All Questions
214
questions
1
vote
1
answer
95
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
0
answers
29
views
how to find circle of curvature centre point
For this question I am asked to find the radius and centre-point of the
circle of curvature for the following function:
$−7.87e^{2.65x}$
I calculate the radius correctly with the formula: $R =\frac{...
0
votes
1
answer
47
views
How to find the circle of curvature centre
For the following question I am asked to
find the radius for circle of curvature for the function:
$-0.18e^{4.88x}$
I found the radius 1.681459915,
by using the formula: R =1/ρ
and this was correct ...
0
votes
3
answers
54
views
Trying to understand why a trigonometric substitution for the x value in an equation describing a circle uses Sin($\theta$).
Essentially I am trying to solve a definite integral for an equation that describes a circle.
I have $\sqrt(R^2 - (x - A)^2) - B)$ (A and B being the circle origin offsets and R the radius)
At a point ...
3
votes
2
answers
174
views
Simplify a formula with 449 terms - Radical circle
Context
The other day I wanted to answer this question.
Which is now closed so doesn't accept answers (but this isn't the important part).
Since I didn't know the topic I went to look it up but I ...
0
votes
2
answers
85
views
What location on a hypersphere maximizes the Manhattan distance of the radius?
In two dimension picture a unit circle. While the distance of the radius is constantly one, the Manhattan distance of the radius at zero degrees is equal to 1 while the Manhattan distance at 45 ...
- 300
0
votes
1
answer
64
views
Area under a circular arc confusion
I apologize that this is a basic question.
I have a circle with radius $2.5 \sqrt{2}$ (the center is the origin).
Consider the arc of the circle between $x=0$ and $x=1$. I want to know if the area ...
- 437
1
vote
2
answers
105
views
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
votes
1
answer
46
views
Parametric equations for a point traversing the circumference of a laterally accelerating circle (not rolling) with a max speed for the point.
Variables:
e -> point on a circle
r -> radius of said circle (constant)
x(t), y(t) -> parametric equations describing the position of point e
v -> velocity of the center of the circle
c -&...
1
vote
1
answer
81
views
Differential equation of orthogonal curves
Let us suppose we want to find the curve which is perpendicular to the curve $y=3x$. From the concept of straight lines,we know that the slope of that curve will be $-\frac{1}{3}$. Whose equation ...
- 681
0
votes
0
answers
45
views
Finding The Area of a Circle With Calculus [duplicate]
This is my first attempt to actually go ahead and prove the area of a circle is $\pi r^2$ using the methods shown on calculus. I first used a coordinate system and placed the centre of my circle (with ...
- 1,457
2
votes
2
answers
206
views
Maximizing the area enclosed by a curve of fixed length that passes through two fixed points: do the two arcs have equal length?
A closed curve of length $L>2$ passes through two fixed points that are $1$ unit apart. Suppose the enclosed area is maximized. The isoperimetric problem implies that each of the two sections of ...
- 25.5k
0
votes
0
answers
58
views
Parametrization of circle in clockwise
How to parametrize a circle in a clockwise direction? The problem was "$C$ is the portion of the circle $x^2 + y^2 = 1$ from $(0,1)$ to $(1,0)$ traced clockwise."
What I did was $c(t) = (\...
- 55
1
vote
1
answer
155
views
Evaluating area of a circle using integration. $\int_{0}^{R} \sqrt{R^2 - x^2} dx$ [duplicate]
I became curious about the alternative methods to write a formula for the area of a circle rather than the popular method of dividing a circle into equal sections of an infinitesimal angle.
I gave it ...
user1174597
2
votes
2
answers
312
views
Circumference of a ring
Circumference of a Circle is $2 \pi r$ , what about a ring though ? It will have two radiuses : Which one will we take into consideration while measuring the perimeter ? Will it have two different ...
- 135