Question

prob @Physics

Answer 1

A wire 10 m long is cut into 2 parts. One part is bent into the shape of a circle and other into shape of equilateral triangle .How should the wire be cut so that the combined area of two figures is as small as possible???

Answer 2

Suppose the two lengths are A and B.

Write down for me the equation for the area of the circle in terms of A and then the equation for the area of the triangle in terms of B.

Answer 3

pi*r*r= area of circle

Answer 4

here 2 pi r=A

Answer 5

R=A/2PI

Answer 6

AREA OF TRIANGLE =(1/2)*B/3*(B/3)

Answer 7

Let C be the area of the circle. You need to write down that area as a function of A,
C = C(A).

And T = area triangle, T = T(B). What you just wrote isn't correct.

Answer 8

y?

Answer 9

Because the idea is once we know those functions, the combined area is
C(A) + T(B)

Write now x = A, then as A + B = 10, B = 10 - A = 10 - x.

Hence the problem is now finding the global minimum of the function

f(x) = C(x) + T(10-x).

This is why we need the functions C and T. So find them.

Answer 10

k find it

Answer 11

The ball is in your court, as we say in English. Which means, I'm waiting now for you to say something. It's up to you to find C(A) and T(B). This part of the problem should be elementary, high school level work.

Answer 12

if x is bent into a circle,what's the radius of this circle?

Answer 13

Still waiting for your answer here :-)

Answer 14

and to tell you honestly I'm not happy about helping you with another problem until I see you work one yourself. So I'd like to see work this one.

Answer 15

i honestly dont know

Answer 16

Show me. What is C(A), T(B) and f(x). Then what value of x minimizes f(x)

Answer 17

i got it

Answer 18

i found the value

Answer 19

What is the function f(x) and what is that value of x?

Answer 20

As A = 2.pi.r, r = A/(2.pi) hence
C(A) = pi.r^2 = A^2/(4.pi)

Now what's T(B)?

Answer 21

R= 1-PI/PI+3ROOT3

Answer 22

SRRY NOT 1- ITS 10