To find the height of the hill in the painting 3 inches from the left side of the picture, we need to evaluate the given height function [tex]\(h(x)\)[/tex] at [tex]\(x = 3\)[/tex].
The height function is given by:
[tex]\[
h(x) = -\frac{1}{5}x(x - 13)
\][/tex]
Let's substitute [tex]\(x = 3\)[/tex] into the height function and calculate [tex]\(h(3)\)[/tex]:
[tex]\[
h(3) = -\frac{1}{5} \cdot 3 \cdot (3 - 13)
\][/tex]
First, calculate the expression inside the parentheses:
[tex]\[
3 - 13 = -10
\][/tex]
Next, multiply [tex]\(3\)[/tex] by [tex]\(-10\)[/tex]:
[tex]\[
3 \cdot (-10) = -30
\][/tex]
Now, multiply [tex]\(-\frac{1}{5}\)[/tex] by [tex]\(-30\)[/tex]:
[tex]\[
-\frac{1}{5} \cdot (-30) = 6
\][/tex]
So, the height of the hill [tex]\(3\)[/tex] inches from the left side of the painting is:
[tex]\[
h(3) = 6
\][/tex]
Therefore, the height of the hill in the painting 3 inches from the left side is:
[tex]\[
6 \text{ inches}
\][/tex]
