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# Block and cylinder down an incline
131
1. The problem statement, all variables and given/known data
A block of mass m1 is attached to the axle of a uniform solid cylinder of mass m2 and radius R by massless strings. The two accelerate down a slope that makes an angle $\theta$ with the horizontal. The cylinder rolls ... | {
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131
how did you go about getting that result
8. ### sArGe99
133
Write the correct force equations for both the block and the cylinder and also the torque equation for the cylinder since its rolling.
Hint : Friction provides torque for the cylinder to rotate.
131
ahh yes the correct force equations... i am guessing i... | {
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You have three unknowns and you'll need three equations.
131
note: x axis taken to be parallel to the slope of the incline
Torque equation for cylinder:
$$-RF_{f}=\frac{1}{2}m_{2}R^2\alpha$$
=>
$$F_{f} = -\frac{1}{2}m_{2}R\alpha$$
Forces for block: y direction
$$N-m_{1}g\cos\theta=0$$
Forces on block: x direction (*... | {
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# Revision history [back]
I will try to answer to questions 3 and 4. I don't really know if you can directly place on the surface the level curves generated by contour_plot or put them on the $xy$ plane. It seems to me that SageMath doesn't have a command or function for doing so. In fact, the plot3d method for 2D gra... | {
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# Surface plot using implicit_plot3d
zmin, zmax = -1, 1
def col3(x,y,z):
return float(0.5*dz+floor((z-z1)/dz)/ni)
surf_new = implicit_plot3d(z==f(x,y), (x,-2,2), (y,-2,2), (z,zmin,zmax),
color=(col,colormaps.jet), plot_points=[50,50,300])
show(surf_new, aspect_ratio=[1,1,2])
Here we have again a view from above:
sho... | {
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# Question on openness in the topology generated by a basis
As some context, a question I posted Munkres exercise 13.1 was closed as a duplicate, but I'm not interested just in solving Munkres 13.1, but in a verification of whether my understanding of a basis for a topology is correct. I'm going to try to reduce the s... | {
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My question is whether this approach here and my understanding of the basis for a topology is correct, or if I have made any mathematical errors. I surely would have to start out with "choose a basis for $$\mathcal{T}$$," which could just be $$\mathcal{T}$$ itself. This is certainly not ideal, but is it incorrect?
• S... | {
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# If $28a + 30b + 31c = 365$, then what is the value of $a +b +c$?
Question: For 3 non negative integers $a, b, c$; if $28a + 30b + 31c = 365$ what is the value of $a +b +c$ ?
How I approached it : I started immediately breaking it onto this form on seeing it :
$28(a +b +c) +2b +3c = 365 .......(1)$ $30(a +b +c) -2a... | {
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Since we know that $c-2a\equiv 5\mod 30$, it suffices to show that $-25< c-2a < 35$ to conclude that $c-2a = 5$. The upper bound is easy, since $$31c\le 365\implies c\le 11\implies c-2a\le 11 < 35$$ as $a$ is nonnegative. To get the lower bound, we note that $$28a\le 365\implies a\le 13.$$ Furthermore, if $a=13$, then ... | {
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$c=5$ works also. $31(5)=155$, and $365-155= 210$, which is $30(7)$. So $(0,7,5)$ is a third solution.
$c=3$ doesn't work because $365-3(31) = 272$, which is greater than $30(9)$.
$c=1$ doesn't work either, because $365-31 = 334 > 30(11)$.
So, three solutions: $(2,1,9), (1,4,7), (0,7,5).$
• 1 + 6 + 7 = 14. I think ... | {
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# Constant case CRT: $\,x\equiv a\pmod{\! 2},\ x\equiv a\pmod{\! 5}\iff x\equiv a\pmod{\!10}$
Problem: Find the units digit of $3^{100}$ using Fermat's Little Theorem (FLT).
My Attempt: By FLT we have $$3^1\equiv 1\pmod2\Rightarrow 3^4\equiv1\pmod 2$$ and $$3^4\equiv 1\pmod 5.$$ Since $\gcd(2,5)=1$ we can multiply th... | {
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Your proof is correct. It invokes a simple special case of CRT = Chinese Remainder Theorem when the values $$\,a_1 = a_2\,$$ are constant, say $$\,a,\,$$ which is equivalent to the following basic result
UL = Universal property of LCM: $$\ \rm \,\ j,k\mid n\!\!\color{#0a0}{\overset{\rm UL\!\!}\iff} {\rm lcm}(j,k)\mid ... | {
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• Thanks for your beautiful answer! – Postal Model Oct 19 '18 at 19:29
The phrase ‘Since gcd(2,5)=1 we can multiply the moduli’ is not clear at all. I would rather say something like ‘since $$3^4\equiv 1\mod 2$$ and $$\bmod5$$, we have $$3^4\equiv 1\mod \operatorname{lcm}(2,5)=10$$’ by the Chinese remainder theorem.
... | {
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Let $M$ be a row substochastic matrix, with at least one row having sum less than 1. Also, suppose $M$ is irreducible in the sense of a markov chain. Is there an easy way to show the largest eigenvalue must be strictly less than 1? I hope that this result is true as stated. I know that Cauchy interlacing theorem gives ... | {
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-
I'm not quite seeing that the sub stochastic eigenvector, when extended with a zero coordinate becomes an eigenvector of the new markov chain, particularly when looking at what happens to the last coordinate of the eigenvector upon multiplication – SKS May 4 '11 at 22:25
The last coordinate is zero in both "input" a... | {
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-
A bit late to the game, but I thought of this proof.
Suppose $A$ is an irreducible sub-stochastic matrix and $\lambda$ is the the Perron-Frobenius eigenvalue of $A$ (i.e. $\rho\left(A\right) = \lambda$) with $v$ the corresponding eigenvector normalized such that $\|v\|_{1} = 1$. By the Perron-Frobenius theorem for ... | {
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IntMath Home » Forum home » Factoring and Fractions » Fraction algebra
# Fraction algebra [Solved!]
### My question
The following question was asked on a sample test:
3/((x+2b)(x-b)) + 2/((3b-x)(x+2b)) +1/((x-3b)(b-x))
We tried answering two ways to find the LCD: first, by negating the denominator only; second, ... | {
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<a href="/factoring-fractions/5-equivalent-fractions.php">5. Equivalent Fractions</a>
What I've done so far
The first way: when the third denominator was multiplied by -1 to get the LCD, the denominator was negated but the numerator was not.
= 3 / [(x+2b)(x-b)] + 2 / [(3b-x)(x+2b)] + 1 / [(3b-x)(x-b)]
= [3(3b... | {
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X
Please use the math input system. It's easy, and others can read your question much more easily.
Your first answer is correct, but some of your explanation is not quite right (which is maybe where the confusion has arisen).
For this problem we need to remember that in general,
-(x-y) = y-x.
That's what you are u... | {
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# Can I execute this division at this point?
I realize this is basic, but this little doubt has been around with me for quite a while:
I have this:
$$\frac{(2n+3)n+1}{(2n+1)(2n+3)}$$
I need it to end up with this shape:
$$\frac{n+1}{2n+3}$$
At first, I thought "well, I simply remove the $(2n+3)$ from the numerato... | {
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# When Integrating (2x)/(4x^(2)+2) I get two different integrals ?
1. Aug 19, 2014
### FurryLemon
Hi
So lets have ∫(2x)/(4x^(2)+2) dx
Without factorising the 2 from the denominator, I integrate and I get
1/4*ln(4x^(2)+2)+c which makes sense as when I differentiate it I get the original derivative.
BUT when I fac... | {
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5. Aug 19, 2014
### pasmith
The other classic example is $$\int \cos \theta \sin\theta\,d\theta = -\frac12\cos^2\theta + C = \frac12\sin^2\theta - \frac12 + C = -\frac14 \cos(2\theta) + C - \frac14.$$ | {
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GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 18 Apr 2019, 21:34
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... | {
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$$\frac{1}{1 \times 2}+\frac{1}{2 \times 3}$$ = 1/2 + 1/6
= 3/6 + 1/6
= 4/6
= 2/3
$$\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}$$ = 2/3 + $$\frac{1}{3 \times 4}$$
= 2/3 + 1/12
= 8/12 + 1/12
= 9/12
= 3/4
$$\frac{1}{1 \times 2}+\frac{1}{2 \times 3}+\frac{1}{3 \times 4}+\frac{1}{4 \times 5}$$ = 3/4 + ... | {
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A. $$\frac{98}{99}$$
B. $$\frac{99}{100}$$
C. $$\frac{100}{101}$$
D. $$\frac{98}{101}$$
E. $$\frac{99}{101}$$
We begin by noting that 1/(1x2) = 1/1 - 1/2, 1/(2x3) = 1/2 - 1/3, 1/(3x4) = 1/3 - 1/4, … , 1/(99x100) = 1/99 - 1/100.
If we substitute each term in the definition of A by the above, we obtain:
A = 1/1 - ... | {
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### Show Tags
15 Dec 2016, 07:18
n=1: 1/2
n=2: 1/2 + 1/2x3 = 1/2 + 1/6 = 2/3
n=3: 4/6 + 1/3x4 = 4/6 + 1/12 = 3/4
n=4: 3/4 + 1/4x5 = 3/4 + 1/20 = 4/5
So, we can deduce that: n(x) = (x-1/x) + (1/x(x+1))
Therefore, n(99) = (98/99) + (1/99*100) = 9801/9900 = 99/100
Intern
Status: One more try
Joined: 01 Feb 2015
Posts: ... | {
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since 1/(2x3)= 1/6 = 1/2-1/3, In a similar way all terms can be written in to this form
=1/2 + 1/2 -1/3 + 1/3 - 1/4 + 1/4- 1/5+............-1/99+1/99-1/100
=1/2 + 1/2 -1/100 (all others cancelled)
=1-1/100 = 99/100
B
Re: What is the value of 1/(1*2)+1/(2*3)+...+1/(99*100)? [#permalink] 26 Jul 2017, 02:00
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# Complex logarithm, my answer is wrong
I am trying to calculate $$\log(-1+i)$$
I have $$\log(-1+i) = \ln|(-1+i)| + i\operatorname{Arg}(-1+i)$$
$$= \ln\sqrt2 + i3\pi/4$$
However when I checked that in matlab and wolfram alpha they have
$$\frac{\ln\sqrt2}{2} + i3\pi/4$$
Can't see what Im doing wrong.
-
## 1 Answ... | {
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# Math Help - Integral proofs
1. ## Integral proofs
Actually I have 2 questions?
1) Prove that the integral of (df/dx) from a to be is equal to f(b) - f(a) using the definition of Riemann Integration and the definition of derivative.
I tried using the antiderivative proof but I dont think that is the right directio... | {
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5. Originally Posted by ThePerfectHacker
$\int_a^b f'(x) dx = f(b) - f(a)$
This is because $f(x)$ is antiderivative of $f'(x)$.
i might be misunderstanding something here, but aren't you using what you're supposed to be proving? namely the fundamental theorem of calculus. i would think we had to go through all that stu... | {
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$s(P)\le \sum\limits_{i=1}^{n}{f\left( \mu _{i} \right)\cdot \Delta x_{i}}\le S(P)\implies s(P)\le \varphi (b)-\varphi (a)\le S(P).$
Hence, $\varphi (b)-\varphi (a)$ is included between the lower and upper sums of $f$ for any $P$ partition, and this property has the integral $\int_a^b f,$ from here $\int_a^b f(x)\,dx=\... | {
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9. What about the definition of the derivative that I'm supposed to use along the the definition of Riemann integration??
10. Originally Posted by Jhevon
where are you stuck on this one? you've learned about partitions and all that, right?
note that $-1 \le \sin \left( \frac 1x \right) \le 1$ for $x \ne 0$
thus, $-x... | {
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Show that the diagonal entries of symmetric & idempotent matrix must be in [$0,1$]
Show that the diagonal entries of symmetric & idempotent matrix must be in [$0,1$].
Let $A$ be a symmetric and idempotent $n \times n$ matrix. By the definition of eigenvectors and since $A$ is an idempotent,
$Ax=\lambda x \implies A^2... | {
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With this result at hand the following observation gets us to the desired answer:
Let $e_{i}$ and $q_{ii}$ denote the standard unit vector and $i_{th}$ diagonal element of $Q$, respectively. Then we have
$$0= min \{\lambda_1 ,...,\lambda_{n} \} \leq q_{ii} = e_{i}' Q e_{i} \leq max \{\lambda_{1},...,\lambda_n\}=1$$
... | {
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# Geometry Problem
1. Feb 26, 2005
### Jameson
In $$\bigtriangleup ABC , AB = BC$$ and $$CD$$ bisects angle C.
If $$y = \frac{1}{3}x$$ then z = ....
--------------------------------------------
Ok. I've tried to make a bunch of substitutions for each of the angles and I can't seem to solve any for z.
I have found... | {
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### honestrosewater
Eh, doesn't 2z + y = 180? So knowing y = x/3 you can solve for z in terms of x.
Plus, if it's the CB's "10 Real SAT's", it has the answers. And any other SAT prep book should have the answers too.
Last edited: Feb 27, 2005
9. Feb 27, 2005
### apchemstudent
ok, that equation is essential to solv... | {
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# What is the geometric interpretation behind the method of exact differential equations?
Given an equation in the form $M(x)dx + N(y)dy = 0$ we test that the partial derivative of $M$ with respect to $y$ is equal to the partial derivative of $N$ with respect to $x$. If they are equal, then the equation is exact. What... | {
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The differential equation $M(x) \, dx + N(y) \, dy = 0$ is then equivalent to the condition that $p$ is a constant, and since this is not a differential equation it is a much easier condition to work with. The analogous one-variable statement is that $M(x) \, dx = 0$ is equivalent to $\int M(x) \, dx = \text{const}$. G... | {
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# Are real numbers a subset of the complex numbers? [duplicate]
I am having an argument with a friend. I think that in a sense, the answer is no. My reasoning is that in linear algebra, a vector $(a, b)$ is not the same as a vector $(a, b, 0)$ because the first one is in $\mathbb{R}^2$, while the second is in $\mathbb... | {
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## marked as duplicate by Matthew Towers, Bungo, user137731, GEdgar, Lee MosherAug 1 '16 at 16:55
• $\mathbb{R}$ is a subfield of $\mathbb{C}$ – reuns Aug 1 '16 at 16:39
• Recall that the set of complex numbers $\Bbb C$ is defined as $\Bbb C=\{a+ib\mid a,b\in\Bbb R\}$ where $i$ is the imaginary unit. You may see each ... | {
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# Colored balls into groups
If 3 red, 3 blue, and 3 green balls are randomly divided into three groups of three balls each, what is the probability that none of the groups have all the balls of the same color?
My attempt:
Let $A$ be the event that all groups have all balls of the same color. There is 1 way that this... | {
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Now let's consider the probability that the first three balls drawn will all be the same color. The first ball we draw can be any color; call it color X. We now want to draw a second ball of the same color, but there are now $8$ balls in the urn with $2$ of color X, so we have a $\frac14$ chance to draw color X again. ... | {
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As a hint of how to get back on track, assuming you consider my drawing-from-the-urn scheme to be sufficiently random, I have already calculated the probability that the first group will be all one color. You can continue the process to find the probability that all three groups will be the same color. From this you ca... | {
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• Thanks. Your description of the randomization process is correct, and I incorrectly assigned equal probabilities to the identified outcomes. I'm going to hold off on marking this is the answer though because I'd like a full solution (from you or someone else) to understand how I should be approaching the problem. – u... | {
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# 7.5. Dimension reduction#
The SVD has another important property that proves very useful in a variety of applications. Let $$\mathbf{A}$$ be a real $$m\times n$$ matrix with SVD $$\mathbf{A}=\mathbf{U}\mathbf{S}\mathbf{V}^T$$ and (momentarily) $$m\ge n$$. Another way of writing the thin form of the SVD is
(7.5.1)#$... | {
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The rank of a sum of matrices is always less than or equal to the sum of the ranks, so $$\mathbf{A}_k$$ is a rank-$$k$$ approximation to $$\mathbf{A}$$. It turns out that $$\mathbf{A}_k$$ is the best rank-$$k$$ approximation of $$\mathbf{A}$$, as measured in the matrix 2-norm.
Theorem 7.5.1
Suppose $$\mathbf{A}$$ has... | {
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The rapid decrease suggests that we can get fairly good low-rank approximations.
plt = plot(layout=(2,2),frame=:none,aspect_ratio=1,titlefontsize=10)
for i in 1:4
k = 3i
Ak = U[:,1:k]*diagm(σ[1:k])*V[:,1:k]'
plot!(Gray.(Ak),subplot=i,title="rank = \$k")
end
plt
Consider how little data is needed to reconstruct these... | {
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# Can you ignore 'unused' quantifiers?
My question is simple, as the title says: can I safely remove (or add) a quantifier if the variable bound to it is not used in any predicate following it?
As an example: I wanted to prove $$\exists x(P(x) \implies \forall yP(y))$$ My proof went like this: $$\exists x(P(x) \impli... | {
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Null Quantification
Where $\varphi$ does not contain $x$ as a free variable:
$\forall x \varphi \Leftrightarrow \varphi$
$\exists x \varphi \Leftrightarrow \varphi$
• How can you prove this? – Ben-ZT Feb 26 '18 at 3:34
• @Ben-ZT Are you looking for a proof based on the formal semantics of the quantifiers, or a form... | {
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A First Course in Mathematical Analysis, David Alexander Brannan, ch 1, 1.6 exercises, section 1.3, problem 3
Prove the inequality $$3^{n}\ge2n^{2}+1$$
for $$n=1,2,\dots$$
This looks like a problem which might be solved using the binomial theorem. Recall \begin{align*} (1+x)^{n} & =1+nx+{n \choose 2}x^{2}+\dots\\ & ... | {
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I don't have a solution to check against. Are my proofs valid?
• your proofs look basically correct; you could choose base case $0$ to prove the proposition for $0, 1, 2, ...$ or base case $1$ to prove it for $1, 2, ...$ – J. W. Tanner Sep 24 '19 at 2:18
• How and why do you choose 0 or 1? For me, I chose 0 because th... | {
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# Monotonicity of quadratic function at its vertex?
In my school text book, It say that the quadratic function is increasing and decreasing at some intervals based on the function, however both intervals didn't include the vertex and it was't discussed at all.
Should the vertex be constant because its slop is equal t... | {
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There is no requirement (or guarantee) that the intervals of monotonicity cover the entire domain.
For example $f(x) = x \cdot sin \frac{1}{x}$ for $x \ne 0$ with $f(0)=0$ is a continuous function which is not monotonic on any interval that includes $0$. For an example of a discontinuous function which is not monotoni... | {
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Related Rates:
Gas is escaping from a spherical balloon at the rate of 2ft^3/min. How fast is the surface area shrinking (ds/dt) when the radius is 12ft? (A sphere of radius r has volume v=4/3 pi r^3 and surface area S=4pi r^2.)
Remember that ds/dt = ds/dr X dr/dt
Step 1: Find ds/dr
I have no clue where to start. I... | {
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2. ### Math
A spherical balloon is to be deflated so that its radius decreases at a constant rate of 12 cm/min. At what rate must air be removed when the radius is 5 cm? Must be accurate to the 5th decimal place. It seems like an easy
3. ### math
The launch site for trigon balloon co. is 250 ft above sea level. A ho... | {
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2. ### calculus
A spherical balloon is losing air at the rate of 2 cubic inches per minute. How fast is the radius of the ballon shrinking when the radius is 8 inches.
3. ### Calculus
A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2cm/min. At what rates are the volume ... | {
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# Proof verification- Let $(X,\tau)$ be a topological space such that every subset is closed then prove that $(X,\tau)$ is a discrete space.
Let $(X,\tau)$ be a topological space. I need to show that if every subset is closed then it is a discrete space.
For finite $X$, let $S$ be a subset of $X$. Since $S$ is closed... | {
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• Does the same logic apply to both finite and infinite subsets of $X$? – Parth May 6 '17 at 12:28
• @Parth yes, it does. On your proof, which step did you think not work for infinite set? - Are you concerning "arbitrary choice of subset s from an infinite set X"? Notice we are not involving any additional axiom here -... | {
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## Section2.11A few notes on computation
Many of the results in these notes have been illustrated on the computer and some of the exercises require a computational approach. Whenever using the computer, it is always wise to examine the results critically. Here's a simple numerical example where things clearly go awry.... | {
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The same can be said for the bifurcation diagram in figure Figure 2.6.3. In much of that image, we see a gray smear indicating chaos. How can we trust that? Well, first, theory tells us that there really is chaos. That is, there are orbits that are dense in some interval for many $c$ values. Furthermore, much of the im... | {
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# Asymptotic expansion of the integral $\int_0^1 e^{x^n} dx$ for $n \to \infty$
The integrand seems extremely easy:
$$I_n=\int_0^1\exp(x^n)dx$$
I want to determine the asymptotic behavior of $I_n$ as $n\to\infty$. It's not hard to show that $\lim_{n\to\infty}I_n=1$ follows from Lebesgue's monotone convergence theore... | {
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where
$$K_m = \sum_{k=1}^{\infty} \frac{1}{k^{m} k!}$$
To first order in $n$:
$$I_n \sim 1+\frac{K_1}{n} \quad (n \to \infty)$$
where
$$K_1 = \sum_{k=1}^{\infty} \frac{1}{k\, k!} = \text{Ei}(1) - \gamma \approx 1.3179$$
This checks out numerically in Mathematica.
BONUS
As a further check, I computed the followi... | {
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Now we can estimate $e^x$ on the interval $[0,1]$ to get
$$\frac{1}{n}\int_0^1 x^{\frac{1}{n}-1}(1+x)\, dx < I_n < \frac{1}{n}\int_0^1 x^{\frac{1}{n} - 1} (1 + (e-1)x)\, dx$$ or $$1 + \frac{1}{n+1} < I_n < 1 + \frac{e-1}{n+1}.$$
• -- very nice! -- Apr 29, 2013 at 7:00
A related technique. Here is a start. Integratin... | {
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# Prove that $\sum_{i=0}^{2n}(-1)^i\frac{1}{i!(2n-i)!} = 0$ for any $n>2$
I've been trying to solve this problem lately, but I have been unable to do it. I want to prove that
$$\sum_{i=0}^{2n}(-1)^i\frac{1}{i!(2n-i)!} = 0$$
For any $n>2$. We can generalize the problem changing $2n$ to $a$, I don't mind, although I a... | {
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The probability of picking a set in $C$ with an even number of elements is exactly $\frac{1}{2}$, which is the same as the probability of picking a set in $C$ with an odd number of elements.
To finish the proof, note that the probability of picking an element in $C$ of size $j\in\{0,1,2,\ldots,k\}$ is $$\frac{1}{k!}\,... | {
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# Secant Method to find root of any function
#### algorithm mathematical algorithm
Reading time: 35 minutes | Coding time: 10 minutes
Secant Method is a numerical method for solving an equation in one unknown. It is quite similar to Regula falsi method algorithm. One drawback of Newton’s method is that it is necessa... | {
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6. Print root as x_new
7. Stop
## Sample Problem
Now let's work with an example:
Find the root of f(x) = x3 + 3x - 5 using the Secant Method with initial guesses as x0 = 1 and x1 =2 which is accurate to at least within 10-6.
Now, the information required to perform the Secant Method is as follow:
• f(x) = x3 + 3... | {
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cout << "\nEnter precision of method: ";
cin >> precision;
int iter=0;
cout<<setw(3)<<"\niterations"<<setw(8)<<"x0"<<setw(16)<<"x1"<<setw(25)<<"function(x_new)"<<endl;
auto start = high_resolution_clock::now();
do{
x_new=x1-(function(x1)*(x1-x0))/(function(x1)-function(x0));
iter++;
cout<<setprecision(10)<<setw(3)<... | {
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# Is there a name for the value $x$ such that $f(x)$ is maximum?
Obviously, $f(x)$ is called the "maximum value" or simply "maximum", but what is $x$ called? The maximizer?
Additionally, what if $f(x)$ is minimum or simply an extremum?
• "maximizer" sounds fine to me. – David Mitra Oct 11 '13 at 22:04
• The Maximize... | {
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5,941 views
To pass a test, a candidate needs to answer at least $2$ out of $3$ questions correctly. A total of $6,30,000$ candidates appeared for the test. Question $A$ was correctly answered by $3,30,000$ candidates. Question $B$ was answered correctly by $2,50,000$ candidates. Question $C$ was answered correctly by... | {
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# Solving Rational Inequalities Calculator | {
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zip: 1k: 12-09-18: Absolute Value Solver This program will solve absolute value equations and inequalities of the form a|bx+c| + d = e. For inequalities involving absolute values ie. Solve the rational equation. Enter a polynomial inequality along with the variable to be solved for and click the Solve button. Double ta... | {
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be finding a common denominator that has 'x's. Less Than Or Equal To Type = for "less than or equal to". Exclude such values from the solution set. com and read and learn about inequalities, dividing rational and numerous other algebra subject areas. Solve equation. Example 1: to solve $\frac{1}{x} + 2x = 3$ type 1/x +... | {
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Total duration: 11:49. UNIT 7: Polynomial Functions. The calculator uses cross multiplication to convert proportions into equations which are then solved using ordinary equation solving methods. Find the yearly rate when the amount of interest, the principal, and the number of days are all known. This is a Math solver ... | {
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This results in a parabola when plotting the inequality on a coordinate plane. This set features two-step addition and subtraction inequalities such as “2x + 5 > 15″ and “ 4x -2 = 14. "vertical asymptotes" (where the function is undefined). Students develop understanding by solving equations and inequalities intuitivel... | {
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5 - Solving Inequalities Algebraically and Graphically Linear Inequalities. Solving Rational Equations ©2001-2003www. about Math Solver. A rational number is a number that can be written as a ratio. Just fill in what’s on the left and right side of your inequality. It’ll help you solve various types of problems and it’... | {
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us recall that an inequality is almost like an equation, but instead of the "=" sign, we have "≤" or "≥". How to Use the Calculator. divide 1 2/6 by 2 1/4. The TI-89 won't manipulate a "double inequality" like this directly, you need to separate it into two separate inequalities as shown on the right. The following is ... | {
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you write this solution as (-2, 3]. Solving Rational Equations Date_____ Period____ Solve each equation. Solving Rational Equations and Inequalities. You can find the. Graphing and Solving Inequalities. Back to Assignment Back to BrainPOP 101 Course. For example, do not enter 5 (3-4). There is no cost or registration r... | {
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To find the key/critical values, set the numerator and denominator of the fraction equal to zero and solve. Sets of Linear Equations. Understand solving an equation or inequality as a process of. Online Algebra Math Solver for second degree, third degree and fourth degree polynomials, inequalities, vector and sets. It ... | {
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proof that the set of prime numbers is endless, and Goldbach's conjecture. If perhaps you actually have assistance with math and in particular with free algebra solver step by step or polynomials come pay a visit to us at Rational-equations. UNIT 3: Absolute Value & Piecewise Functions. The calculator uses cross multip... | {
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in the category - Solving For The Variable Calculator. Solving Quadratic Inequalities with a Sign Graph: Writing a Rational Expression in Lowest Terms: Solving Quadratic Inequalities with a Sign Graph: Solving Linear Equations: The Square of a Binomial: Properties of Negative Exponents: Inverse Functions: fractions: Ro... | {
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functions with holes. I am new to sympy but want to solve the following problem: I have multiple inequality constraints of the form. Namespace: Microsoft. Chicago Public Schools is the third largest school district in the United States with more than 600 schools and serves 361,000 children. Any equation with one or mor... | {
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statements or are excluded values that make a denominator equal to 0. Any lowercase letter may be used as a. Even I faced similar problems while solving rational expressions, interval notation and adding exponents. Problem: I have no clue what the formula is to solve this. The TI-89 won't manipulate a "double inequalit... | {
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This website uses cookies to ensure you get the best experience. Get Started. 1 Determine whether a relationship is a function and identify independent and dependent variables, the domain, range, roots, asymptotes and any points of discontinuity of functions;. Solve quadratic equations using the quadratic formula. Simp... | {
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this great program. The following is a method for solving rational inequalities. Inequalities: In Depth. Here are the steps required for Solving Rational Inequalities: Step 1: Write the inequality in the correct form. Look for common denominators when solving inequalities with fractions Example: 2/3 + 1/3 < 2/3. Even I... | {
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into your online assignment. This calculator will solve the linear, quadratic, polynomial, rational and absolute value inequalities. BMI Calculator » Triangle Calculators » Length and Distance Conversions » SD SE Mean Median Variance » Blood Type Child Parental Calculator » Unicode, UTF8, Hexidecimal » RGB, Hex, HTML C... | {
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In this section, we solve equations and inequalities involving rational functions and explore associ-ated application problems. Knowing that the sign of an algebraic expression changes at its zeros of odd multiplicity, solving an inequality may be reduced to finding the sign of an algebraic expression within intervals ... | {
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system of equations and rational inequalities because I just can’t seem to figure out a way to solve problems based on them. com contains insightful resources on free polynomial and rational inequalities online calculator, linear systems and worksheet and other math topics. Williams “Thank you for shipping my TI83 grap... | {
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as well. If you like this Site about Solving Math Problems, please let Google know by clicking the +1 button. Augmented Matrix. Let’s just jump straight into some examples. Solve the rational equation. 567x+2y-7z=123. Explanation:. What are Functions? Basic Linear Functions. English (Oregon State University), Irrigatio... | {
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of a number on the number line from 0 without considering which direction from zero the number lies. divide 1 2/6 by 2 1/4. Rational-equations. Evaluating expressions. 45x-24y+78z=12. A solution of a simplified version of an equation that does not satisfy the original equation. Solve equation. Thus the set of our solut... | {
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breaking down key steps. Section 2-13 : Rational Inequalities. Rational Functions Test Review (2015) Solutions (2015) Lesson 9-5 Adding and Subtracting Rational Expressions. Any help is appreciated, thank you!! In the mean time, I'll keep sorting through the lessons on this site to see if I can find the one that pertai... | {
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that is a solution to the original equation. 25 and 1/5 = 0. Model Algebra Equations - Learning Connections. Quadratic equations word problems. Like normal algebraic equations, rational equations are solved by performing the same operations to both sides of the equation until the variable is isolated on one side of the... | {
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, if f(x) is below the x-axis. Just fill in what's on the left and right side of your inequality. But because rational expressions have denominators (and therefore may have places where they're not defined), you have to be a little more careful in finding your solutions. Why should we clear fractions when solving equat... | {
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scatter plot and draw an informal inference about any correlation between the variables. What is the best way to go about this? The values for R and a in this equation vary for different implementations of this formula, but are fixed at particular values. MathPlanetVideos. Translate verbal phrases into algebraic expres... | {
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and adapt a variety of appropriate strategies to solve problems. Free inequality calculator - solve linear, quadratic and absolute value inequalities step-by-step This website uses cookies to ensure you get the best experience. Multiplying each side of. How to Use the Calculator. We are so glad that you are taking resp... | {
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"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9869795121840873,
"lm_q1q2_score": 0.8408599627455497,
"lm_q2_score": 0.8519528038477825,
"openwebmath_perplexity": 856.2827349084015,
"openwebmath_score": 0.41914433240890503,
"tag... |
up with a particular solution. Welcome to Educator. Examples shown for infinite, jump, and removable discontinuities. The diagram below illustrated the difference between an absolute value equation and two absolute value inequalities. Therefore, the solver will be efficient only if $$\min(n,e)+r$$ is small. It has prov... | {
"domain": "tuningfly.it",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9869795121840873,
"lm_q1q2_score": 0.8408599627455497,
"lm_q2_score": 0.8519528038477825,
"openwebmath_perplexity": 856.2827349084015,
"openwebmath_score": 0.41914433240890503,
"tag... |
− m + 1 m = 5 m2 − m 9) 1. we try to find interval (s), such as the ones marked "<0" or ">0" These are the steps: find "points of interest": the "=0" points (roots), and. Understand solving an equation or inequality as a process of. distance from 0: 5 units. , using technology to graph the functions, make tables of val... | {
"domain": "tuningfly.it",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9869795121840873,
"lm_q1q2_score": 0.8408599627455497,
"lm_q2_score": 0.8519528038477825,
"openwebmath_perplexity": 856.2827349084015,
"openwebmath_score": 0.41914433240890503,
"tag... |
least one rational expression. Come to Algebra-equation. Wolfram|Alpha is a great tool for finding polynomial roots and solving systems of equations. Math Central is supported by the University of Regina and the Imperial Oil Foundation. Here is an example: Greater Than Or Equal To. We can model the solution set both wi... | {
"domain": "tuningfly.it",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9869795121840873,
"lm_q1q2_score": 0.8408599627455497,
"lm_q2_score": 0.8519528038477825,
"openwebmath_perplexity": 856.2827349084015,
"openwebmath_score": 0.41914433240890503,
"tag... |
both sides by LCD. Model Algebra Equations - Learning Connections. Double tap ")" to enter "greater" sign. Extraneous solutions are solutions that don't satisfy the original form of the equation because they produce untrue statements or are excluded values that make a denominator equal to 0. exp (-tau))/ (1. Like norma... | {
"domain": "tuningfly.it",
"id": null,
"lm_label": "1. Yes\n2. Yes\n\n",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9869795121840873,
"lm_q1q2_score": 0.8408599627455497,
"lm_q2_score": 0.8519528038477825,
"openwebmath_perplexity": 856.2827349084015,
"openwebmath_score": 0.41914433240890503,
"tag... |
# When to use indefinite & definite integration to solve a problem
In a certain country , the population is projected to grow at a rate of
$$P'(t) = 400(1+\frac{2t}{\sqrt{25+t^2}} )$$
People per year $t$ years from now. The current population is $60,000$ . What will be the population $5$ years from now ?
To solve t... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9869795083542037,
"lm_q1q2_score": 0.8408599613376698,
"lm_q2_score": 0.8519528057272543,
"openwebmath_perplexity": 351.3614057704971,
"openwebmath_score": 0.9266781806945801,
"tag... |
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