answer in detail please Assume that the rate of homicide in Chicago can be model

Question

answer in detail please

Assume that the rate of homicide in Chicago can be modeled by the function R(t) below, where t is the time since year 2000. What does R'(4) represent? R(t) = -1.57t2 + 119t + 125 Assume that the rate of homicide in Chicago can be modeled by the function R(t) below, where t is the time since year 2000. Compute the values of R'(4) and R'(6) and explain the difference. R(t) = -1.57t2 + 119t + 125 If you drop a rock off a bridge and its distance is given by H(t) in ft where t is in seconds, then what is the velocity of the rock after 2 seconds? H(t) = 16t2 Find the derivative using implicit differentiation. 2y + 3x + 15 = 0 Assume that C(x) represents the cost of producing x calculators. If C(100) = $500 and C'(100) = $4.75, what is the average cost of producing 100 calculators?

Explanation / Answer

1. R(t) = -1.57t^2 + 119t + 125

R'(t) = -3.14t + 119

So, R'(4) = -3.14*4 + 119 = 106.44

So, R'(t) = 106.44

2. R(t) = -1.57t^2 + 119t + 125

R'(t) = -3.14t + 119

So, R'(4) = -3.14*4 + 119 = 106.44

So, R'(t) = 106.44

R'(6) = -3.14*6 + 119 = 100.16

So, R'(4) - R'(6) = 106.44 - 100.16 = 6.28 = 3.14*2 = -3.14*(4-6)

So, R'(t) - R'(t') = -3.14*(t-t')

3) H(t) = 16t^2

Velocity is H'(t) = 32t

So, velocity after 2 sec = H'(2) = 32*2 = 64 ft

4) 2y + 3x + 15 = 0

So, 2*(dy/dx) + 3 = 0

=> dy/dx = -3/2

At (-5,0)

So, y - 0 = (-3/2)*(x+5)

=> 5y = -3x - 15

=> 3x + 5y + 15 = 0

5) Given, C(x) = $500

So, cost of producing 100 calculators is C(100) = $500

So, average cost of producing 100 calculators is C(100) = $500

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