A police officer hiding between two bushes 50 ft from a straight highway sights two points A , and B . The angle from the police car to A is 62 ° and the angle to point B is 72 ° . a. Find the distance between A and B . Round to the nearest foot. b. Suppose that a motorist takes 2.7 sec to pass from A to B . Using the rounded distance from part (a), find the motorist's speed in ft/ sec . Round to 1 decimal place. c. Determine the motorist's speed in mph. Round to the nearest mph.
A police officer hiding between two bushes 50 ft from a straight highway sights two points A , and B . The angle from the police car to A is 62 ° and the angle to point B is 72 ° . a. Find the distance between A and B . Round to the nearest foot. b. Suppose that a motorist takes 2.7 sec to pass from A to B . Using the rounded distance from part (a), find the motorist's speed in ft/ sec . Round to 1 decimal place. c. Determine the motorist's speed in mph. Round to the nearest mph.
Solution Summary: The author calculates the distance between A and B when the police officer is hiding between two bushes.
A police officer hiding between two bushes
50
ft from a straight highway sights two points
A
, and
B
. The angle from the police car to
A
is
62
°
and the angle to point
B
is
72
°
.
a. Find the distance between
A
and
B
. Round to the nearest foot.
b. Suppose that a motorist takes
2.7
sec to pass from
A
to
B
. Using the rounded distance from part (a), find the motorist's speed in ft/
sec
. Round to
1
decimal place.
c. Determine the motorist's speed in mph. Round to the nearest mph.
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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