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Diving problem Math 1475 Prof. Mingla

Diving problem Math 1475 Prof. Mingla. Group 3 Randy Medina Abdullah Zafar Julia Chang Henry Lam Ahmed Taher Joel Silva Jonathan Camacho. What can you say about the tangent line to the graph at the lowest point?.

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Diving problem Math 1475 Prof. Mingla

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  1. Diving problem Math 1475 Prof. Mingla Group 3 Randy Medina Abdullah Zafar Julia Chang Henry Lam Ahmed Taher Joel Silva Jonathan Camacho

  2. What can you say about the tangent line to the graph at the lowest point? The tangent line at the lowest point of the graph had a constant slope as the submarine slowed down transitioning into going upwards. Also, the tangent line to the lowest point will be horizontal making the slope equal to 0.

  3. B. After how many minutes will the submarine reach the lowest point on the dive? a(t)=500cos(t/2)+125t-564 => a(t’)=-250sin(t/2)+125 -250sin(t/2)+125=0 => -250sin(t/2)=-125 => sin(t/2)=(-125/-250) ½=sin(t/2) => sin^-1(½)=pi/6, 1/2sin=pi/6 & 10pi/6 5pi/6*2=10pi/6=5.24

  4. C. What is the greatest depth the submarine will reach on this dive? Round to nearest foot a(5.24)=500cos(5.24/2)+125(5.24)-564 a(5.24)=-433.51+655-564 a(5.24)=-342.51ft a(5.24)=-343ft

  5. D. What is the greatest rate at which the submarine’s depth will increase during the dive. Find the 2nd derivative, to find the acceleration. a(t)=125cos(t/2) a(0)=125cos(0/2) a(0)=125cos(0) a(0)=125

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