Answer:
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
If y is inversely proportional to a³ and a is directly proportional to x. Then the relation between y and x is,
[tex]\rm y = \dfrac{16}{25x^3}[/tex]
The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
y is inversely proportional to a³.
Then we have
[tex]\rm y \propto \dfrac{1}{a^3}\\\\y = \dfrac{k}{a^3}[/tex]
When a = 2, y = 10. Then we have
[tex]\rm k = y a^3\\\\k = 10 * 2^3\\\\k = 80[/tex]
Then y will be
[tex]\rm y = \dfrac{80}{a^3}[/tex] ...1
a is directly proportional to x.
[tex]\rm a \propto x \\\\a = cx[/tex]
When x = 4, a = 20.
[tex]20 = 4c \\\\c \ = 5[/tex]
Then a will be
[tex]\rm a = 5x[/tex] ...2
Put equation 2 in equation 1. Then we have
[tex]\rm y = \dfrac{80}{(5x)^3}\\\\\\y = \dfrac{16}{25x^3}[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
