Modeling with Functions – Homework
1.
A rectangle has perimeter 100 feet. Find a function that models its area A in
terms of its length l .
2.
A rectangle has area 20 square feet. Find a function that models its perimeter
P in terms of its width w.
3.
A rectangle has width 4 feet. Find a function that models its area A in terms
of its perimeter P.
4.
A rectangle has length 5 feet. Find a function that models its perimeter P in
terms of its area A.
5.
The length of a rectangle is 5 feet longer than the width. Find a function that
models its area A in terms of its perimeter P.
6.
The length of a rectangle is 5 times the width. Find a function that models its
perimeter P in terms of its area A.
7.
The short leg of a right triangle is 4 feet. Find a function that models its area
A in terms of its hypotenuse z.
8.
The long leg of a right triangle is 5 feet. Find a function that models its
perimeter P in terms of its short leg x.
9.
The hypotenuse of a right triangle is 10 feet. Find a function that models its
area A in terms of its short leg x.
10.
The hypotenuse of a right triangle is 6 feet. Find a function that models its
perimeter P in terms of its long leg y.
11.
The long leg of a right triangle is 5 times the short leg. Find a function that
models its area A in terms of its hypotenuse z.
12.
The hypotenuse of a right triangle is 6 inches longer than the short leg. Find a
function that models its perimeter P in terms of its short leg x.
13.
Find a function that models the area A of a circle in terms of the
circumference C.
14.
Find a function that models the circumference C of a circle in terms of the
area A.
15.
Find a function that models the area A of a square in terms of the diagonal d.
16.
Find a function that models the diagonal d of a square in terms of the
perimeter P.
©2006 Joe Vasta
Modeling with Functions – Homework Answers
1. A(l ) = 50l − l 2
2. P ( w) =
40
+ 2w
w
3. A( P) = 2 P − 16
4. P ( A) = 10 +
2A
5
5. A( P) =
p 2 − 100
16
6. P ( A) =
12 A
5
7. A( z ) = 2 z 2 − 16
8. P ( x) = x + 5 + x 2 + 25
9. A( x) =
x 100 − x 2
2
10. P ( y ) = y + 6 + 36 − y 2
5z 2
11. A( z ) =
52
12. P ( x) = 2 x + 6 + 2 3 x + 9
13. A(C ) =
C2
4π
14. C ( A) = 2 πA
15. A(d ) =
d2
2
16. d ( P) =
P 2
4
©2006 Joe Vasta