For Exercises 65-66, refer to the table giving the angle of the Sun at noon at the first day of each season based on the latitude of the observer in the northern hemisphere. The term 23.5 ° represents the tilt of the Earth to the ecliptic plane (plane of the Earth's orbit around the Sun). In 1987, a group of protesters lead by Jacqueline kennedy Onassis defeated a plan to build two high rises that would have blocked sunlight to a significant swath of New York City’s Central Park. Eventually the design was scaled down and the buildings height reduced from appropriately 1020 ft to what is now the Time Warner Center at 750 ft. a. The latitude of New York City is 40.7 ° N . Find the angle of elevation of the Sun at noon on the winter solstice (shortest day of the year). b. At noon on the winter solstice, how long is the shadow cast by a 1020 -ft building? c. At noon on the winter solstice, how long is the shadow cast by a 750 -ft building?
For Exercises 65-66, refer to the table giving the angle of the Sun at noon at the first day of each season based on the latitude of the observer in the northern hemisphere. The term 23.5 ° represents the tilt of the Earth to the ecliptic plane (plane of the Earth's orbit around the Sun). In 1987, a group of protesters lead by Jacqueline kennedy Onassis defeated a plan to build two high rises that would have blocked sunlight to a significant swath of New York City’s Central Park. Eventually the design was scaled down and the buildings height reduced from appropriately 1020 ft to what is now the Time Warner Center at 750 ft. a. The latitude of New York City is 40.7 ° N . Find the angle of elevation of the Sun at noon on the winter solstice (shortest day of the year). b. At noon on the winter solstice, how long is the shadow cast by a 1020 -ft building? c. At noon on the winter solstice, how long is the shadow cast by a 750 -ft building?
Solution Summary: The author calculates the angle of elevation of the sun at noon on the winter solstice.
For Exercises 65-66, refer to the table giving the angle of the Sun at noon at the first day of each season based on the latitude of the observer in the northern hemisphere. The term
23.5
°
represents the tilt of the Earth to the ecliptic plane (plane of the Earth's orbit around the Sun).
In 1987, a group of protesters lead by Jacqueline kennedy Onassis defeated a plan to build two high rises that would have blocked sunlight to a significant swath of New York City’s Central Park. Eventually the design was scaled down and the buildings height reduced from appropriately 1020 ft to what is now the Time Warner Center at 750 ft.
a. The latitude of New York City is
40.7
°
N
. Find the angle of elevation of the Sun at noon on the winter solstice (shortest day of the year).
b. At noon on the winter solstice, how long is the shadow cast by a
1020
-ft
building?
c. At noon on the winter solstice, how long is the shadow cast by a
750
-ft
building?
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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