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
°
.
4
In the integral dxf1dy (7)², make the change of variables x = ½(r− s), y = ½(r + s), and
evaluate the integral. Hint: Find the limits on r and s by sketching the area of integration in the (x, y) plane along
with the r and s axes, and then show that the same area can be covered by s from 0 to r and r from 0 to 1.
7. What are all values of 0, for 0≤0<2л, where 2 sin² 0=-sin?
-
5π
6
π
(A) 0, л,
and
6
7π
(B) 0,л,
11π
, and
6
6
π 3π π
(C)
5π
2 2 3
, and
π 3π 2π
(D)
2' 2'3
, and
3
4元
3
1
די
}
I
-2m
3
1
-3
บ
1
#
1
I
3#
3m
8. The graph of g is shown above. Which of the following is an expression for g(x)?
(A) 1+ tan(x)
(B) 1-tan (x)
(C) 1-tan (2x)
(D) 1-tan
+
X
-
9. The function j is given by j(x)=2(sin x)(cos x)-cos x. Solve j(x) = 0 for values of x in the interval
Quiz A: Topic 3.10
Trigonometric Equations and Inequalities
Created by Bryan Passwater
can you solve this question using the right triangle method and explain the steps used along the way
Elementary Statistics: Picturing the World (7th Edition)
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