Question

All 4 questions please

Answer 1

1. π = S/2πrh
2. v = √2E/m
3. b = (-7a+c)/2
4. x =3y-1

Explanation:

1.

`S = 2\pi rh\\Divide\:both\sides\:of\:the\:equation\:by\:2rh\\\\(S)/(2rh) = (2 \pi rh)/(2 rh) \\\\\pi = (S)/(2rh)`

2.

`E = (1)/(2) mv^2\\\\E = (mv^2)/(2) \\\\Cross\:multiply\\\\2E =mv^2\\Divide\:both\:sides\:of\:the\:equation\:by\:m\\(2E)/(m) = (mv^2)/(m) \\\\(2E)/(m) =v^2\\Square\:root\:both\:sides\:of\:the\:equation\\\sqrt{(2E)/(m) } = √(v^2) \\\\\sqrt{(2E)/(m) } =v\\\\v =\sqrt{(2E)/(m) }`

3.

`7a+2b =c\\Isolate\:b\\\\2b =c-7a\\2b= -7a+c\\Divide\:both\:sides\:of\:the\:equation\:by \:2\\(2b)/(2) =(-7a+c)/(2) \\\\b = (-7a+c)/(2)`

4.

`y = (1)/(3) (x+1)\\\\y = (x+1)/(3)\\\\Cross\:multiply \\3y =x+1\\Isolate \:x\\3y -1=x\\\\x =3y-1`