unique_id stringlengths 2 7 | problem stringlengths 9 11.6k | answer stringlengths 0 2.49k | answer_type stringclasses 11
values | category stringclasses 16
values | difficulty stringclasses 5
values |
|---|---|---|---|---|---|
1932856 | A hot-air balloon is descending at a rate of 1.7 m/s when a passenger drops a camera. If the camera is 44 m above the ground when it is dropped, how long does it take for the camera to reach the ground? | 2.83 s | Float | Physics | Senior High School |
368295 | Find the eigenvalues of the following matrix:
$\left(
\begin{array}{ccc}
-2 & -4 & -9 \\
4 & -1 & 0 \\
-4 & -9 & 3 \\
\end{array}
\right)$. | $\lambda =8.6517$ or $\lambda =-4.32585-5.39805 i$ or $\lambda =-4.32585+5.39805 i$ | List | Mathematics | University |
988470 | Advertising, interviewing, screening, hiring
a) hiring costs
b) on-boarding costs
c) lost engagement
d) actively disengaged employees
e) error costs | a | Multiple Choice | Business | University |
433100 | What would be the optimum wavelength for measuring the absorbance versus concentration of a series of fd&c blue 1 dye solutions? | 630 nm | Integer | Chemistry | Senior High School |
215421 | Use integrating factor to solve the initial value problem.
{eq}\frac{dy}{dx}+\frac{3}{x} y=\frac{\sin x}{x^3},\; x>0,\; y(\frac{\pi}{2})=1
{/eq} | y.x^3 = -cosx+\frac{\pi^3}{8} | Expression | Mathematics | University |
1172157 | If #19 L# of a gas at room temperature exerts a pressure of #4 kPa# on its container, what pressure will the gas exert if the container's volume changes to #7 L#? | 11*10^3 Pa | Expression | Physics | Senior High School |
2036801 | During a spontaneous chemical reaction, it is found that {eq}S_{sys} < 0
{/eq}. This means:
a) {eq}S_{surr} < 0
{/eq} and its magnitude is {eq}< S_{sys}
{/eq}.
b) {eq}S_{surr} < 0
{/eq} and its magnitude is {eq}>S_{sys}
{/eq}.
c) {eq}S_{surr} > 0
{/eq} and its magnitude is {eq}< S_{sys}
{/eq}.
d) {e... | D | Multiple Choice | Chemistry | University |
849229 | I am reading 'Introduction to nonlinear dispersive equations' by Linares and Ponce. In section 4.2 (local smoothing effects) I found these equalities difficult to understand. Making the variable change $2\pi \xi ^2 = r$, they write for $f_+ = \chi_{\mathbb{R}^+} f$ $$ c\int_{-\infty}^\infty \begin{vmatrix} \displaystyl... | \int_0^\infty |g(r)|^2\ dr | Expression | Mathematics | University |
1950848 | A straight 16 gauge copper wire carries a current of {eq}10 \, \mathrm{A}
{/eq} parallel to the floor in a lab. The wire is placed in a uniform magnetic field such that the resulting magnetic force causes the wire to float. (The magnetic force is equal and opposite to the gravitational force on the wire.) Find the str... | 11.4mT out of the plane | Float | Physics | Senior High School |
945091 | A polyphonic composition based on one main theme, a cornerstone of baroque music, is called the | fugue | String | Other | Senior High School |
576572 | How can I efficiently compute the set subtraction between two rectangles in $\mathbb R^2$, where each rectangle is encoded by its bottom-left and top-right corner points, and express the result as a union of rectangles, without manually considering all possible relative positions of the input rectangles? | [x_1,x_3)×[y_3,y_2)∪[x_3,x_2)×[y_4,y_2)∪[x_4,x_2)×[y_1,y_4)∪[x_1,x_4)×[y_1,y_3) | Expression | Mathematics | University |
1900484 | Fill in the blank.
An oncogene might become active when placed on the chromosome in a position where normal controls are not active; this is termed _____. | translocation | String | Biology | University |
1030404 | The discount rate or cost of capital that the IRR must exceed if a project is to be accepted is called the _____. | weighted average cost of capital (WACC) | String | Business | University |
1499632 | A 1.6-kg block is attached to the end of a 2.0-m string to form a pendulum. The pendulum is released from rest when the string is horizontal. At the lowest point of its swing when it is moving horizontally, the block is hit by a 10-g bullet moving horizontally in the opposite direction. The bullet remains in the block ... | 1001.76 m/s | Float | Physics | Senior High School |
544185 | You are attempting to value a call option with an exercise price of $65 and one year to expiration. The underlying stock pays no dividends, its current price is $65, and you believe it has a 50% chance of increasing to $90 and a 50% chance of decreasing to $35. The risk-free rate of interest is 8%. Based upon your assu... | 13.7 | Float | Finance | University |
520769 | In 1988, when Sherry was 55 years old with an additional life expectancy of 20 years, she purchased a single life annuity for $200,000 that was to pay her $15,000 per year for life starting in 1989. Sherry just received her $15,000 payment for 2011. How much of the $15,000 must Sherry include in income?
a. 0
b. $5,00... | b | Multiple Choice | Business | University |
2086343 | Evaluate the integral {eq}\displaystyle \iint (3 x + 2 y)^2 \sqrt {2 y - x}\ dA{/eq}, over the region {eq}R{/eq} bounded by {eq}\displaystyle A (0,\ 0),\ B (-2,\ 3),\ C (2,\ 5),\ D (4,\ 2){/eq}. | 16384\sqrt{2}/9 | Fraction | Mathematics | University |
545650 | On January 2, Year 1, Sanders Company purchased equipment costing $37,900 with an estimated salvage value of $2,550 and an estimated useful life of 7 years.
On December 31, Year 2, Sanders Company sold the equipment to Used Machine Company for $23,012.
Required:
Prepare the journal entry to record the sale of the as... | Date Account Title Debit Credit
Dec. 31, Year 2Cash$23,012
Loss on sale of equipment$4,788
Accumulated depreciation - Equipment$10,100
Equipment $37,900 | Other | Business | University |
115171 | Consider this generic chemical reaction:
{eq}A + 2B \rightarrow 2C
{/eq}
By experimentation, it was found that the initial rate is unaffected when {eq}[A]
{/eq} doubles, but doubles when {eq}[B]
{/eq} doubles.
What is the experimental rate law for this reaction?
a) Rate = {eq}k[B]
{/eq}
b) Rate = {eq}k[A][B]
... | a | Multiple Choice | Chemistry | Senior High School |
1585534 | Which systems allow the molecules from food you eat to be distributed to your cells? NAME TWO!!!!! * | digestive system and circulatory system | List | Biology | Junior High School |
637569 | Find the indefinite integral.
{eq}\int \left [ v + \frac{1}{(5v - 6)^8} \right ] \, \mathrm{d}v
{/eq} | \frac{v^2}{2}- \frac{(5v-6)^{-7}}{7}+C | Expression | Mathematics | University |
45293 | Niobium metal becomes a superconductor when cooled below {eq}9 K
{/eq}. Its superconductivity is destroyed when the surface magnetic field exceeds {eq}0.100 T
{/eq}.In the absence of any external magnetic field, determine the maximum current a {eq}3.92-mm
{/eq}-diameter niobium wire can carry and remain superconduct... | 980 A | Float | Physics | University |
1566537 | Explain the energy transformation process needed to create an electromagnet . | Chemical energy -> Electrical energy -> Electromagnetic energy | List | Physics | Junior High School |
25127 | Find the amount of each payment to be made into a sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period. The interest rate given is per period.
$91,000; money earns 5% compounded quarterly for 4 3/4 years.
A) $4,272.95
B) $1,949.47
C) $887.26
D)... | A | Multiple Choice | Finance | Senior High School |
876261 | Is the following integral formulation for the area of a sector of an ellipse that does not include the center of the ellipse correct: $$\frac{1}{2}\int_{\alpha}^{\theta+\alpha}a^2cos^2(\phi )+(h-b(1+sin(\phi )))^2 d\phi$$ where $\alpha = sin^{-1}(\frac{h-b}{b})$ and $\theta$ is constant? Furthermore, is the calculated ... | \frac{a}{2b}\left[h_{2}\sqrt{b^{2}-h_{2}^{2}}-h_{1}\sqrt{b^{2}-h_{1}^{2}}+b^{2}\left(sin^{-1}\Big(\frac{h_{2}}{b}\Big)-sin^{-1}\Big(\frac{h_{1}}{b}\Big)\right)\right]-\frac{1}{2}\sqrt{1-\frac{h_{2}^{2}}{b^{2}}} | Expression | Mathematics | University |
412093 | A baseball diamond is a square 90.0 ft on a side. As a player runs from first base toward second base at 18 ft/s, at what rate is the player's distance from home plate increasing when the player is 40 ft from first base? | 8.77ft/s | Float | Physics | Senior High School |
1869906 | Given the finite fields $$F_1=\frac{\mathbb{Z}_2[x]}{\langle x^3+x+1\rangle}$$ and $$F_2=\frac{\mathbb{Z}_2[x]}{\langle x^3+x^2+1\rangle},$$ how can I find an isomorphism between them? | Map $\alpha \in \mathbb{F}_1$ to $1/\beta = \beta^2+\beta \in \mathbb{F}_2$. | Expression | Mathematics | University |
524832 | Consider the set $A$ and the function $f(x, y)$ such that $$A = \{(x, y)\in\mathbb{R}^2; x > 0, y < e^{-1/x}\}$$ $$f(x, y) = \begin{cases} 2x & (x, y) \in A \\\\ y & (x, y) \not\in A \end{cases}$$ For which points of $\partial A$ is the function continuous? | (0,0) | Expression | Mathematics | University |
1595205 | In an arcade game, a 0.18 kg disk is shot across a frictionless horizontal surface by being compressed against a spring and then released. If the spring has a spring constant of 237 N/m and is compressed from its equilibrium position by 6.6 cm, what is the magnitude of the spring force on the disk at the moment it is r... | 15.642 N | Float | Physics | Senior High School |
1782540 | Light from a helium-neon laser (MathJax fullWidth='false'
\lambda
}] = 633 nm) is used to illuminate two narrow slits. The interference pattern is observed on a screen 3.0 m behind the slits. Eleven bright fringes are seen, spanning a distance of 56 mm.
Part A
What is the spacing (in mm) between the slits? Express ... | 0.34 mm | Float | Physics | Senior High School |
649540 | How many kilometers is Neptune away from the sun? | 4.504E+09 km | Float | Physics | Junior High School |
1114379 | Chester Corp. ended the year carrying $20,657,000 worth of inventory. Had they sold their entire inventory at their current prices, how much more revenue would it have brought to Chester Corp.?
a. $43,704,100
b. $32,615,000
c. $20,657,000
d. $11,369,000 | C | Multiple Choice | Business | Junior High School |
309234 | A small object has a mass 3.80g and charge -18uC "floats" in a uniform electric field. What is the magnitude and direction of the electric field? | |E| = 2100 N/C, downward | Float | Physics | Senior High School |
38685 | A 500 N weight is attached to a stiff rod of negligible weight that is hinged to one end. The rod is released from rest in horizontal position and allowed to swing freely in vertical arc.
Through what angle with the horizontal must it swing to cause a tension of 1000 N in it? | 41.8 degrees | Float | Physics | Senior High School |
1782824 | What society didnt have a centralized government | Pastoral society | String | History | Senior High School |
175151 | Find the $\ell_2$ norm of the following vector:
$\left(
\begin{array}{c}
-\frac{77}{100} \\
-\frac{7}{5} \\
\frac{107}{100} \\
-\frac{81}{25} \\
-\frac{347}{50} \\
-\frac{379}{100} \\
-\frac{141}{100} \\
-\frac{327}{100} \\
\end{array}
\right)$. | \frac{\sqrt{894041}}{100} | Fraction | Mathematics | University |
571229 | A United States investor writes five naked call option contracts. Each contract is on 100 shares. The option price is $4.00, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement on the five contracts? (must show two methods). | $6,200 | Integer | Finance | University |
144477 | If the pupil of your eye is a circle 5.0 mm in diameter, how much energy enters your eye per second? (Assume that 5.0% of the lightbulb's power is converted to light.) You are standing 3.0 m from a 110-W lightbulb. | 9.55e-7 W | Float | Physics | Senior High School |
1805685 | What is the size of earth in miles? | 7926 miles | Integer | Physics | Junior High School |
1811705 | Given the two reactions shown with their equilibrium constants,
PCl{eq}_3
{/eq}(g) + Cl{eq}_2
{/eq}(g) {eq}\to
{/eq} PCl{eq}_5
{/eq}(g), K{eq}_1
{/eq}
2NO(g) + Cl{eq}_2
{/eq}(g) {eq}\to
{/eq} 2NOCl(g), K{eq}_2
{/eq}
What is the equilibrium constant for the reaction,
PCl{eq}_5
{/eq}(g) + 2NO(g) {eq}\to
{/e... | d | Multiple Choice | Chemistry | Senior High School |
1140073 | Which franchise model do automobile dealerships usually follow? | Franchised dealerships | String | Business | Junior High School |
501776 | It is a type of text which presents information that are found in radio, print or television. | Journalistic text | String | Other | Junior High School |
1524738 | Under which presidential administration did the progress of reconstruction stall fail and in many cases reverse completely | President Johnson | String | History | Senior High School |
853994 | As the human resource director, Trisha provides each manager with a breakdown of the metrics for employee performance measurement. She asks them to evaluate their staff against the standards provided in these metrics. Trisha is providing the managers with a(n) _____ device. | control | String | Business | University |
482334 | A satellite in geostationary orbit is used to transmit data via electromagnetic radiation. The satellite is at a height of 3.3 x 10{eq}^4
{/eq}km, above the surface of the earth, and we assume it has anisotropic power output of 33.5 kW, (although, in practice, satellite antennas transmit signals that are less powerful... | 4.3e-5 V/m | Float | Physics | University |
917486 | Evaluate {eq}\lim_{x\rightarrow 0} \frac{\ln(1 + x) - x + x^2/2}{x^3} using Taylor Series. | 1/3 | Fraction | Mathematics | University |
1586485 | Give the word derived from Greek and/or Latin elements that matches the following: "On the same side". | ipsilateral | String | Other | University |
1964284 | I'm trying to solve the following integral: $\int \frac{1}{\cos (x)-1}dx$ without using the Weierstrass substitution. | cot(x/2) + C | Expression | Mathematics | University |
887569 | Reparametrize the curve with respect to arc length, where the position function for a parametric curve is given by {eq}\displaystyle r (t) = \bigg\langle \frac {\sqrt 2} {2} t,\ \frac {1} {2} e^t,\ \frac {1} {2} e^{-t} \bigg\rangle{/eq}. | < (sqrt(2)/2) arccosh(s), (1/2)e^(arccosh(s)), (1/2)e^(-arccosh(s)) > | Expression | Mathematics | University |
52708 | What animal classification is a jellyfish? | Phylum Cnidaria, Class Scyphozoa | String | Biology | Junior High School |
109893 | Which one of the following statements presents a condition required for the Hardy-Weinberg principle to be in effect?
(a) Genetic drift occurs.
(b) Gene flow is present.
(c) Mutations are present.
(d) Random mating occurs. | d | Multiple Choice | Biology | Senior High School |
1708119 | A diffraction grating with {eq}375\text{ lines/mm}
{/eq} is {eq}1.00\text{ m}
{/eq} in front of a screen. What is the wavelength of light whose first-order maxima will be {eq}16.4\text{ cm}
{/eq} from the central maximum on the screen? | 4.37e-7 m | Float | Physics | Senior High School |
817246 | A golf tube has total charge {eq}-0.1 \mu C
{/eq}. Compute the total electric flux out of the lab room containing the charged gold tube and no other net charge. | -1.13e4 N.m^2/C | Float | Physics | Senior High School |
1601828 | Solve IVP:
{eq}y' + \frac{k}{x}y = 0, y(1) = 3{/eq}. | y(x) = 3x^(-k) | Expression | Mathematics | University |
655623 | The body falling with speed {eq}v_0
{/eq} strikes and maintains contact with the platform supported by a nest of springs. The acceleration of the body after impact is a = g - cy where c is a positive constant and y is measured from the original platform position. If the maximum compression of the springs is observed t... | c = \frac{2gym+v_0^2}{ym^2} | Expression | Physics | University |
1407174 | What is an example of oxidation and reduction? | Cu(s) + 2AgNO3(aq)→2Ag(s) + Cu(NO3)2(aq) | Expression | Chemistry | Senior High School |
1313174 | $X^{T}$ is the transpose of $X$. $A$ is a $n$ x $n$ matrix and $B$ is a $m$ x $m$ matrix, $m$ > $n$, both of them are known, $A$ is positive definitive and $B$ is symmetric. I would like to find $X$. | $Y=\begin{pmatrix}Y_{1,1}&Y_{1,2}&Y_{1,3}\\0&0&Y_{2,3}\\0&0&Y_{3,3}\\0&0&Y_{4,3}\end{pmatrix}$ where $Y_{1,1}Y_{1,1}^T+Y_{1,2}Y_{1,2}^T=I_r$, and $X = PYQ^{-1}$ where $Y=P^{-1}XQ$, and $P, Q$ are invertible matrices such that $B = P\text{diag}(I_r,0_{m-r})P^T$ and $A = Q\text{diag}(I_s,0_{n-s})Q^T$ | Matrix | Mathematics | University |
988692 | Consider the sample of {eq}n = 20
{/eq} scores: 2.3 ..... 5.7 5.7 ..... 7.7 ..... 8.9 10.1 10.6
11.1 11.3 ..... 12.0 12.1 12.4 12.8 ..... 13.9 18.6. Notice that they are listed in order from 2.3 to 18. 6, but that some of the scores are obscured by ..... . The mean, {eq}M
{/eq}, of these scores is 10. 0. Suppose yo... | a | Multiple Choice | Mathematics | University |
546816 | What is the ideal banking angle for a gentle turn of 1.20 km radius on a highway with a 110 km/h speed limit (about 68 mph), assuming everyone travels at the limit? | 4.3^° | Float | Physics | Senior High School |
17043 | Find the first three nonzero terms of the Taylor series for the function {eq}f(x) = \sqrt{10x - x^2} {/eq} about the point {eq}a = 5 {/eq}. | 5 - (1/10)(x-5)^2 - (1/1000)(x-5)^4 | Expression | Mathematics | University |
2020721 | There are $10$ people each with $1$ hat that is indistinguishable. Every person picks up a random hat. What is the probability that over $\frac12$ of the people chooses the wrong hat? | 3615536/3628800 | Fraction | Mathematics | University |
964628 | Let $f(x)$ be a continuous function on $[0,\infty)$. Find $f$ such that $\int_0^{\infty} f(x) \left(\frac{x^2}{1+x^2} \right)^n dx =\infty$ for all integers $n \geq1$. Is the condition that $f$ is continuous a condition that should be relaxed? Or is there an error in the reasoning that shows the integral must be finite... | f(x)=\frac{1}{x+1} | Expression | Mathematics | University |
1594774 | How do you balance this equation: #?NaHCO_3 → ?NaOH + ?CO_2#? | NaHCO_3 → NaOH + CO_2 | Expression | Chemistry | Junior High School |
483980 | Find the derivative of x^3 + 4xy^2 - y^4 = 7. | $y' = \frac{-3x^2-4y^2}{8xy-4y^3}$ | Expression | Mathematics | University |
2056734 | Find {eq}\dfrac {dy}{dx}{/eq} by implicit differentiation, given {eq}\displaystyle x \ln y + y = x^4 y^6{/eq}. | {eq}\frac{{dy}}{{dx}} = \frac{{y\left( {4{x^3}{y^6} - \ln y} \right)}}{{\left( {x +y- 6{x^4}{y^6}} \right)}}{/eq} | Expression | Mathematics | University |
874492 | In Young's experiment, a mixture of orange light (611 nm) and blue light (471 nm) shine on the double slit. The centers of the first-order bright blue fringes lie at the outer edges of a screen that is located 0.452 m away from the slits. However, the first-order bright orange fringes fall off the screen. By how much a... | 0.104 m | Float | Physics | Senior High School |
1293318 | If 25.0 mL of urine has a mass of 25.725 g and contains 1.929 g of urea, what is the mass percent concentration of the specimen? (Assume the rest of the urine is water.) | 7.498 | Float | Chemistry | Senior High School |
1784683 | Assume that f(z) is an entire function and $|f(z)| \leq Me^{|z|}$. How can I show something about f(z) using the Cauchy estimate and a circle line integral, given that I have gotten it down to something like $n!M/k!r^n$? | $|\frac{f^{(k)}(0)}{k!}| \le \frac{Me^r}{r^k}$ | Expression | Mathematics | University |
267990 | Use the data to obtain a 95.44% confidence interval for the mean forced vital capacity for all asthmatics, given the following data on forced vital capacity in liters for a random sample of 15 asthmatics: 5.1, 4.9, 4.7, 3.1, 4.3, 3.7, 3.7, 4.3, 3.5, 5.2, 3.2, 3.5, 4.8, 4.0, 5.1. Assume that {eq}\sigma{/eq} = 0.7. | (3.8457, 4.5683) | List | Mathematics | University |
1421944 | Is the market structure of firms like the global luxury eyewear business Luxottica an example of a monopoly or monopolistic competition? | Monopolistic Competition | String | Economics | Senior High School |
771442 | Suppose {eq}\displaystyle
f(t)=\begin{cases}
1 & \text{ if } 0\leq t< \pi \\
e^{t} & \text{ if } \pi\leq t< 2\pi \\
\sin t & \text{ if } t\geq 2\pi
\end{cases}
{/eq}
Use the definition to find the Laplace transform. | - \frac{e^{-s\pi}}{s} + \frac{1}{s} - \frac{e^{-2\pi(s-1)}}{(s-1)} + \frac{e^{-\pi(s-1)}}{(s-1)} + \frac{e^{-2\pi s}}{s^2+1} | Expression | Mathematics | University |
1130201 | Does payroll tax expense add up with payroll tax liability? | Yes | Boolean | Business | Senior High School |
1190417 | How do you divide #(i+12) / (9i-10)# in trigonometric form? | #sqrt(145/181)(cos(tan^-1(1/12)-tan^-1(9/-10)-pi)+isin(tan^-1(1/12)-tan^-1(9/-10)-pi))# | Expression | Mathematics | University |
747039 | Give the general solution of the differential equation {eq}\displaystyle y'' + 4 y' + 20 y = 2 e^{4 x} \cos (2 x) {/eq}. | y=e^{-2x}(c_1cos(4x)+c_2sin(4x))+\frac{1}{60}e^{4x}sin(2x)+\frac{1}{30}e^{4x}cos(2x) | Expression | Mathematics | University |
668199 | Which practice contributes the most to environmental pollution?
A. Cutting down trees to make way for a mall
B. Eating food for convenience
C. Driving instead of using public transportation | A | Multiple Choice | Other STEM | Junior High School |
1906833 | Find the Taylor series about the indicated center, and determine the interval of convergence.
$$f(x) = \cos x, c = \frac{-\pi}{2}$$ | $\sum _{n=0}^{\infty } {\frac { (-1)^{n} (x-\frac{\pi}{2} )^{2n+1} } { (2n+1)! } }$, Interval of convergence: $(-\infty, \infty)$ | Expression | Mathematics | University |
1628883 | Convert {eq}\displaystyle
30 \text{ miles per hour to } m/s
{/eq}. | 13.41 m/s | Float | Physics | Junior High School |
1416814 | Who did the Christians fight in the First Crusade? | Seljuk Turks | String | History | Junior High School |
1050266 | Would the statement 2^n/n^1000 ∈ Ω(n^1000000) be considered valid if it is true for n=1 but not for n>1? | No | Boolean | Mathematics | University |
1136863 | Distress is a form of what? | negative stress | String | Psychology | Junior High School |
1607141 | St. Johns River Shipyard's welding machine is 15 years old, fully depreciated, and has no salvage value. However, even though it is old, it is still functional as originally designed and can be used for quite a while longer. The new welder will cost $81,000 and have an estimated life of 8 years with no salvage value. T... | $33,680, Yes | Float | Finance | University |
96815 | Given a general nonlinear system where we want to show that the error system $e=x-x_d$ is stable, is it necessary for the Lyapunov candidate to be continuously differentiable at the equilibrium point, especially since we are only concerned about what happens around the equilibrium point? Specifically, can $\vert\vert e... | No, it is not necessary for the Lyapunov candidate to be continuously differentiable at the equilibrium point. If $\dot{e} = 0$ at $e = 0$, then $||e||$ is a valid Lyapunov candidate even though it's not differentiable at $e=0$. | Boolean | Mathematics | University |
1496483 | Are October Sky and Rocket Boys the same book? | Yes | Boolean | Other | Primary School |
273181 | Solve the given differential equation: {eq}\displaystyle {y}' = \frac{3x}{y + x^2 y}
{/eq}. | y = ±\sqrt{3\ln |1+x^2| + 2C} | Expression | Mathematics | University |
1280787 | According to John Maynard Keynes, _____ is necessary for the efficient functioning of the economy. | Fiscal policy | String | Economics | Senior High School |
1970513 | Find the maximum and minimum values of the function {eq} f(x,y,z) = x^2 y^2 z^2 {/eq} subject to the constraint {eq}x^2 + y^2 + z^2 = 81{/eq}. | The maximum function value subject to this constraint is 19683 and the minimum is 0. | List | Mathematics | University |
492276 | How could you define (using spherical coordinate system) all the adjacent vertices directly connected to a central vertex in a tetrahedral octahedral honeycomb? Alternatively it would be useful to get the answer in cartesian coordinates. | The twelve immediate neighbors, where one coordinate remains 0 and the others are 1 or -1. | List | Mathematics | University |
945163 | What is the distribution function of a random variable $\zeta = \xi + \eta$, where $\xi$ and $\eta$ are independent random variables with distributions $P(\xi=k) = p_1 q_1^k$ and $P(\eta=k) = p_2 q_2^k$, respectively? | $\Pr[\xi + \eta = k] = \sum_{j=0}^k \Pr[\xi = j] \Pr[\eta = k-j] = \sum_{j=0}^k p_1 q_1^j p_2 q_2^{k-j}$ | Expression | Mathematics | University |
469386 | Suppose $\mathbf{q} = \left[\begin{array}{cccc}q_1 & q_2& \dots &q_n\end{array}\right]\in \mathbb{Q}_{>0}^n$ is a vector of positive rational numbers with relatively prime numerator and denominator $q_i = \frac{\eta_i}{d_i}$. Find $\alpha\in \mathbb{Q}$ such that $\mathbf{x} = \alpha\,\mathbf{q}$ is the smallest intege... | \alpha=\text{lcm}[d_1,\ldots,d_n] | Expression | Mathematics | University |
187188 | A net force of 72 N is applied to a 48 kg box starting from rest for 8 s.
What is the final velocity of the box? | 12 m/s | Float | Physics | Senior High School |
318683 | Is it okay for pharmaceutical companies and medical device companies to pay physicians to be expert advisors to the company for their products? | Yes | Boolean | Philosophy | Senior High School |
459602 | Where did Mark Twain write Roughing It? | Buffalo, New York | String | Other | Junior High School |
349276 | A particle (mass = 0.42 kg) moves in one dimension (x) and the potential energy is V(x) = (-1/2)*q*x² with q = 6.74 J/m². The initial conditions at t = 0 are velocity = 0 and position x₀ = 3.0 m. From conservation of energy, x(t) has the form Acosh(at). Calculate the value of a. | 3.85 rad/s | Float | Physics | University |
993202 | Evaluate the triple integral {eq}\iiint_{E} 5xy \, \mathrm{d}V, where {eq}E{/eq} is bounded by the parabolic cylinders {eq}y = x^2{/eq} and {eq}x = y^2, and the planes {eq}z = 0{/eq} and {eq}z = 7x + y{/eq}. | 2.143 | Float | Mathematics | University |
1491551 | Which of the following depreciation methods is used by most companies for their tax returns?
a. Units-of-production
b. Straight-line
c. Declining-balance
d. All of the above methods are used about equally. | b | Multiple Choice | Business | University |
1352091 | Name two functional groups that contain ionic charges? | carboxylate and protonated amines | List | Chemistry | Senior High School |
1407548 | Evaluate the integral. (Use C for the constant of integration.)
{eq}\displaystyle \int \frac {x + 14}{x^2 + 2x + 5} \ dx
{/eq} | 1/2ln(x^2+2x+5)+3/2arctan((x+1)/2) + C | Expression | Mathematics | University |
2037230 | A student wants to use western blotting to confirm the presence of human Sonic hedgehog (Shh) in samples run on SDS-PAGE and transfered to a nitrocellulose membrane. The antibody reagent box in their lab contains Mouse anti-Shh MAb and Chicken anti-mouse IgG-HRP. What substrate will they need in order to perform colori... | BCIP/NBT | String | Biology | University |
1514714 | Kiss the Sky Enterprises has bonds on the market making annual payments, with 13 years to maturity, and selling for $1,045. At this price, the bonds yield 7.5 per cent. What is the coupon rate on the bonds? | 8.05% | Percentage | Finance | University |
270312 | Activist judges believe that federal judges should always overrule state legislatures and governors when making decisions. interpret the u.s. constitution according to the intentions of its framers and defer to the views of congress when interpreting federal statutes. be more aggressive and ideological than the preside... | go beyond the words of a constitution or statute to consider the broader societal implications of their decisions. | String | Other | Senior High School |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.