Question

the cube of y varies directly as a. when y=8, z=8. heathers work finding the value of y when z = 64 is shown: (picture of heathers work below) what is the first error, if any, in heathers work?a: she did not make any errors.b: she substituted incorrectly when calculating the constant of variation.c: she used an equation that models inverse variation instead of direct variation.d: she cubed the wrong variable when making her equation.

Answer 1

Answer: just took the test

Explanation:

Answer 2

B

1) Let's redo the steps Heather did when calculating this. Note that direct variation can be generally written as:

`y=kx`

2) Heather was told that when y=8 then z=8 so let's find the constant of proportionality (k) plugging into the formula below into y and z the given values:

`\begin{gathered} y^3=kz \\ (8)^3=k(8) \\ 512=8k \\ 8k=512 \\ (8k)/(8)=(512)/(8) \\ k=64 \end{gathered}`

Now we know the value of k, let's test that and then mark the right choice

`\begin{gathered} y^3=k\cdot z \\ y³=64\cdot8 \\ y=\sqrt[3]{512} \\ y=8 \end{gathered}`

The first error then was:

b. She substituted incorrectly when calculating the constant of variation.