How do you do these problems ?

Question

Write an equation to describe the variation. Use k for the constant of proportionality.
a varies inversely as s^4




Problem 2


Solve the proportion.

(1) / (w + 10 ) = ( 3) / (5w )

Answer 1

1.
a = k / s^4.

2.
1 / (w + 10) = 3 / 5w
Take reciprocals:
w + 10 = 5w / 3
Multiply by 3:
3w + 30 = 5w
Subtract 3w:
30 = 2w
Divide by 2:
w = 15.

Answer 2

1)

a = k(1/s^4)

as you can see, a is varying as the inverse of s^4 ( or 1/s^4)

2)
multiply both sides by the denominators

(5w)(w+10) ( 1/(w+10) ) = (5w)(w+10)(3/(5w))

5w = 3(w+10)

5w = 3w +30

solve for w

2w = 30

w = 15

Answer 3

a= k/s^4

(1) / (w + 10 ) = ( 3) / (5w )
Just cross multiply getting:
3(w+10) = 5w(1)
3w +30 = 5w
30 = 2w
15 = w

Answer 4

k = a * s^4 or a = k/s^4


1/(w + 10) = 3 / 5w

cross multiply
5w = 3(w + 10)

distribute
5w = 3x + 30

subtract 3x for both sides
2x = 30

divide 2 for both sides
x = 15

domain: x can't be -10 or 0