math problems

1. Since x - y varies directly as x + y

So, let x - y = k(x + y), where k is a constant.

x - y = k(x + y)

x - y = kx + ky

(1 - k)x = (1 + k)y

y = (1 - k)x/(1 + k), where (1 - k)/(1 + k) is a constant.

So, y varies directly as x.



Let A and R be the surface area and the radius of the sphere respectively.

Given, A varies directly as square of radius.

So, A = kR² , where k is a constant.

When R = 8, A = k(8)² = 64k cm²

When R = 10, A' = k(10)² = 100k cm²

So, percentage change

= (A' - A)/A X 100%

= (100k - 64k)/64k X 100%

= +56.25%

1.) x-y = k(x+y)
x-kx = ky+y
(1-k)x = (k+1) y
i.e. y= (1-k)x / (k+1)
hence, y varies directly as x.