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
°
.
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A certain unit produced by the
company can be sold for 200-0.02x
pesos where x is the number of units
manufactured. What would be the
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O P100
O P200
OP50
OP150
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Your answer is:
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$=?
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