Question 1127059: A rectangle has a fixed width of 8 inches and a length of 0 inches. The length of the rectangle then begins increasing at 2.4 inches per second.
A)Write a formula that expresses the length of the rectangle in inches, l, in terms of the number of seconds t since the rectangle began growing.
B)Write a formula that expresses the perimeter of the rectangle in inches, P, in terms of the length of the rectangle in inches, l.
C)Write a formula that expresses the perimeter of the rectangle in inches, P, in terms of the number of seconds t since the rectangle began growing.
D)Suppose the function g determines the perimeter of the rectangle in inches given a number of seconds t since the rectangle started growing. Write a function formula for g.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the perimeter of a rectangle is equal to 2L + 2W.
the perimeter of the rectangle is represented by P.
P = 2L + 2W
when W is fixed at 8, the perimeter of the rectangle becomes P = 2L + 16
A)Write a formula that expresses the length of the rectangle in inches, l, in terms of the number of seconds t since the rectangle began growing.
time in seconds is represented by T.
the length of the rectangle increases by 2.4 inches every second.
L = 2.4 * T
B)Write a formula that expresses the perimeter of the rectangle in inches, P, in terms of the length of the rectangle in inches, l.
P = 2L + 16
C)Write a formula that expresses the perimeter of the rectangle in inches, P, in terms of the number of seconds t since the rectangle began growing.
P = 2 * 2.4 * T + 16 which becomes P = 4.8 * T + 16
D)Suppose the function g determines the perimeter of the rectangle in inches given a number of seconds t since the rectangle started growing. Write a function formula for g.
g(T) = 4.8 * T + 16
when T = 0, the perimeter of the rectangle is equal to 0 + 16 = 16.
when T = 1, the perimeter of the rectangle is equal to 4.8 + 16 = 20.8.
when T = 2, the perimeter of the rectangle is equal to 9.6 + 16 = 25.6.
etc...
keep in mind that the formula for the perimeter of the rectangleis P = 2 * L + 2 * W.
W is always 8, so the formula becomes P = 2 * L + 16.
L is equal to 2.4 * T, so the formula becomes P = 2 * 2.4 * T + 16.
after simplification, the formula becomes P = 2.8 * T + 16.
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