Answer:
Answer:
y = 16/25x³
Step-by-step explanation:
If y is inversely proportional to a^3, this is expressed as;
y∝1/a³
y = k/a³ where k is the proportionality constant
Given a=2, y=10, then 10 = k/2³
k = 10*2³
k = 80
Substituting k = 80 back into the formula;
y = 80/a³ ............. 1
Similarly, if a is directly proportional to x, then a ∝ x i.e a = kx
If x=4, a=20 then;
20 = 4k
k = 20/4
k = 5
Substituting k = 5 back into the formula;
a = 5x ....... 2
Substitute equation 2 into 1;
y = 80/a³
y = 80/(5x)³
y = 80/125x³
y = 16/25x³
Hence the formula for y in terms of x is y = 16/25x³
Step-by-step explanation:
Answer:
y = [tex]\frac{80}{a^3}[/tex]
Step-by-step explanation:
Given y is inversely proportional to a³ then the equation relating them is
y = [tex]\frac{k}{a^3}[/tex] ← k is the constant of variation
To find k use the condition a = 2, y = 10 , then
10 = [tex]\frac{k}{2^3}[/tex] = [tex]\frac{k}{8}[/tex] ( multiply both sides by 8 )
80 = k
y = [tex]\frac{80}{a^3}[/tex] ← equation of variation
