4. A road perpendicular to a highway leads to a farmhouse located d = 5 km away from the
the highway. A car travels on the highway at a speed of U = 75 km/h. How fast is
intersection distance between of the the road car and the farmhouse increasing when the car is 6 km past the
and the highway?
Solve this problem in the following three steps.
(a) (2 pts) Label the distance between the car and the house X. Label the distance
between the car, and the junction of the road and the highway, 1. In terms of X and
l, what rate of change (or derivative) are you asked to find? Which rate of change
(or derivative) are you given?
(b) (4pts) Find an equation that relates the variables here, and differentiate to obtain
a relation between the rates of change (or derivatives) in part (a).
(c) (2 pts) Use the given data to find the unknown rate of change. Give a value accurate
to 4 decimal places, and include correct units.
6. area of
Find the beneath the graph f (x) = 11 over the interval [0,9]. The region is
shaded below. Give an exact 2.+ work. Answers based on numerical or
answer and show all
graphical work done on a calculator will receive no credit.
8. Suppose the velocity (in m/s) of particle 16-second time interval given by
a over a is the
function a(t)=5-5e-0227 = - for O(a) (5 pts) Write a definite integral whose value gives the distance traveled over the
16-second time interval.
(b) (5pts) Evaluate the definite integral you wrote above, to calculate the distance
traveled the 16-second time interval. (Show work for your anti-derivative. A
value for the integral arrived at solely by using a calculator will receive no credit.)
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