All Questions
81
questions
3
votes
2
answers
81
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calculus optimization problem: rectangle inscribed in a triangle.
I have a solution to the problem below from my course materials, but I cannot understand where I went wrong with my own attempt at a solution. Any advice much appreciated.
Problem:
Given a right ...
- 491
1
vote
1
answer
97
views
Area of the wet part of a horizontal cylinder
So, my math teacher gave me an interesting problem on mensuration.
Given, a cylinder of Height $H$ and radius $r$ is filled with water upto height h. Then the cylinder is pushed and it lies down ...
- 11
0
votes
1
answer
44
views
Maximum Length of a Triangle [closed]
I am stuck on a question concerning right triangles. I will list my approach out below:
Question
Consider a right-angled triangle with hypothenuse (i.e. diagonal side) of length 2 and draw a vertical ...
- 173
1
vote
2
answers
106
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Surface area of sphere coming out as $\pi^2 r^2$ [duplicate]
Take a hemisphere and divide its surface area into strips like on a watermelon.
Each strip can be approximated as a triangle with the long two sides = $\pi \frac r2$ (quarter of circumference) and if ...
- 19
1
vote
0
answers
98
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Is the area of a triangle is less than that of its mean triangle of equal area?
Definitions: We generate random triangles using various distribution (uniform, gaussian etc) for $\theta$ to get the polar coordinates of the vertices $𝑟\cos \theta,𝑟\sin \theta$ in a circle of ...
- 20.8k
3
votes
1
answer
184
views
What is the minimum and the maximum perimeter of a triangle with area $x$ that can be inscribed in a circle?
Posted in MO since it has been open in MSE for over 2 months.
The area of the largest triangle that can be inscribed in a circle of raidus $1$ is $\displaystyle \frac{3 \sqrt{3}}{4}$ for a equilateral ...
- 20.8k
0
votes
5
answers
440
views
Shortest distance from point to a curve and Estimation of error of an incorrect approach
Today I wrote an answer to a question in regards to the topic of shortest distance between a point and a curve, more precisely an ellipse, check here. Turns out the answer was incorrect, yet it was a ...
- 2,183
0
votes
1
answer
126
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Calculation of Areas of Leaf-like Segments in an Equilateral Triangle [duplicate]
I hope this message finds you well. I recently came across a captivating geometry problem involving an equilateral triangle and leaf-like segments formed by intersecting arcs. I encountered this ...
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-1
votes
1
answer
136
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Solution Check for a Related Rates Problem Involving Shadow Length and Position
I am working on the following problem:
A girl 5 ft tall is running at the rate of 12 ft/s and passes under a
street light 20 ft above the ground. Find how rapidly the tip of her
shadow is moving when ...
- 687
1
vote
0
answers
209
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Prove the Pythagoras theorem through calculus
Prove the Pythagoras theorem using calculus, by using the fact that the area of a circle is proportional to the square of its radius.
I was reading a routine morning message in a local chat group. ...
-1
votes
1
answer
25
views
Maximize the area of a triangle by differential [closed]
Two sides of a triangle have lengths "a" and "b" and the angle between them is "θ". What value of "θ" will maximize the area of the triangle?
pd. sorry my bad ...
- 1
15
votes
2
answers
521
views
Differentiating The Law of Cosines
Alright, I've got a stupid question (maybe). I took the equation given by the law of cosines and I differentiated it with respect to some other parameter.
Right, so we begin be considering a triangle ...
user1059904
0
votes
1
answer
58
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How do I make a formula to find the dimensions of a shape that is offset from the original by 1/4 inch?
I am trying to make a formula that given 3 lengths (left height, right height and base) it can give me new lengths of a shape that is 1/4" offset out from every side.
For example given this shape:...
- 3
6
votes
5
answers
728
views
The hardest geometry question with "a triangle" and "a circle" - Circle intersecting triangle equally in 5 parts
I received this question long time ago from one of my old friends who is mathematician/physicist. He called it the hardest geometry question with "a triangle" and "a circle". I am ...
- 725
1
vote
1
answer
52
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Can this function have a minimum or maximum value? If yes, is my function correct?
The problem is the following (Ron Larson's Calculus for AP - 2nd Edition):
My solution to part a). was found by proving that the triangles are similar by the AA property (by comparing Alternate ...
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