Solved on Nov 07, 2023

Find the value of tt that satisfies the equation V(t)=4t327t2V(t)=4t^3-27t^2.

STEP 1

Assumptions1. The equation is V(t)=4t327tV(t)=4 t^{3}-27 t^{} . We need to find the value of tt for which V(t)=0V(t)=0

STEP 2

To find the value of tt, we need to set the equation equal to zero and solve for tt.
4t27t2=04 t^{}-27 t^{2} =0

STEP 3

We can factor out a t2t^{2} from each term to simplify the equation.
t2(t27)=0t^{2}(t -27) =0

STEP 4

Now we can set each factor equal to zero and solve for tt.
t2=0t^{2} =04t27=04t -27 =0

STEP 5

olving the first equation t2=0t^{2} =0 gives us one solution.
t=0t =0

STEP 6

olving the second equation 4t27=04t -27 =0 gives us the second solution.
4t=274t =27t=274=6.75t = \frac{27}{4} =6.75So, the values of tt for which V(t)=0V(t)=0 are t=0t=0 and t=6.75t=6.75.

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