Deck 59: Lines

Question 1

Find the angle $$\theta$$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $$\begin{array} { l } 4 x - 4 y = 4 \\5 x + 4 y = 7\end{array}$$ ​ ​

A) $\Theta \approx 1.4601 \text { radians } \approx 83.7 ^ { \circ }$
B) $$\Theta \approx 1.4601 \text { radians } \approx 82.7 ^ { \circ }$$
C) $$\Theta \approx 1.4601 \text { radians } \approx 84.7 ^ { \circ }$$
D) $\Theta \approx 1.4601 \text { radians } \approx 85.7 ^ { \circ }$
E) $\Theta \approx 1.4601 \text { radians } \approx 81.7 ^ { \circ }$

Answer 1

$\Theta \approx 1.4601 \text { radians } \approx 83.7 ^ { \circ }$

Question 2

Find the inclination Θ (in degrees)of the line with a slope of m.Round your answer to one decimal places.​ $m = - 3$ ​

A) $\Theta \approx 108.4 ^ { \circ }$
B) $\Theta \approx 109.4 ^ { \circ }$
C) $\Theta \approx 110.4 ^ { \circ }$
D)​ $\Theta \approx 107.4 ^ { \circ }$
E) $\Theta \approx 106.4 ^ { \circ }$

Answer 2

$\Theta \approx 108.4 ^ { \circ }$

Question 3

Find the inclination $\theta$ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $( 12,9 ) , ( 4,3 )$ ​

A) $\Theta \approx 0.6435 \text { radians } \approx 36.9$
B) $\Theta \approx 0.6435 \text { radians } \approx 37.9$
C) $\Theta \approx 0.6435 \text { radians } \approx 35.9$
D) $\Theta \approx 0.6435 \text { radians } \approx 38.9$
E) $\Theta \approx 0.6435 \text { radians } \approx 34.9$

Answer 3

$\Theta \approx 0.6435 \text { radians } \approx 36.9$

Question 4

Find the inclination $\theta$ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $8 x - 2 y + 14 = 0$ ​

A) $\theta \approx 1.4289 \text { radians } \approx 82.9 ^ { \circ }$
B)​ $\Theta \approx 1.4289 \text { radians } \approx 80.9 ^ { \circ }$
C) $\theta \approx 1.4289 \text { radians } \approx 83.9 ^ { \circ }$
D) $\theta \approx 1.4289 \text { radians } \approx 79.9 ^ { \circ }$
E) $\theta \approx 1.4289 \text { radians } \approx 81.9 ^ { \circ }$

Question 5

Find the inclination $\theta$ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $( 0,200 ) , ( 20,0 )$ ​

A)​ $\Theta \approx 1.6705 \text { radians } \approx 96.7 ^ { \circ }$
B) $\theta \approx 1.6705 \text { radians } \approx 94.7 ^ { \circ }$
C) $\theta \approx 1.6705 \text { radians } \approx 97.7 ^ { \circ }$
D) $\theta \approx 1.6705 \text { radians } \approx 95.7 ^ { \circ }$
E) $\theta \approx 1.6705 \text { radians } \approx 93.7 ^ { \circ }$

Question 6

Find the angle $$\theta$$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $$\begin{array} { l } x - y = 10 \\3 x - 2 y = 1\end{array}$$ ​

A) $$\Theta \approx 0.0907 \text { radians } \approx 6.2 ^ { \circ }$$
B) $$\Theta \approx 0.0907 \text { radians } \approx 4.2 ^ { \circ }$$
C) $\Theta \approx 0.0907 \text { radians } \approx 5.2 ^ { \circ }$
D) $\Theta \approx 0.0907 \text { radians } \approx 7.2 ^ { \circ }$
E) $\Theta \approx 0.0907 \text { radians } \approx 3.2 ^ { \circ }$

Question 7

Find the angle $\theta$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $$\begin{array} { l } x - y = 0 \\5 x - 4 y = - 3\end{array}$$ ​ ​

A) $\Theta \approx 0.1107 \text { radian } \approx 7.3 ^ { \circ }$
B) $\Theta \approx 0.1107 \text { radian } \approx 5.3 ^ { \circ }$
C) $\Theta \approx 0.1107 \text { radian } \approx 6.3 ^ { \circ }$
D) $\Theta \approx 0.1107 \text { radian } \approx 8.3 ^ { \circ }$
E) $\Theta \approx 0.1107 \text { radian } \approx 4.3 ^ { \circ }$

Question 8

Find the inclination $\theta$ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $3 x - 6 y - 11 = 0$ ​

A)​ $\Theta \approx 0.2450 \text { radians } \approx 15.0 ^ { \circ }$
B) $\theta \approx 0.2450 \text { radians } \approx 14.0 ^ { \circ }$
C) $\theta \approx 0.2450 \text { radians } \approx 13.0 ^ { \circ }$ ​
D) $\theta \approx 0.2450 \text { radians } \approx 16.0 ^ { \circ }$
E) $\theta \approx 0.2450 \text { radians } \approx 12.0 ^ { \circ }$

Question 9

Find the angle $\theta$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $\begin{array} { l } x - 2 y = 9 \\10 x + 2 y = 7\end{array}$ ​

A) $$\Theta \approx 1.3045 \text { radians } \approx 75.7 ^ { \circ }$$
B) $\Theta \approx 1.3045 \text { radians } \approx 74.7 ^ { \circ }$
C) $$\Theta \approx 1.3045 \text { radians } \approx 73.7 ^ { \circ }$$
D) $\theta \approx 1.3045 \text { radians } \approx 76.7 ^ { \circ }$
E) $\Theta \approx 1.3045 \text { radians } \approx 72.7 ^ { \circ }$

Question 10

Find the angle $$\theta$$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​​ $$\begin{array} { l } 6 x + y = 6 \\x - y = 5\end{array}$$ ​

A) $\theta \approx 0.9505 \text { radians } \approx 54.5 ^ { \circ }$
B) $\theta \approx 0.9505 \text { radians } \approx 55.5 ^ { \circ }$
C) $\theta \approx 0.9505 \text { radians } \approx 53.5 ^ { \circ }$
D) $\theta \approx 0.9505 \text { radians } \approx 56.5 ^ { \circ }$
E) $\theta \approx 0.9505 \text { radians } \approx 52.5 ^ { \circ }$

Question 11

Find the inclination Θ (in degrees)of the line with a slope of m.Round your answer to one decimal places.​ $m = - 1.5$ ​

A) $\Theta \approx 124.7 ^ { \circ }$
B) $\Theta \approx 125.7 ^ { \circ }$
C) $\Theta \approx 123.7 ^ { \circ }$
D) $\Theta \approx 121.7 ^ { \circ }$
E) $\Theta \approx 122.7 ^ { \circ }$

Question 12

Find the inclination $\theta$ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $7 x + 5 y = 0$ ​

A)​ $\Theta \approx 2.2318 \text { radians } \approx 127.9 ^ { \circ }$
B) $\theta \approx 2.2318 \text { radians } \approx 128.9 ^ { \circ }$
C) $\theta \approx 2.2318 \text { radians } \approx 126.9 ^ { \circ }$
D) $\theta \approx 2.2318 \text { radians } \approx 129.9 ^ { \circ }$
E) $\theta \approx 2.2318 \text { radians } \approx 125.9 ^ { \circ }$

Question 13

Find the inclination $\theta$ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $( - 2,20 ) , ( 10,0 )$ ​

A) $\theta \approx 2.1112 \text { radians } \approx 122.0 ^ { \circ }$
B) $\theta \approx 2.1112 \text { radians } \approx 120.0 ^ { \circ }$
C) $\theta \approx 2.1112 \text { radians } \approx 123.0 ^ { \circ }$
D) $\theta \approx 2.1112 \text { radians } \approx 119.0 ^ { \circ }$
E) $\theta \approx 2.1112 \text { radians } \approx 121.0 ^ { \circ }$

Question 14

Find the inclination $\theta$ (in radians and degrees)of the line passing through the points.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $( 4,5 ) , ( 7,8 )$ ​

A) $\Theta \approx 0.7854 \text { radians } \approx 46.0 ^ { \circ }$ ​
B) $\Theta \approx 0.7854 \text { radians } \approx 44.0 ^ { \circ }$
C) $\Theta \approx 0.7854 \text { radians } \approx 47.0 ^ { \circ }$
D) $\Theta \approx 0.7854 \text { radians } \approx 43.0 ^ { \circ }$
E) $\Theta \approx 0.7854 \text { radians } \approx 45.0 ^ { \circ }$

Question 15

Find the inclination $\theta$ (in radians and degrees)of the line.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $6 x + 7 y - 13 = 0$ ​

A) $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$
B) $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ .
C) $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ ..
D) $\theta \approx 2.5536 \text { radians } \approx 146.3 ^ { \circ }$
E) $\Theta \approx 2.5536 \text { radians } \approx 147.3 ^ { \circ }$ ...

Question 16

Find the slope of the line with inclination $\Theta$ .Round your answer to four decimal places. ​​ $\Theta = 2.40 \text { radians }$ ​

A) $m \approx - 1.0160$
B) $m \approx - 1.1160$
C) $m \approx - 1.2160$
D) $m \approx - 0.9160$
E) $m \approx - 1.3160$

Question 17

Find the inclination Θ (in degrees)of the line with a slope of m.Round your answer to one decimal places.​ $m = 2$ ​

A) $\Theta \approx 63.4 ^ { \circ }$
B) $\Theta \approx 64.4 ^ { \circ }$
C) $\Theta \approx 65.4 ^ { \circ }$
D) $\Theta \approx 62.4 ^ { \circ }$
E) $\Theta \approx 61.4 ^ { \circ }$

Question 18

Find the slope of the line with inclination $\Theta$ .Round your answer to four decimal places.​ $\Theta = 1.41 \text { radians }$ ​ ​

A) $m \approx 7.1654$
B) $m \approx 5.1654$
C) $m \approx 8.1654$
D) $m \approx 6.1654$
E) $m \approx 4.1654$

Question 19

Find the inclination Θ (in degrees)of the line with a slope of m.Round your answer to one decimal places.​ $m = 0.6666666667$ ​

A) $\Theta \approx 35.7 ^ { \circ }$
B) $\Theta \approx 34.7 ^ { \circ }$
C)​ $\Theta \approx 33.7 ^ { \circ }$
D) $\Theta \approx 32.7 ^ { \circ }$
E) $\Theta \approx 31.7 ^ { \circ }$

Question 20

Find the angle $\theta$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. $\begin{array} { l } 12 x + 6 y = 18 \\3 x - 2 y = - 1\end{array}$ ​

A)​ $\Theta \approx 1.1071 \text { radians } \approx 64.4 ^ { \circ }$
B) $\theta \approx 1.1071 \text { radians } \approx 62.4 ^ { \circ }$
C) $\theta \approx 1.1071 \text { radians } \approx 65.4 ^ { \circ }$
D) $\theta \approx 1.1071 \text { radians } \approx 63.4 ^ { \circ }$
E) $\theta \approx 1.1071 \text { radians } \approx 61.4 ^ { \circ }$

Question 21

Find the angle $\theta$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $\begin{array} { l } 0.04 x + 0.02 y = - 0.06 \\0.05 x - 0.04 y = 0.03\end{array}$ ​

A)​ $\Theta \approx 1.1071 \text { radians } \approx 64.4 ^ { \circ }$
B) $\theta \approx 1.1071 \text { radians } \approx 62.4 ^ { \circ }$
C) $$\theta \approx 1.1071 \text { radians } \approx 65.4 ^ { \circ }$$
D) $\theta \approx 1.1071 \text { radians } \approx 61.4 ^ { \circ }$
E) $\theta \approx 1.1071 \text { radians } \approx 63.4 ^ { \circ }$

Question 22

Find the distance between the point and the line.Round your answer to four decimal places.​ Point Line
$( 9,8 ) - 8 x + y - 8 = 0$ ​

A)​ $d \approx 9.0554$
B) $$d \approx 10.0554$$
C) $d \approx 11.0554$
D) $d \approx 8.0554$
E) $d \approx 12.0554$

Question 23

Find the distance between the point and the line.Round your answer to four decimal places.​ Point Line
$( 14,12 ) \quad 11 x - y = 0$ ​

A) $d \approx 2.1626$
B) $d \approx 3.1626$
C) $d \approx 1.1626$
D) $d \approx 0.1626$
E) $d \approx 4.1626$

Question 24

A straight road rises with an inclination of 0.22 radian from the horizontal.Find the slope of the road and the change in elevation over a one-mile stretch of the road.Round your answer to four decimal places for the m round your answers to nearest whole number for change in elevation. ​

A) $$\begin{array} { l } m \approx 0.2236 \\x \approx 1,153 \text { feet }\end{array}$$
B) $\begin{array} { l } m \approx 0.2236 \\x \approx 1,154 \text { feet }\end{array}$
C) $\begin{array} { l } m \approx 0.2236 \\x \approx 1,152 \text { feet }\end{array}$
D) $\begin{array} { l } m \approx 0.2236 \\x \approx 1,151 \text { feet }\end{array}$
E) $\begin{array} { l } m \approx 0.2236 \\x \approx 1,150 \text { feet }\end{array}$

Question 25

Find the distance between the point and the line.​ Point $~~~~~~~~~~$ Line
$( 4,5 ) \quad x + 2 = 0$ ​

A) $d = 8$
B) $d = 9$
C) $d = 6$
D) $d = 10$
E) $d = 7$

Question 26

A moving conveyor is built so that it rises 3 meter for each 5 meters of horizontal travel.The conveyor runs between two floors in a factory.The distance between the floors is 4 meters.Find the length of the conveyor.Round your answers to one decimal place. ​

A) $24.3 \mathrm {~m}$
B) $25.3 \mathrm {~m}$
C) $22.3 \mathrm {~m}$
D) $21.3 \mathrm {~m}$
E) $23.3 \mathrm {~m}$

Question 27

A moving conveyor is built so that it rises 7 meter for each 9 meters of horizontal travel.Select a diagram that gives a visual representation of the problem. ​

A)​ a = 7m,b = 9m
B)​ a = 7m,b = 9m
C)​ a = 7m,b = 9m
D)​ a = 7m,b = 9m
E)​ a = 7m,b = 9m

Question 28

Find the distance between the point and the line.Round your answer to four decimal places.​ Point Line
$( 7,5 ) \quad x - y = 50$ ​

A) $d \approx 24.3345$
B) $d \approx 25.3345$
C) $d \approx 23.3345$
D) $d \approx 22.3345$
E) $d \approx 26.3345$

Question 29

Find the distance between the point and the line.Round your answer to four decimal places.​ Point $~~~~~~~$ Line
$( 2,3 ) \quad x - y = 2$ ​

A) $d \approx 6.6569$
B) $d \approx 7.6569$
C) $d \approx 4.6569$
D) $d \approx 8.6569$
E) $d \approx 5.6569$

Question 30

A roof has a rise of 9 feet for every horizontal change of 11 feet (see figure).Find the inclination of the roof.Round your answers to one decimal place.​ ​ $$a = 9 , b = 11$$ ​

A) $\Theta \approx 39.3 ^ { \circ }$
B) $\Theta \approx 40.3 ^ { \circ }$
C) $\Theta \approx 41.3 ^ { \circ }$
D) $\Theta \approx 38.3 ^ { \circ }$
E) $\Theta \approx 37.3 ^ { \circ }$

Question 31

Find the angle $\theta$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $\begin{array} { l } 0.04 x + 0.02 y = 0.06 \\0.07 x - 0.06 y = 0.05\end{array}$ ​

A) $\theta \approx 1.1903 \text { radians } \approx 69.2 ^ { \circ }$
B) $$\theta \approx 1.1903 \text { radians } \approx 67.2 ^ { \circ }$$
C) $\theta \approx 1.1903 \text { radians } \approx 70.2 ^ { \circ }$
D) $\theta \approx 1.1903 \text { radians } \approx 66.2 ^ { \circ }$
E) $\theta \approx 1.1903 \text { radians } \approx 68.2 ^ { \circ }$

Question 32

A moving conveyor is built so that it rises 9 meter for each 11 meters of horizontal travel.Find the inclination of the conveyor.Round your answers to one decimal place. ​

A) $\Theta \approx 40.3 ^ { \circ }$
B) $\Theta \approx 41.3 ^ { \circ }$
C) $\Theta \approx 38.3 ^ { \circ }$
D) $\Theta \approx 39.3 ^ { \circ }$
E) $\Theta \approx 37.3 ^ { \circ }$

Question 33

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane.​ $$A = \left( - \frac { 1 } { 6 } , \frac { 1 } { 7 } \right) , B = ( 6,7 ) , C = \left( \frac { 6 } { 7 } , 0 \right)$$ ​

A)​ ​
B)​ ​
C)​
D)​
E)​

Question 34

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (-4,-5),B = (2,7),C = (5,7)
​

A)​
B)​
C)​
D)​
E)​

Question 35

Find the angle $\theta$ (in radians and degrees)between the lines.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ $\begin{array} { l } 6 x - 8 y = 8 \\6 x + 8 y = 7\end{array}$ ​

A)​ $\Theta \approx 1.3221 \text { radians } \approx 76.7 ^ { \circ }$
B) $\theta \approx 1.3221 \text { radians } \approx 74.7 ^ { \circ }$
C) $\Theta \approx 1.3221 \text { radians } \approx 75.7 ^ { \circ }$
D) $\Theta \approx 1.3221 \text { radians } \approx 77.7 ^ { \circ }$
E) $\theta \approx 1.3221 \text { radians } \approx 73.7 ^ { \circ }$

Question 36

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (0,0),B = (3,6),C = (6,0)
​

A)​
B)​
C)​
D)​
E)​

Question 37

Find the distance between the point and the line.Round your answer to four decimal places. Point Line
$( 2,4 ) \quad 5 x - y = 10$ ​

A) $d \approx 2.7889$
B) $d \approx 1.7889$
C) $$d \approx 3.7889$$
D) $$d \approx 0.7889$$
E) $d \approx 4.7889$

Question 38

Find the distance between the point and the line.Round your answer to four decimal places. Point $~~~~~~~~~~~~$ Line
$( 4,5 ) \quad 7 x + y = 1$ ​

A) $d \approx 4.7068$
B) $d \approx 5.7068$
C) $d \approx 6.7068$
D) $$d \approx 3.7068$$
E) $d \approx 7.7068$

Question 39

A straight road rises with an inclination of 0.21 radian from the horizontal (see figure).Find the slope of the road and the change in elevation (x)over a two-mile stretch of the road.Round your answer to four decimal places for the m round your answers to nearest whole number for change in elevation.​ ​ $a = 2 , b = 0.21$ ​

A) $$\begin{array} { l } m \approx 0.2131 \\x \approx 2,203 \text { feet }\end{array}$$
B) $\begin{array} { l } m \approx 0.2131 \\x \approx 2,202 \text { feet }\end{array}$
C) $\begin{array} { l } m \approx 0.2131 \\x \approx 2,200 \text { feet }\end{array}$
D) $\begin{array} { l } m \approx 0.2131 \\x \approx 2,199 \text { feet }\end{array}$
E) $\begin{array} { l } m \approx 0.2131 \\x \approx 2,201 \text { feet }\end{array}$

Question 40

The given points represent the vertices of a triangle.Select the triangle ABC in the coordinate plane. ​
A = (0,0),B = (3,4),C = (4,-3)
​

A)​
B)​
C)​
D)​
E)​

Question 41

Consider a line with slope m and y-intercept (0,2).Write the distance d between the origin and the line as a function of m. ​

A) $d = \frac { m } { \sqrt { m ^ { 2 } + 2 } }$
B) $d = \frac { 1 } { \sqrt { m ^ { 2 } - 2 } }$
C) $d = \frac { 1 } { \sqrt { m ^ { 2 } + 2 } }$
D) $d = \frac { 2 } { \sqrt { m ^ { 2 } - 1 } }$
E) $d = \frac { 2 } { \sqrt { m ^ { 2 } + 1 } }$

Question 42

Consider a line with slope m and y-intercept (0,7).Select the graph of the distance between the origin and the line. ​

A)​
B)​
C)​
D)​
E)​

Question 43

Consider a line with slope m and y-intercept (0,3).Find the slope that yields the maximum distance between the point (2,1)and the line. ​

A) $m = 3$
B) $m = - 1$
C) $m = 2$
D) $m = - 2$
E) $m = 1$

Question 44

The Falls Incline Railway in Niagara Falls,Ontario,Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 110 feet long with a 28% uphill grade (see figure).Find the change in elevation from the base to the top of the railway.Round your answers to one decimal place.​ ​ $a = 110$ ​

A) $z \approx 29.7 \mathrm { ft }$
B) $$z \approx 30.7 \mathrm { ft }$$
C) $$z \approx 28.7 \mathrm { ft }$$
D) $z \approx 31.7 \mathrm { ft }$
E) $z \approx 27.7 \mathrm { ft }$

Question 45

The Falls Incline Railway in Niagara Falls,Ontario,Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 170 feet long with a 40% uphill grade (see figure).Using the origin of a rectangular coordinate system as the base of the inclined plane,find the equation of the line that models the railway track.​ ​ $a = 170$ ​

A) $y = 170 x$
B) $y = 0.40 x$
C) $y = 40 x$
D) $y = - 0.40 x$
E) $y = - 170 x$

Question 46

Consider a line with slope m and y-intercept (0,5).Find the slope that yields the maximum distance between the origin and the line. ​

A)The maximum distance of $- \frac { 1 } { 5 }$ occurs when the slope m is $- \frac { 1 } { 5 }$ and the line through (0,5)is horizontal.
B)The maximum distance of 5 occurs when the slope m is 0 and the line through (0,5)is horizontal.
C)The maximum distance of $\frac { 1 } { 5 }$ occurs when the slope m is 0 and the line through (0,5)is horizontal.
D)The maximum distance of 6 occurs when the slope m is 0 and the line through (0,6)is horizontal.
E)The maximum distance of $- 5$ occurs when the slope m is $\frac { 1 } { 5 }$ and the line through (0,5)is horizontal.

Question 47

Consider a line with slope m and y-intercept (0,3).Select the graph of the distance d between the point (2,1)and the line as a function of m. ​

A)​
B)​
C)​
D)​
E)​

Question 48

Consider a line with slope m and y-intercept (0,8).Write the distance d between the point (7,1)and the line as a function of m. ​

A) $\frac { 7 | m - 1 | } { \sqrt { m ^ { 2 } + 1 } }$
B) $$\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } - 1 } }$$
C) $\frac { 7 | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$
D) $$\frac { 7 | m + 7 | } { \sqrt { m ^ { 2 } + 1 } }$$
E) $\frac { | m + 1 | } { \sqrt { m ^ { 2 } + 1 } }$

Question 49

The Falls Incline Railway in Niagara Falls,Ontario,Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 130 feet long with a 46% uphill grade (see figure).Find the inclination $$\theta$$ of the railway.Round your answer to four decimal places for radians and round your answer to one decimal places for degree.​ ​ $a = 130$ ​

A) $\Theta \approx 0.4311 \text { radian, or } 25.7 ^ { \circ }$
B) $\Theta \approx 0.4311 \text { radian, or } 23.7 ^ { \circ }$
C) $\Theta \approx 0.4311 \text { radian, or } 26.7 ^ { \circ }$
D) $\Theta \approx 0.4311 \text { radian, or } 24.7 ^ { \circ }$
E) $\Theta \approx 0.4311 \text { radian, or } 22.7 ^ { \circ }$

Question 50

The Falls Incline Railway in Niagara Falls,Ontario,Canada is an inclined railway that was designed to carry people from the City of Niagara Falls to Queen Victoria Park.The railway is approximately 180 feet long with a 42% uphill grade (see figure).Select the graph of the equation of the line that models the railway track.​ ​ $a = 180$ ​

A)​
B)​
C)
D)​
E)​