All Questions
31
questions
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Using the trapezoidal rule for the Maxwell-Boltzman function
Background
I approached my physics professor with question 1 from this LibreTexts resource. (at the bottom of the page), to better understand the material via self-study.
Question
Using the Maxwell-...
- 1,426
1
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0
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41
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Sequence of Logic in Diffusion Problem DQ
Problem: If a tank is filled with 100 gallons of water and mistakenly added 300 pounds of salt. To fix the mistake the brine is drained at 3 gallons per minute and replaced with water at the same rate....
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0
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Arc length vs Surface of revolution.
I don't understand why these two problems are solved differently here the first one $fig(1)$ and 2nd one $fig(2)$. Why did we take the limit $\displaystyle \lim_{r\to0^+}\int_r^\pi \sqrt{2-2cost}\...
user1062191
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1
answer
63
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Why can we apply the surface area of revolution theorem to a spiral?
To find the surface area generated by revolving function f which is smooth on the interval [a,b] and $f(y) \ge0$ around the y-axis we can use the formula $$S=\int_a^b 2\pi rdl =\int_a^b 2\pi f(y)\...
- 318
1
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2
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538
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When can I apply the trapezoidal rule?
An artificial lake has the shape illustrated below , with adjacent measurements 20 feet apart. Use suitable numerical method to estimate the surface area of the lake.
I know how to solve this problem ...
- 318
1
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1
answer
61
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Why can we say here that $\Delta x_i=dx$ as $i$ approaches infinity?
In the proof of the arc length formula we assume that an element of the arc length is $$\Delta L_i=\sqrt{(\Delta x_i)^2+(\Delta y_i)^2}=\sqrt{1+\left(\frac{\Delta y_i}{\Delta x_i}\right)^2}\space \...
user1062191
1
vote
1
answer
50
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Calculus application question
My attempt:
Step 1: Find $x$ in terms of $t$.
$\frac{dt}{dx} = \frac{1}{-0.15x}$
$t = \frac{1}{-0.15}\ln(x) = x^{-1}(t)$
$x(t) = e^{-0.15t}+c$
However, here is where I am stuck. Without any extra ...
- 1,190
4
votes
1
answer
387
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I've never been so confused (Application of Integral Calculus)
Here's a problem on Application of Integral calculus to find the work done in moving a particle. I was able to 'reach' the 'right answer'. But I'm totally confused and utterly dissatisfied with the ...
- 1,156
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2
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2k
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Work on a chain (applications of the integral)
A 10-foot-long chain weighs 25 lbs. And hangs from a ceiling. Calculate the work done in raising the lower end of the chain to the ceiling so that it is at the same level as the upper end.
Please, ...
0
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1
answer
100
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Calculus applications - oil leaking from a boat
So here is the question:
The fuel from a ship leaks into the sea forming a circular oil slick. The area of this circle is increasing at the rate of $20$ $m^2$ per minute.
They asked me to prove that ...
- 1,190
3
votes
2
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295
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Can we clarify this "accumulated money flow" application of integration?
I read about this model/application in Calculus with Applications, 11th Edition by Lial, Greenwell, and Ritchey (example), where if you have a function $f(t)$ that models some revenue stream, the rate ...
- 19k
0
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1
answer
320
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Calculus - Calculate Work done to lift water out of tank
I need help setting up the integral so that I can calculate the work done. I've tried it many times and have referred to Youtube, slader, the textbook, and also this site, but I still don't get how to ...
- 133
-3
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1
answer
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set up an integral when the following functions revolve around the $x$, $y$ and $y=\frac{1}{2}$ [closed]
$y=\sin x$, $y=\frac{1}{2}$, $x=0$
i got the same integral which is
$$
\int_0^{ \frac{5 \pi}{6}} \pi \left(\sin^2(x)- \frac{1}{4}\right) \, \mathrm d x.
$$
Anyone help
- 107
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votes
1
answer
109
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Help with volume integration application problem using Disk or Washer Methods, revolving about x-axis, revolving about y-axis.
I need to find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines: y = $\sqrt {x}$ $y=0$, and $x=3$. A) the $x-axis$ B) the $y-...
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1
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Moment of inertia of a cone frustum with a cylinder cut out (using integral)
How can I find moment of inertia of this frustum when the mass M is uniformly distributed through the grey region using integration?
The hints said to break the region into two pieces, one with ...
