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Question 61285This question is from textbook Elementary and Intermediate Algebra
: Comparing Dart Boards: A toy store sells two sizes of circular dart boards. The larger of the two has a radius that is 3 inches greater than that of the other. The radius of the smaller dartboard is t inches. Find a polynominal that represents the difference in area between the two dartboards.
This question is from textbook Elementary and Intermediate Algebra
Answer by jai_kos(139)   (Show Source):
You can put this solution on YOUR website! Given two dartboards, one smaller and other larger.
Given the radius of the smaller dart board = t inches.
And the radius of thr bigger dart board = t + 3 inches.
Let first find the area of the smaller dart board = pi r^2 = pi * t^2 ---->(1)
Because the radius is equal to t inches.
Now let us find the area of the bigger dart board = pi r^2 = pi * (t+3)^2 ---->(2)
Because the radius of the biggger dart board.
Now since there are asking for the difference in the area's, we subtract equation(2) with one...
We get,
Area of the bigger dartboard - Area of the smaller dart board =
pi (t+3) ^2 - pi t^2
Taking the pi common out,
pi[ (t+3)^2 - t^2]
Splitting the terms , we get
pi[ t^2 + 6t + 9 -t^2]
pi[ 6t+ 9]
The above gives us a polynominal that representsthe difference in the areas of
the dart boards.
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