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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.

The Cube Of Y Varies Directly As A When Y8 Z8 Heathers Work Finding The Value Of Y When Z 64 Is Shown Picture Of Heathers Work Below What Is The First Error If class=

Sagot :

B

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

[tex]y=kx[/tex]

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:

[tex]\begin{gathered} y^3=kz \\ (8)^3=k(8) \\ 512=8k \\ 8k=512 \\ \frac{8k}{8}=\frac{512}{8} \\ k=64 \end{gathered}[/tex]

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

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

The first error then was:

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

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