MATHEMATICS

JAMB 2009 - Question 37

Mathematics 2009 JAMB Past Questions - Question 37: If s=(2+3t)(5t-4), find ds/dt when t=4/5 secs

If s=(2+3t)(5t-4), find ds/dt when t=4/5 secs
A:
B:
C:
D:
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Correct Answer

C

Explanation

S=(2+3t)(5t-4)10t-8+15t² -12t=15t² -2t-8ds/dt=30t-230/1*4/5-224-2=22To find ds/dt, we need to differentiate the expression s = (2 + 3t)(5t - 4) with respect to t.Using the product rule, we differentiate each term separately and then add them together.The derivative of (2 + 3t) with respect to t is 3, and the derivative of (5t - 4) with respect to t is 5.Therefore, ds/dt = 3(5t - 4) + (2 + 3t)(5) = 15t - 12 + 10 + 15t = 30t + 10.Now, we can substitute t = 4/5 secs into the expression to find the value of ds/dt:ds/dt = 30(4/5) + 10 = 24 + 10 = 34.Hence, when t = 4/5 secs, ds/dt is equal to 34.