Answer:
s(t)=7t
Explanation:
We are given that
Length of side of square initially=0 cm
Side of square increasing at the rate=[tex]\frac{ds}{dt}=[/tex]7 cm/s
We have to find the formula to express the side length of the square s(in cm) in terms of the number of seconds t.
According to question
[tex]\frac{ds}{dt}=7[/tex]
[tex]ds=7dt[/tex]
Taking integration on both sides then, we get
[tex]\int ds=7\int dt[/tex]
[tex]s=7t+C[/tex]
Substitute t=0 and s=0
[tex]0=0+C[/tex]
[tex]C=0[/tex]
Now, substitute the value of C then, we get
s(t)=7t
This is required formula that express the side length of the square s(in cm) in terms of the number of seconds t, since the square's side length began growing.
