Pipe for a water line must be installed from a main water line at point A to a building on Hontoon Island State Park at point B as shown in the figure. The cost to install water pipe over land is $ 10 per foot and the cost to install pipe under water is $ 20 per foot a. Write an expression in terms of 6 to represent the total cost c (in dollars) to lay pipe from point A to point B . b. Use the TABLE function on a calculator to find the cost for 6 = 20 ° , 25 ° , 30 ° , 35 ° , and 40 ° . Round to 1 decimal place. c. Which angle from part (b) yields the least cost? d. Using calculus, we can show that the angle needed to minimize the total cost is a solution to the equation 4000 sec θ tan θ − 2000 sec 2 = 0 . Solve the equation for 6 , where 0 ° < θ < 90 ° .
Pipe for a water line must be installed from a main water line at point A to a building on Hontoon Island State Park at point B as shown in the figure. The cost to install water pipe over land is $ 10 per foot and the cost to install pipe under water is $ 20 per foot a. Write an expression in terms of 6 to represent the total cost c (in dollars) to lay pipe from point A to point B . b. Use the TABLE function on a calculator to find the cost for 6 = 20 ° , 25 ° , 30 ° , 35 ° , and 40 ° . Round to 1 decimal place. c. Which angle from part (b) yields the least cost? d. Using calculus, we can show that the angle needed to minimize the total cost is a solution to the equation 4000 sec θ tan θ − 2000 sec 2 = 0 . Solve the equation for 6 , where 0 ° < θ < 90 ° .
Solution Summary: The author calculates theta to represent the total cost to lay the pipe from a main water line in HintonIsland State Park.
Pipe for a water line must be installed from a main water line at point A to a building on Hontoon Island State Park at point B as shown in the figure. The cost to install water pipe over land is $
10
per foot and the cost to install pipe under water is $
20
per foot
a. Write an expression in terms of
6
to represent the total cost c (in dollars) to lay pipe from point A to point B.
b. Use the TABLE function on a calculator to find the cost for
6
=
20
°
,
25
°
,
30
°
,
35
°
,
and
40
°
. Round to 1 decimal place.
c. Which angle from part (b) yields the least cost?
d. Using calculus, we can show that the angle needed to minimize the total cost is a solution to the equation
4000
sec
θ
tan
θ
−
2000
sec
2
=
0
. Solve the equation for
6
, where
0
°
<
θ
<
90
°
.
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) =…
Elementary Statistics: Picturing the World (7th Edition)
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