# Thread: How to find this angle using application of differentitation

1. ## How to find this angle using application of differentitation

Part circle(radius is "r" ) is made from a string.string's lenght is "L".so the part
circle's circumference is also "L".If part circle's area is "A",Find the angle of the part
circle when Area is maximum

,here what I did but never got the answer.what is wrong in this?

$\displaystyle L=\frac{x}{360}2\pi r + 2r$

$\displaystyle A=\frac{x}{360}\pi r^{2}$

$\displaystyle x=\frac{360L-720r}{2\pi r}$

$\displaystyle A=\frac{360L-720r}{r}\pi r^{2}$

$\displaystyle \frac{\mathrm{dA} }{\mathrm{d} r}=360\pi L-2\ast 720\pi r$

setting to zero for the maximum value

$\displaystyle 360L=720*2r$
$\displaystyle r=4/L$
now what? answer has to be r(L-2r)/2(as books says).

2. ## Re: How to find this angle using application of differentitation

Anyone else getting Latex errors here?

3. ## How to find this angle using application of differentitation

Part circle(radius is "r" ) is made from a string.string's lenght is "L".so the part
circle's circumference is also "L".If part circle's area is "A",Find the angle of the part
circle when Area is maximum

,here what I did but never got the answer.what is wrong in this?

$\displaystyle L=\frac{x}{360}2\pi r + 2r$
$\displaystyle A=\frac{x}{360}\pi r^{2}$
$\displaystyle x=\frac{360L-720r}{2\pi r}$
$\displaystyle A=\frac{360L-720r}{r}\pi r^{2}$
$\displaystyle \frac{\mathrm{dA} }{\mathrm{d} r}=360\pi L-2\ast 720\pi r$

setting to zero for the maximum value

$\displaystyle 360L=720*2r$
$\displaystyle r=4/L$
now what? answer has to be r(L-2r)/2(as books says).

[can any admin or mod help me with this Latex error please ]

4. ## Re: How to find this angle using application of differentitation

Yeah I am getting the latex error too :/

5. ## Re: How to find this angle using application of differentitation

Originally Posted by silvercats
I think its your responsibility to check the errors.

6. ## Re: How to find this angle using application of differentitation

Originally Posted by silvercats

Yeah I am getting the latex error too :/
use [tex] and not [tex].

7. ## Re: How to find this angle using application of differentitation

(Corrected post)

Originally Posted by silvercats
Part circle(radius is "r" ) is made from a string.string's lenght is "L".so the part
circle's circumference is also "L".If part circle's area is "A",Find the angle of the part
circle when Area is maximum

,here what I did but never got the answer.what is wrong in this?

$\displaystyle L=\frac{x}{360}2\pi r + 2r$
$\displaystyle A=\frac{x}{360}\pi r^{2}$

$\displaystyle x=\frac{360L-720r}{2\pi r}$

$\displaystyle A=\frac{360L-720r}{r}\pi r^{2}$

$\displaystyle \frac{\mathrm{dA} }{\mathrm{d} r}=360\pi L-2\ast 720\pi r$

setting to zero for the maximum value

$\displaystyle 360L=720*2r$
$\displaystyle r=4/L$
now what? answer has to be r(L-2r)/2(as books says).

8. ## Re: How to find this angle using application of differentitation

Originally Posted by silvercats
Part circle(radius is "r" ) is made from a string.string's lenght is "L".so the part
circle's circumference is also "L".If part circle's area is "A",Find the angle of the part
circle when Area is maximum

,here what I did but never got the answer.what is wrong in this?

$\displaystyle L=\frac{x}{360}2\pi r + 2r$
$\displaystyle A=\frac{x}{360}\pi r^{2}$
$\displaystyle x=\frac{360L-720r}{2\pi r}$
$\displaystyle A=\frac{360L-720r}{r}\pi r^{2}$
$\displaystyle \frac{\mathrm{dA} }{\mathrm{d} r}=360\pi L-2\ast 720\pi r$

setting to zero for the maximum value

$\displaystyle 360L=720*2r$
$\displaystyle r=4/L$
now what? answer has to be r(L-2r)/2(as books says).

[can any admin or mod help me with this Latex error please ]

How did you come to the Equation in A the second time?

I get:

$\displaystyle A = \dfrac{180(L-2r)}{360\pi r}\pi r^2$

Also, you did the differentiation wrongly as L is a function of r and has to be considered in the differentiation process.

When you have substituted correctly x into A, you get the relationship between A and L. That seems what your book was looking for.

9. ## Re: How to find this angle using application of differentitation

yup [TEX] worked well.thanks
I got "A" because that is the equation to find the area of a part circle?

$\displaystyle A = \dfrac{180(L-2r)}{360\pi r}\pi r^2$ <<< how did you get that

10. ## Re: How to find this angle using application of differentitation

Strange... there weren't any posts when I checked this thread and suddenly, there are 6 posts before my first post here

Anyway, Show me how you got your second equation for A. You did a mistake in the substitution of x.