Question

S=16Ad^-2/3

Write d in terms of A and S.
Anyone know how ?

Answer 1

so first divide boths sides by 16A and will get

S/16A = 1/cuberoot(d^2)

so because d^-2/3 = 1/cuberoot(d)^2

cross multiplie and will get

S*cuberoot(d^2) =16A than now divide both sides by S

cuberoot(d^2)=16A/S make on exponent 3 both sides

d^2 = (16A/S)^3 make squareroot from both sides

d=(+/-) sqrt((16A/S)^3) = 16A/S *(+/-)sqrt(16A/S) = 4*16A/S *(+/-)sqrt(A/S) =
=64A/S *(+/-)sqrt(A/S)

so this (+/-) sign that like for example sqrt(9)= +/- 3 so because 3*3=9 and
(-3)*(-3)=9 too

hope so much that is understandably sure right

good luck

bye