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Z is proportional to x^3. describe exactly what will happen to x when z became 8 times greater

User Mslowiak
by
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1 Answer

4 votes

Answer: x is doubled.

Explanation:

A proportional relationship between x and y is written as:

y = k*x

where k is called the constant of proportionality.

In this case, we know that we have a proportional relationship between z and x^3

Then:

z = k*x^3

What will happen to x when z is 8 times greater?

Let's rewrite this equation for two new quantities, z' and x'

z' = k*(x')^3

Now we need to replace z' by 8*z, then:

8*z = k*(x')^3

We want to find a relationship between x' and x.

And by the first relationship, we know that:

z = k*x^3

Then we can replace this in the equation "8*z = k*(x')^3" to get:

8*(k*x^3) = k*(x')^3

8*k*x^3 = k*(x')^3

Now we can divide both sides by k, so we get:

8*x^3 = (x')^3

Now we can apply the cubic root to both sides, to get:

∛(8*x^3) = ∛(x')^3

∛(8)*x = x'

2*x = x'

Then when we increase the value of z 8 times, the value of x will be doubled.

User CEarwood
by
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