Find f. (antiderivative) . f '(t) = 4 cos (t) + sec^2(t), −π/2 < t < π/2, f(π/3) = 3

1 answer:

6 0

The antiderivative of the function f '(t) = 4 cos (t) + sec^2(t) is determined by applying integral calculus. The antiderivative of 4 cos (t) is -4 sin(t) while the antiderivative of sec^2(t) is tan (t). The total term is -4 sin(t) + tan (t). We try to replace pi/3 and the answer is 3.

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Someone please explain (:

GaryK [48]

Answer:

a.) 1.38 seconds

b.) 17.59ft

Step-by-step explanation:

h(t) = -16t^2 + 22.08t + 6

if we were to graph this, the vertex of the function would be the point, which if we substituted into the function would give us the maximum height.

to find the vertex, since we are dealing with something called "quadratic form" ax^2+bx+c, we can use a formula to find the vertex

-b/2a

b=22.08

a=-16

-22.08/-16, we get 1.38 when the minuses cancel out. since our x is time, it will be 1.38 seconds

now since the vertex is 1.38, we can substitute 1.38 into the function to find the maximum height.

h(1.38)= -16(1.38)^2 + 22.08t + 6 -----> is maximum height.

approximately = 17.59ft -------> calculator used, and rounded to 2 significant figures.

for c the time can be equal to (69+sqrt(8511))/100, as the negative version would be incompatible since we are talking about time. or if you wanted a rounded decimal, approx 1.62 seconds.

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