Answer:
c = 10
Step-by-step explanation:
Given that H varies directly as c³ then the equation relating them is
H = kc³ ← k is the constant of variation
To find k use the condition when H = 40, c = 2 , then
40 = k × 2³ = 8k ( divide both sides by 8 )
5 = k
H = 5c³ ← equation of variation
When H = 5 000, then
5000 = 5c³ ( divide both sides by 5 )
1000 = c³ ( take the cube root of both sides )
[tex]\sqrt[3]{1000}[/tex] = c , so
c = 10
