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Calculate G(17), where dG/dt = t^−1/2 and G(3) = −3. (Round your answer to two decimal places.) G(17)=?

User KaoriYui
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1 Answer

3 votes

Answer:


G(17) \approx 1.782

Explanation:

Let
(dG)/(dt) = t^(-1/2) and
G(3) = -3, we proceed to find
G(t) by integrating
(dG)/(dt) in time:


G(t) = \int {t^(-1/2)} \, dt


G(t) = (t^(1/2))/((1)/(2) ) + C


G(t) = 2\cdot t^(1/2) + C (1)

Where
C is the constant of integration. If we know that
t = 3 and
G(3) = -3, then the constant of integration:


-3 = 2\cdot 3^(1/2) + C


C = -6.464

The resultant function is
G(t) = 2\cdot t^(1/2) -6.464.

Lastly, we evaluate this function at
t = 17:


G(17) = 2\cdot 17^(1/2)-6.464


G(17) \approx 1.782

User Reuel
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