Question 1127058: The side length of a square starts at 0 cm and then begins increasing at a constant rate of 10 cm per second.
A) Write a formula that expresses the side length of the square in cm, s, in terms of the number of seconds t since the square started growing.
B)Write a formula that expresses the area of the square in cm2, A, in terms of the side length of the square in cm, s.
C)Write a formula that expresses the area of the square in cm2, A, in terms of the number of seconds t since the square started growing.
D)Suppose the function f determines the area of the square in cm2 given a number of seconds t since the square started growing. Write a function formula for f.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! S = the length of the side of the square.
A = the area of the square.
the formula for the area of a square is A = S^2.
the length of the side of the suare increased by 10 centimeters every second.
T = the number of seconds.
A) Write a formula that expresses the side length of the square in cm, s, in terms of the number of seconds t since the square started growing.
S = 10 * T
B)Write a formula that expresses the area of the square in cm2, A, in terms of the side length of the square in cm, s.
A = S^2
C)Write a formula that expresses the area of the square in cm2, A, in terms of the number of seconds t since the square started growing.
A = (10 * T) ^2 which can be simplified to A = 100 * T^2.
D)Suppose the function f determines the area of the square in cm^2 given a number of seconds t since the square started growing. Write a function formula for f.
f(T) = 100 * T^2
when T = 0, f(0) = 100 * 0^2 = 0
this is derived as follows:
A = S^2
S = 10 * T
when T = 0, S = 10 * 0 = 0
when S = 0, A = 0^2 = 0
when T = 1, f(1) = 100 * 1^2 = 100
this is derived as follows:
A = S^2
S = 10 * T
when T = 1, S = 10 * 1 = 10
when S = 10, A = 10^2 = 100
when T = 2, f(2) = 100 * 2^2 = 100 * 4 = 400
this is derived as follows:
A = S^2
S = 10 *T
when T = 2, S = 10 * 2 = 20
when S = 20, A = 20^2 = 400
etc for all values of T
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