Question

Linear equations-transposition-How to do the starred equations

Answer 1

I can't see the instructions, so I assume you're solving for the variable to the right.

(a)
A = pi*r(l+L), first divide both sides pi*r
A/(pi*r) = l + L, next subtract l from both sides
L = A/(pi*r) - l

(b)
V = pi*r^2*h, first isolate the variable r by dividing both sides by pi*h
V/(pi*h) = r^2, next take the inverse operation of square, which is the square root
r = sqrt root [ V/(pi*h)], assume r is a positive number only, so you do not need to consider the - square root option

(d)
t = 2*pi*sqrt (L/g), first divide both sides by 2*pi to isolate the radical
t/(2*pi) = sqrt (L/g), next square both sides to remove the radical sign over L
[t/(2*pi)]^2 = L/g, last multiply both sides by g
L = g*[t/(2*pi)]^2

(e) (actually it should say KE for kinetic energy)
E = (1/2)mv^2, multiply both sides by 2 and divide both sides by m
2*E/m = v^2, next take the inverse operation of square, square root of both sides 
v = sqrt [2*E/m], again assume v is a positive quantity, although velocity is a vector quantity and should indicate both magnitude and direction