{2})=\cos(\delta ,\delta _{3})=0.}$ 5')
According to (4'), the three directions δ1, δ2, δ3 are perpendicular to each other, according to (5') ${\displaystyle \delta _{1}}$ falls into δ, then it must be:
${\displaystyle \mu =\mu _{1},\ \nu =\nu _{1},\ \pi =\pi _{1}\ {\text{ and }}\ {\frac {\varkappa }{\omega ^{2}q_{1}d}}=1.}$ 6)
Substituting this in (3'), q1, q2, q3 are determined.
At first we obtain, since only positive signs are meaningful:
${\displaystyle q_{1}=1{\text{ or }}{\frac {\varkappa }{\omega }}}$ ${\displaystyle d={\frac {\varkappa }{\omega ^{2}}}{\text{ or }}{\frac {1}{\omega }}.}$
I will only use the first solution, the second is of no interest;[1] it follows from it:
${\displaystyle d={\frac {\varkappa }{\omega ^{2}}},\ q_{1}=1,\ q_{2}=q_{3}={\sqrt {1-{\frac {\varkappa ^{2}}{\omega ^{2}}}}}=q.}$ 7)
Consequently, we can write equations (2):
{\displaystyle {\begin{aligned}\xi _{1}&=x_{1}\mu _{1}+y_{1}\nu _{1}+z_{1}\pi _{1}-\varkappa t&&=a_{1}-\varkappa t\\\eta _{1}&=\left(x_{1}\mu _{2}+y_{1}\nu _{2}+z_{1}\pi _{2}\right)q&&=b_{1}q\\\zeta _{1}&=\left(x_{1}\mu _{3}+y_{1}\nu _{3}+z_{1}\pi _{3}\right)q&&=c_{1}q\\\tau &=t-{\frac {\varkappa }{\omega ^{2}}}(\mu _{1}x+\nu _{1}y+\pi _{1}z)&&=t-{\frac {\varkappa a_{1}}{\omega ^{2}}}{,}\end{aligned}}} 8)
where for μh, νh, πh no more other conditions apply than those which result from their meaning as direction cosines of three successive perpendicular but otherwise quite arbitrary directions.
Therefore, the aggregates designated by ${\displaystyle a_{1}\ b_{1}\ c_{1}}$ can be considered as the coordinates of the point ${\displaystyle x_{1}\ y_{1}\ z_{1}}$ in relation to a coordinate system, which falls into the direction ${\displaystyle \delta _{1}\ \delta _{2}\ \delta _{3}}$.
Any such system μh, νh, πh gives a solution (U), (V), (W) from given U, V, W. If U, V, W adopt on a surface f(x, y, z) = 0 the given values ${\displaystyle {\overline {U}}}$, ${\displaystyle {\overline {V}}}$, ${\displaystyle {\overline {W}}}$, so (U), (V), (W) from those derivable ${\displaystyle ({\overline {U}}),({\overline {V}}),({\overline {W}})}$ to the surface ${\displaystyle (f)=f({\overline {\xi _{1}}},{\overline {\eta _{1}}},{\overline {\zeta _{1}}})=0}$, which because of the values of ξ1, η1, ζ1 has the property to move with uniform velocity ϰ parallel to a direction δ1 or A given by direction cosines ϰ. The solutions (U), (V), (W) give thus the laws by which certain surfaces in progressive motion are shining, if they only comply with the condition
${\displaystyle {\frac {(\partial U)}{\partial x}}+{\frac {\partial (V)}{\partial y}}+{\frac {\partial (W)}{\partial z}}=0}$
The two surfaces f = 0 and (f) = 0 have identical forms only if q = 1, i.e. ϰ is so small against ω, that ϰ² can be neglected with respect to ω². If this is the case, then they differ only by their position against the coordinate axes. By appropriate use of the arbitrary constants and the functions U, V, W we can obtain vivid special cases. By coordinate transformation we are lead to a (at least formally) general case, in which the shift of the surface is not parallel to the A-axis parallel, but directed in an arbitrary way.
We follow the special case, in which the three directions δ1, δ2, δ3 fall into the coordinate axes X1, Y1, Z1, that is
${\displaystyle \mu _{1}=\nu _{2}=\pi _{3}=1{,}}$ ${\displaystyle \mu _{2}=\mu _{3}=\nu _{1}=\nu _{2}=\pi _{1}=\pi _{3}=0}$ 9)
Then it is given, in a very simple and natural way, and formally identical with (8):
{\displaystyle {\begin{aligned}\xi _{1}&=x_{1}-\varkappa t\\\eta _{1}&=y_{1}q\\\zeta _{1}&=z_{1}q\\\tau &=t-{\frac {\varkappa x_{1}}{\omega ^{2}}}{,}{\text{ where }}q={\sqrt {1-{\frac {\varkappa ^{2}}{\omega ^{2}}}}}\end{aligned}}}[AU 2] 10)
The condition (1') is in this case
${\displaystyle (1-q){\frac {\partial (U)}{\partial \xi }}={\frac {\varkappa }{\omega ^{2}}}{\frac {\partial (U)}{\partial \tau }}}$
which can easily be exchanged with
${\displaystyle (1-q){\frac {\partial U}{\partial x}}={\frac {\varkappa }{\omega ^{2}}}{\frac {\partial U}{\partial t}}.}$ 10')
This states, that in U the arguments x and t only may occur in connection with ${\displaystyle (1-q)t+{\frac {\varkappa x}{\omega ^{2}}}}$, or not at all. The latter is the case if U = 0, that is, when the propagated vibrations are everywhere normal to the direction of translation of the illuminating surface.
If we pass from the assumed special co-ordinate system X1, Y1, Z1 to the general X, Y, Z, which is connected with the preceding by the relations
${\displaystyle x_{1}=x\alpha _{1}+y\beta _{1}+z\gamma _{1}}$ ${\displaystyle y_{1}=x\alpha _{2}+y\beta _{2}+z\gamma _{2}}$ ${\displaystyle z_{1}=x\alpha _{3}+y\beta _{3}+z\gamma _{3},}$ 11)
we finally get
{\displaystyle {\begin{aligned}\xi &=xq+(x\alpha _{1}+y\beta _{1}+z\gamma _{1})\alpha _{1}(1-q)-\varkappa \alpha _{1}t\\\eta &=yq+(x\alpha _{1}+y\beta _{1}+z\gamma _{1})\beta _{1}(1-q)-\varkappa \beta _{1}t\\\zeta &=zq+(x\alpha _{1}+y\beta _{1}+z\gamma _{1})\gamma _{1}(1-q)-\varkappa \gamma _{1}t\\\tau &=t-{\frac {\varkappa }{\omega ^{2}}}(x\alpha _{1}+y\beta _{1}+z\gamma _{1}).\end{aligned}}} 12)
This is the general form (2) from which we started, but with constants entirely defined by ${\displaystyle \varkappa }$, \${\displaystyle alpha_{1}}$, ${\displaystyle \beta _{1}}$, ${\displaystyle \gamma _{1}}$, it contains what is usually understood by the principle of Doppler, so far it is true.
If it is possible to neglect ϰ² next to ω², then q = 1 and we very simply obtain:
{\displaystyle {\begin{aligned}\xi &=x-\varkappa \alpha _{1}t\\\eta &=y-\varkappa \beta _{1}t\\\zeta &=z-\varkappa \gamma _{1}t\\\tau &=t-{\frac {\varkappa }{\omega ^{2}}}(x\alpha _{1}+y\beta _{1}+z\gamma _{1}).\end{aligned}}} 13)
The condition (1') is in this case:
${\displaystyle 0={\frac {\varkappa }{\omega ^{2}}}{\frac {\partial }{\partial t}}\left(U\alpha _{1}+V\beta _{1}+W\gamma _{1}\right)}$ 13')
and with the assumed negligence it is only to the extent necessary to be fulfilled, that the term, which is multiplied in ${\displaystyle {\frac {\varkappa }{\omega }}}$, is of the first order.
If, besides the illuminating surface, the observer is also in motion, such as with the constant velocity ϰ' in a direction given by the direction cosines α', β ', γ', then the displacements u, v, w,, which are only related to a coordinate system X', Y', Z' moving with the observer, i.e., we must replace in (12) or (13) ${\displaystyle x}$ by ${\displaystyle x'+\varkappa '\alpha 't}$, ${\displaystyle y}$ by ${\displaystyle y'+\varkappa '\beta 't}$, ${\displaystyle z}$ by ${\displaystyle z'+\varkappa '\gamma 't}$.
With those findings we give some applications.
1) Let a plane parallel to the YZ-plane be set in vibrations in accordance with the law
${\displaystyle {\overline {W}}=A\sin {\frac {2\pi t}{T}}{,}}$
then the motion propagated in positive X-axis is given by:
${\displaystyle W=A\sin {\frac {2\pi }{T}}\left(t-{\frac {x}{\omega }}\right).}$
Herein, we make the substitution according to (10), than we have
${\displaystyle (W){=}A\sin {\frac {2\pi }{T}}\left(1-{\frac {\varkappa }{\omega }}\right)\left(t-{\frac {x}{\omega }}\right).}$
This gives for x = ϰt:
${\displaystyle ({\overline {W}})=A\sin {\frac {2\pi t}{T}}\left(1-{\frac {\varkappa ^{2}}{\omega ^{2}}}\right)=A\sin {\frac {2\pi t}{T'}}{,}}$ 14')
thus we have an illuminating plane (moving parallel to the X-axes), which oscillates with a wave-length ${\displaystyle \textstyle {T'=T/\left(1-{\frac {\varkappa ^{2}}{\omega ^{2}}}\right)}}$ (only different of the second order of T). The propagated oscillation can be written:
${\displaystyle (W)=A\sin {\frac {2\pi }{T'\left(1-{\frac {\varkappa }{\omega }}\right)}}\left(t-{\frac {x}{\omega }}\right).}$ 14)
Thus we get, within the propagated wave, a reduced period of oscillation in the relation of ${\displaystyle \left(1-{\frac {\varkappa }{\omega }}\right)/1}$.
Is the observer is in motion as well, then:
${\displaystyle (W'){=}A\sin {\frac {2\pi }{T'\left(1-{\frac {\varkappa }{\omega }}\right)}}\left(t-{\frac {x'+\varkappa 't}{\omega }}\right)}$
${\displaystyle {=}A\sin 2\pi \left(t{\frac {(\omega +\varkappa '}{T'(\omega -\varkappa )}}-{\frac {x'}{T'(\omega -\varkappa )}}\right).}$
This formula gives the principle of Doppler for plane waves. But it is in no way universal, but essentially presupposes a plane wave with constant amplitude throughout.
2) The same plane is to be set in oscillation by the law:
${\displaystyle {\overline {W}}{=}Ae^{(\mu y+\nu z){\frac {2\pi }{T\omega }}}\sin {\frac {2\pi t}{T}}}$
- as it similar occurs when a wave with initially constant amplitude travels through a prism of an absorbing substance - then for the propagated wave it is given:
${\displaystyle W{=}Ae^{\frac {2\pi (\mu y+\nu z)}{T\omega }}\sin {\frac {2\pi }{T}}\left(t-{\frac {x\sigma }{\omega }}\right){\text{ where }}\sigma {=}{\sqrt {1+\mu ^{2}+\nu ^{2}}}.}$
If we substitute according to (10), it is, if ${\displaystyle \textstyle {{\sqrt {1-{\frac {\varkappa ^{2}}{\omega ^{2}}}}}=q}}$ is set:
${\displaystyle (W){=}Ae^{\frac {2\pi (\mu y+\nu z)q}{T\omega }}\sin {\frac {2\pi }{T}}\left[t\left(1+{\frac {\varkappa \sigma }{\omega }}\right)-x\left({\frac {\sigma }{\omega }}+{\frac {\varkappa }{\omega ^{2}}}\right)\right].}$
This gives for x = ϰt, if we write ${\displaystyle {\frac {\mu }{q}}=\mu '}$, ${\displaystyle {\frac {\nu }{q}}=\nu '}$:
${\displaystyle ({\overline {W}}){=}Ae^{\frac {2\pi (\mu 'y+\nu 'z)}{\omega T'}}\sin {\frac {2\pi t}{T}}{\text{, where }}T'{=}{\frac {T}{1-{\frac {\varkappa ^{2}}{\omega ^{2}}}}},}$
thus we have an oscillating and at the same time propagating plane; however, the propagated displacement reads:
${\displaystyle (W)=Ae^{\frac {2\pi (\mu 'y+\nu 'z)}{\omega T'}}\sin {\frac {2\pi t}{T}}\left(t{\frac {1+{\frac {\varkappa \sigma }{\omega }}}{1-{\frac {\varkappa ^{2}}{\omega ^{2}}}}}-x{\frac {{\frac {\sigma }{\omega }}+{\frac {\varkappa }{\omega ^{2}}}}{1-{\frac {\varkappa ^{2}}{\omega ^{2}}}}}\right){,}}$ 15)
where we now have ${\displaystyle \sigma ={\sqrt {1+(\mu ^{'2}+\nu ^{'2})q^{2}}}}$.
We notice that different laws as the Doppler principle are given, even if we limit ourselves to the first approximation, and ϰ²ω² is neglected compared to 1.
3) If the illuminating surface is a very small[AU 3] sphere of radius R, which oscillates according to the law for the rotation angle
${\displaystyle {\overline {\psi }}{=}A\sin {\frac {2\pi t}{T}}}$
around the X-axis, then, at the distance ${\displaystyle r={\sqrt {x^{2}+y^{2}+z^{2}}}}$ from the center of the sphere, the propagated rotations ψ are given by[2][AU 4]
${\displaystyle \psi ={\frac {R^{3}A}{r^{3}}}\left[\sin {\frac {2\pi }{T}}\left(t-{\frac {r-R}{\omega }}\right)+{\frac {2\pi (r-R)}{T\omega }}\cos {\frac {2\pi }{T}}\left(t-{\frac {r-R}{\omega }}\right)\right]}$ ${\displaystyle ={\frac {R^{3}A}{r^{3}}}{\sqrt {1+\left({\frac {2\pi (r-R)}{T\omega }}\right)^{2}}}\cos {\frac {2\pi }{T}}\left(t-{\frac {r-R}{\omega }}-\eta \right){,}}$ 16)
where
${\displaystyle {\frac {2\pi (r-R)}{T\omega }}{=}\operatorname {ctg} {\frac {2\pi \eta }{T}}}$
is set. It is therefore ${\displaystyle \textstyle {\eta ={\frac {T}{4}}}}$ for r = R and η = 0m if r is very great compared with the wavelength Tω.
The propagated displacements follow from ψ by:
${\displaystyle U{=}0,\ V=-\psi z,\ W=\psi y;}$
we briefly set
${\displaystyle U{=}0,\ V=MC,\ W=NC.}$
Substituting herein for x, y, z, the values ξ, η, ζ according to (10), then the periodic part C is given by:
${\displaystyle (C)=\cos {\frac {2\pi }{T}}\left(t-{\frac {\varkappa x}{\omega ^{2}}}-{\frac {1}{\omega }}\left({\sqrt {(x-\varkappa t)^{2}+y^{2}+z^{2}}}-R\right)-(\eta )\right){,}}$ 17)
if ${\displaystyle \operatorname {cotg} {\frac {2\pi (\eta )}{T}}{=}{\frac {2\pi }{T\omega }}\left({\sqrt {(x-\varkappa t)^{2}+y^{2}+z^{2}}}-R\right)}$
For ${\displaystyle (x-\varkappa t)^{2}+y^{2}+z^{2}=R^{2}}$, i.e., on the surface of a sphere which is displaced parallel to the X-axis, this becomes
${\displaystyle ({\overline {C}}){=}\sin {\frac {2\pi }{T}}\left(t\left(1-{\frac {\varkappa ^{2}}{\omega ^{2}}}\right)-{\frac {\varkappa }{\omega ^{2}}}{\sqrt {R^{2}-y^{2}-z^{2}}}\right),}$
thus, since under the assumption ${\displaystyle \textstyle {\frac {\varkappa ^{2}}{\omega ^{2}}}}$ and ${\displaystyle \textstyle {\frac {\varkappa R}{\omega ^{2}}}}$ of second-order it follows:
${\displaystyle ({\overline {C}}){=}\sin {\frac {2\pi t}{T}}.}$
(M) and (N) have the same value, as if the little sphere would oscillate as a state of equilibrium around the attained position ${\displaystyle x_{0}=\varkappa t}$ at time t. Therefore, by (U), (V), (W) we get the motion that was submitted by a rotating "illuminating point" with translational speed ${\displaystyle \varkappa }$ parallel to the direction of the rotation axis.
The propagated wave surfaces are assessed according to the value (17) for (C), which can be written by introduction of relative coordinates against the moving luminous point ${\displaystyle \xi =x-\varkappa t}$, ${\displaystyle y=\eta }$, ${\displaystyle z=\zeta }$ (neglecting ${\displaystyle \textstyle {\frac {\varkappa ^{2}}{\omega ^{2}}}}$ against 1) and for r which is great against ${\displaystyle T\omega }$:
${\displaystyle (C){=}\cos {\frac {2\pi }{T}}\left(t-{\frac {\varkappa \xi }{\omega ^{2}}}-{\frac {1}{\omega }}\left({\sqrt {\xi ^{2}+\eta ^{2}+\zeta ^{2}}}-R\right)\right).}$
The wave surfaces are thus spheres, but not around the illuminating point, but constructed around a center, which location is far off by the ${\displaystyle {\frac {\varkappa }{\omega }}}$ part of their radii to the opposite direction of motion.
Therefore, a stationary observer, since the perpendicular to the wave surface through the location of observation gives the direction in which the light source is to be perceived, would see the illuminating point at the location where it was at time ${\displaystyle {\frac {r}{\omega }}}$, in other words; he would observe, if his radius vector r includes the angle ${\displaystyle \phi }$ with the direction of motion, an "aberration" of the size ${\displaystyle {\frac {r}{\omega }}\ \sin \varphi }$ in the direction opposite to the motion of the point.
Concerning the propagated amplitudes (M) and (N), according to the above they have, at position ${\displaystyle x\ y\ z}$ at time t, those values as if the illuminating point permanently remained at the attained position at this time t, whereas the wave surface in ${\displaystyle x\ y\ z}$ has the form, as if the illuminating point would remain at the attained location at time ${\displaystyle \textstyle {t-{\frac {r}{\omega }}}}$. So, the wave area and amplitude are not connected in the sense of a stationary illuminating point, because the latter depends on the present position, the former depends on an abandoned position of the illuminating point.
Thus, the peculiar result is given that such a moving illuminating point of constant intensity, which at time t has the distance r from the observer, is seen by him in that position, which he attained at time ${\displaystyle {\frac {r}{\omega }}}$, but with the intensity that corresponds to the current (larger or smaller) distance.[AU 5]
The applicability of the above general considerations on the problems of optics is limited by the constraint (1'), which has lead to the formulas (10') and (13').
Such a limitation does not take place in the analogous problems of the acoustics of fluids. For the propagated dilation δ we have as the only condition
${\displaystyle {\frac {\partial ^{2}\delta }{\partial t^{2}}}{=}\omega ^{2}\Delta \delta .}$
The introduction of the substitutions (10), (12) or (13) always gives, if δ is given by the constraints along a given surface as an arbitrary function of time, the transition from the effect of a stationary source to the effect when it is in translational motion.
If, for example, we have ${\displaystyle {\overline {\delta }}=f(t)}$ on a very small sphere of radius R, then the propagated dilation is given by:
${\displaystyle \delta {=}{\frac {R}{r}}f\left(t-{\frac {r-R}{\omega }}\right).}$
}
The substitution (10) gives the influence of a translation of a "sounding" sphere parallel to the X-axis. The discussion of the result is equivalent to that employed under 3).
1. It follows from it ${\displaystyle q_{2}=q_{3}=0}$, as well as ${\displaystyle m_{2}\ n_{2}\ p_{2}}$, ${\displaystyle m_{3}\ n_{3}\ p_{3}}$ and therefore ${\displaystyle \zeta =\eta =0}$
2. W. Voigt, Crelles Journ. Vol. 89, 298.
## Notes by the author (1915)
From the reprint in: Physikalische Zeitschrift (1915), 16, 381-385 Online
The anniversary of the principle of relativity causes the editors to present an almost forgotten predecessor to the readers of the Physikalische Ztschrift. Indeed, in this note from the Nachr. d. Kgl. Ges. d. Wiss. zu Göttingen, meeting of 3. January 1887, the fundamental transformation of the optical differential equation was clearly formulated. Only the supplements (indicated by brackets) were added to this reprint by the author.
1. Due to the same order of all parts of equations (1), the right-hand sides of the substitution formulas (2) can be multiplied by a common factor, without changing the results.
2. This is, except the factor q which is irrelevant for the application, exactly the Lorentz transformation of the year 1904.
3. This will be made more precise, so that the radius should be small compared to the wave-length. Yet the formulas (16) and (17) don't require this assumption:
4. There one also finds the laws for the emission of a linearly oscillating sphere, which allows the same way of use.
5. The subsequent continuation of such problems didn't happen at that time, due to the physical difficulty of a complete realization of the presuppositions of this work - the translation of oscillating surfaces or bodies within the medium that transmits the oscillations - in the field of elasticity. This problem doesn't exist in the field of Lorentz's electrodynamics, in which the aether is extended through all ponderable bodies, and the latter is admitted to be freely movable within the first; therefore, the application of the method explained above is much more suitable for it. Indeed, the sphere problems explained above by an example, have the closest relation to the problem of the oscillating and simultaneously progressive electron, that became important many years after the preceding work.
This work is a translation and has a separate copyright status to the applicable copyright protections of the original content.
Original: This work was published before January 1, 1927, and is in the public domain worldwide because the author died at least 100 years ago. This work is released under the Creative Commons Attribution-ShareAlike 3.0 Unported license, which allows free use, distribution, and creation of derivatives, so long as the license is unchanged and clearly noted, and the original author is attributed. | 8,298 | 25,131 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 127, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2022-21 | latest | en | 0.78138 |
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