Answer to Question #150927 in Calculus for Angelo

Question #150927

The electromotive force for an electric circuit with a simplified generator is 𝐸(𝑑) π‘£π‘œπ‘™π‘‘π‘  at 𝑑 π‘ π‘’π‘π‘œπ‘›π‘‘π‘ , where 𝐸(𝑑) = 50 𝑠𝑖𝑛120πœ‹π‘‘. Find the instantaneous rate of change of 𝐸(𝑑) with respect to 𝑑 at (a) 0.02 𝑠𝑒𝑐 and (b)0.2 𝑠𝑒c


1
Expert's answer
2020-12-15T03:36:34-0500

Rate of change of the function is calculated as it's derivative so in this rate of change would be equal to "E'(t)=(50sin120\\pi t)'=50\\cdot120\\pi\\cdot cos120\\pi t=6000\\pi\\cdot cos(120\\pi t)" . For t=0.02 instantaneous rate of change then is "6000\\pi\\cdot cos(120\\pi \\cdot0.02)=5824.833" and for t=0.2 instantaneous rate of change then is "6000\\pi\\cdot cos(120\\pi \\cdot0.2)=18849.556" .


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