Two residential buildings are to be constructed with a grassy recreational area between them. The taller building is 700 ft high. From the roof of the shorter building, the angle of elevation to the top of the taller building is 78 ° and the angle of depression to the base of the taller building is 62 ° . a. How tall is the shorter building? Round to the nearest foot b. What is the distance between the buildings? Round to the nearest foot
Two residential buildings are to be constructed with a grassy recreational area between them. The taller building is 700 ft high. From the roof of the shorter building, the angle of elevation to the top of the taller building is 78 ° and the angle of depression to the base of the taller building is 62 ° . a. How tall is the shorter building? Round to the nearest foot b. What is the distance between the buildings? Round to the nearest foot
Solution Summary: The author explains the angle of elevation from the shorter building to the top of the higher building is 78°. Then, draw a rough sketch for the considered conditions and label the sides and angles.
Two residential buildings are to be constructed with a grassy recreational area between them. The taller building is
700
ft
high. From the roof of the shorter building, the angle of elevation to the top of the taller building is
78
°
and the angle of depression to the base of the taller building is
62
°
.
a. How tall is the shorter building? Round to the nearest foot
b. What is the distance between the buildings? Round to the nearest foot
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
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