A ranger station at a point R in a wilderness area is located 5.6 mi from a campground at point C (see figure). A camper hikes 4 mi in a linear path away from the campground to point H , and then shoots a flare straight up as a distress signal. The signal is seen from the ranger station such that ∠ H R C = 35 ° . To the nearest tenth of a mile, how far is the camper from the ranger station?
A ranger station at a point R in a wilderness area is located 5.6 mi from a campground at point C (see figure). A camper hikes 4 mi in a linear path away from the campground to point H , and then shoots a flare straight up as a distress signal. The signal is seen from the ranger station such that ∠ H R C = 35 ° . To the nearest tenth of a mile, how far is the camper from the ranger station?
Solution Summary: The author explains how the distance of the camper from the ranger station is given as two triangles Delta RCH.
A ranger station at a point
R
in a wilderness area is located
5.6
mi
from a campground at point
C
(see figure). A camper hikes
4
mi
in a linear path away from the campground to point
H
, and then shoots a flare straight up as a distress signal. The signal is seen from the ranger station such that
∠
H
R
C
=
35
°
. To the nearest tenth of a mile, how far is the camper from the ranger station?
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).
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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