All Questions
Tagged with applications calculus
175
questions
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One train travels north at $140$ mph towards Traveler's Town, while a second train travels west at $150$ mph away from Traveler's Town.
One train travels north at $140$ mph towards Traveler's Town, while a second train travels west at $150$ mph away from Traveler's Town. At time $t=0$, the first train is $70$ miles south and the ...
- 485
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0
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122
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Calculus problem profit of a bakery
Hello guys I have little background on this, I don't know how to attack this problem since I don't know what a "function of benefits" is or how to decide if it generate profits.
I know that if $f$ (...
- 415
3
votes
5
answers
110
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Finding the area bounded by $y = 2 {x} - {x}^2 $ and straight line $ y = - {x}$
$$
y =\ 2\ {x} - {x}^2
$$
$$
y =\ -{x}
$$
According to me , the area
$$
\int_{0}^{2}{2x\ -\ { x} ^2}\, dx \ + \int_{2}^{3}{\ {x} ^2\ -\ 2{x} }\, dx \\
$$
Which gives the area $ \frac{8}{3}$
But ...
user589548
1
vote
0
answers
300
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Any real life example of what happens to something when it is not differentiable at any point?
Can somebody tell any real life example which explains when something is not differentiable at some point. Like, a car moves and we get a graph of position time function, but what actually happens to ...
- 11
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137
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Learn Calculus with applications instead of rigor
OBJECTIVE: I am looking for some resources/books to learn Calculus. I have searched archives here and noticed that recommended books from reputed authors Spivak, Courant, Hardy, Apostol are based on ...
- 347
0
votes
1
answer
4k
views
Amount of work required for pulling rope problem
50 m rope with 8 millimeters in diameter is dangling from an edge. density of rope =40 g/m. how much work to pull it up to edge?
// I've seen different variations of this problem, but I am unsure of ...
- 129
1
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0
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100
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What are some example use cases for Newton's Method being extended to higher dimensions?
I'm currently working on a project to attempt to optimize a program that runs Newton's Method in higher dimensions - the actual computer science isn't important. However, what is a lot more important ...
- 1,908
1
vote
1
answer
104
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Is it important to keep one's goal in mind when learning calculus?
I am learning calculus primarily as a prerequisite to understanding machine learning and other statistics/finance applications (Black Scholes, etc.), but I've found that most of the web content ...
- 1,922
3
votes
1
answer
66
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Dynamics - Sprinter
Question: A sprinter accelerates uniformly to his top speed after running 30 metres of a 100-metre race. He maintains this speed for the remainder of the race and takes 10.4 seconds to complete it. ...
- 838
4
votes
1
answer
1k
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Applications of First Order Differential Equations
Can I get help for this question please?
Suppose that a tank containing a liquid is vented to the air at the top and has an outlet at the bottom through which the liquid can drain. It follows from ...
- 95
-2
votes
4
answers
77
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Acceleration + velocity calculus question [closed]
Explanation for Calculus question needed
The acceleration $a\,\text{m/s}^2$ of a particle $P$ moving in a straight line is given by $a = 3(1-x^2)$ , where $x$ metres is the displacement of the ...
0
votes
1
answer
92
views
A tank is part of a cone with a 10 foot radius on top, 4 foot radius on bottom 12 feet below the top Water in the tank has depth 5 feet
A tank is part of a cone with a 10 foot radius on top and a 4 foot radius on bottom, 12
feet below the top. Water in the tank has depth 5 feet.
Provide an integral for the work
done pumping the water ...
- 9
0
votes
1
answer
341
views
Computing height of water level in tank given dimensions, size of hole and gravity?
I was given a question involving creating a function for the height of the water level in a tank, given gravity, the size of the hole in the tank and dimensions of the tank, as identified here.
I am ...
- 11
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36
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Show that $y(t) = T(t − t_{0})$ also satisfies Newton’s law of cooling, $\frac{dT}{dt} = k(T_{e} − T)$, for any constant $t_{0}$.
This question if from MIT's Open Course Ware for Single Variable Calculus:
Show that $\:y(t) = T(t − t_{0})$ also satisfies Newton’s law of cooling, $\: \frac{dT}{dt} = k(T_{e} - T,)\:$for any ...
- 353
2
votes
2
answers
84
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Is it possible to find angles and length of woods?
With respect to the picture below, is it possible to find the angles and the length of the wooden bars, if we have no further information? Any hint or clue would be appreciated.
- 25.2k