Question

on a snow day, robert created two snowmen in his backyard. snowman a was built to a height of 33 inches and snowman b was built to a height of 45 inches. the next day, the temperature increased and both snowmen began to melt. at sunrise, snowman a’s height decrease by 6 inches per hour and snowman b’s height decreased by 9 inches per hour. let a represent the height of snowman a t hours after sunrise and let b represent the height of snowman b t hours after sunrise. graph each function and determine which snowman is taller after 3 hours. click twice to plot each line. click a line to delete it.

Explanation:

Step1: Define height function for A

$A(t) = 33 - 6t$

Step2: Define height function for B

$B(t) = 45 - 9t$

Step3: Calculate A at t=3

$A(3) = 33 - 6(3) = 33 - 18 = 15$

Step4: Calculate B at t=3

$B(3) = 45 - 9(3) = 45 - 27 = 18$

Step5: Compare the two heights

$18 > 15$, so Snowman B is taller.

Answer:

Snowman B is taller after 3 hours, with a height of 18 inches (Snowman A has a height of 15 inches at that time).

For graphing:

• For Snowman A: Plot points $(0, 33)$ and $(3, 15)$, then draw a line through them.
• For Snowman B: Plot points $(0, 45)$ and $(3, 18)$, then draw a line through them.