Question

p= kq^3. when p= 9 , q= 3 a) calculate the value of k b) calculate p when q= 6 c) calculate p when q= 1 d) calculate q when p= 576

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

p = kq³

(a)

To find k use the condition when p = 9, q = 3, that is

9 = k × 3³ = 27k ( divide both sides by 27 )

k = $\frac{9}{27}$ = $\frac{1}{3}$

p = $\frac{1}{3}$ q³ ← equation of variation

(b)

  When q = 6, then

p = $\frac{1}{3}$ × 6³ = $\frac{1}{3}$ × 216 = 72

(c)

When q = 1, then

p = $\frac{1}{3}$ × 1³ = $\frac{1}{3}$

(d)

When p = 576 , then

576 = $\frac{1}{3}$ q³ ( multiply both sides by 3 )

1728 = q³ ( take the cube root of both sides )

q = $\sqrt[3]{1728}$ = 12