According to the Fundamental Theorem of Calculus, which of the following functions is an anti-derivative of f(x) = sin(x² + 1) ? Sa sin(t? + 1) dt – cos(x² + 1) O sin(r" + 2) o sin(2t) dt A cos(t? + 1) dt A ball rolls along a straight track with velocity v(t) = 1– t for 0 < t< 4, where time is measured in seconds and velocity is measured in feet per second. Find the total distance, in feet, traveled by the ball in the fırst 4 seconds. 4 -5 -4 2.5

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A:

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A: Given that s(t)= -16t2 + 96t. a) the average velocity of the rock between t = 1 s and t = 3 s is:

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A: The given graph is as follows:

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A: v(t)=(1/t^2)-1/25

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Q: The rock hits the surface after 5.38 seconds. With what velocity will the rock hit the surface?

A: Given H=15t-2.79t2 Velocity can be obtained with  differentiation of height. V=dH/dt

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A: Answer: The solution is as given below:

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A: Here it is given that; The daily output of a coal mine after t hours of operation is approximately…

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A:

Q: A ball is dropped from the top of a lighthouse that is 145 feet above sea level. The height…

A: Given height function s( t ) = -16t2 + 145

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A: Given that:Volume=V=314.159Height=h=4 Rate of change of volume=dVdt=20 The question is asking for…

Q: Find P (-2.15 <Z<1.63)

A: Given:  z be the standard normal variate then to find probability p(-2.15&lt;z&lt;1.63)??