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kupik [55]
2 years ago
7

The length of the sides of a square are initially 0 cm and increase at a constant rate of 8 cm per second. Write a formula that

expresses the side length of the square, s (in cm), in terms of the number of seconds, t , since the square's side lengths began growing. s
Mathematics
1 answer:
lesya692 [45]2 years ago
6 0

Answer:

s(t)=8t

Step-by-step explanation:

The length of the sides of a square are initially 0 cm and increase at a constant rate of 8 cm per second.

Let the length of the Square = s

\dfrac{ds}{dt}=8 $cm/seconds, s_0=0 cm

We solve the differential equation above subject to the given initial condition.

\dfrac{ds}{dt}=8\\ds=8$ dt\\Take the integral of both sides\\\int ds=\int 8$ dt\\s(t)=8t+C, where C is the constant of integration\\When t=0, s=0cm\\s(0)=0=8(0)+C\\C=0\\Therefore, s(t)=8t

The formula that expresses the side length of the square, s (in cm), in terms of the number of seconds, t , since the square's side lengths began growing is:

s(t)=8t (in cm)

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