The average round trip speed 5 in mph of a vehicle traveling a distance of d miles in each direction is given by S = 2 d d r 1 + d r 2 where r 1 and r 2 are the rates of speed for the inital trip and the return trip, respectively . a. Suppose that a motorist travels 200 mi from her home to an athletic event and averages 50 mph for the trip to the event. Determine the speeds necessary if the motorist wants the average speed for the round trip to be at least 60 mph. b. Would the motorist be traveling within the speed limit of 70 mph?
The average round trip speed 5 in mph of a vehicle traveling a distance of d miles in each direction is given by S = 2 d d r 1 + d r 2 where r 1 and r 2 are the rates of speed for the inital trip and the return trip, respectively . a. Suppose that a motorist travels 200 mi from her home to an athletic event and averages 50 mph for the trip to the event. Determine the speeds necessary if the motorist wants the average speed for the round trip to be at least 60 mph. b. Would the motorist be traveling within the speed limit of 70 mph?
Solution Summary: The author calculates the average speed of the return trip required by the motorist to be at least 60 mph. The motorist travels 200 miles from home to an athletic event and the initial rate of speed is 50 miles per hour.
The average round trip speed
5
in mph
of a vehicle traveling a distance of d miles in each direction is given by
S
=
2
d
d
r
1
+
d
r
2
where
r
1
and
r
2
are the rates of
speed for the inital trip and the
return trip, respectively
.
a. Suppose that a motorist travels 200 mi from her home to an athletic event and averages 50 mph for the trip to the event. Determine the speeds necessary if the motorist wants the average speed for the round trip to be at least 60 mph.
b. Would the motorist be traveling within the speed limit of 70 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) =…
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