If S = (4t + 3)(t - 2), find ds/dt when t = 5 secs.
The correct answer is B. 35 units per sec
To find \(\frac{ds}{dt}\), we take the derivative of \(S\) with respect to \(t\). Applying the product rule, we get:
\(\frac{ds}{dt} = \frac{d}{dt}(4t + 3) \cdot (t - 2) + (4t + 3) \cdot \frac{d}{dt}(t - 2)\)
Simplify the derivatives:
\(\frac{ds}{dt} = 4 \cdot (t - 2) + (4t + 3) \cdot 1\)
Expand and simplify further:
\(\frac{ds}{dt} = 4t - 8 + 4t + 3\)
Combine like terms:
\(\frac{ds}{dt} = 8t - 5\)
Now, to find \(\frac{ds}{dt}\) when \(t = 5\) secs:
\(\frac{ds}{dt} = 8 \cdot 5 - 5 = 40 - 5 = 35\)
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