Question 1

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)​

Accepted Answer

The answer of Consider a line with slope m and...

Question 2

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A moving conveyor is built so that...

Question 3

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A moving conveyor is built so that...

Question 4

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)​ 
B)​ 
C) 
D)​ 
E)​

Accepted Answer

The answer of The Falls Incline Railway in Niagara Falls,...

Question 5

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The Falls Incline Railway in Niagara Falls,...

Question 6

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  occurs when the slope m is  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  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  occurs when the slope m is  and the line through (0,5) is horizontal.

Accepted Answer

The distance between the origin and a point (x,y) on the line is given by the equation d = sqrt(x^2 + y^2). Since the y-intercept is (0,5), the equation of the line is y = mx + 5. To find where the maximum distance occurs, we want to minimize d^2, which simplifies to x^2 + (mx+5)^2. Taking the derivative of this expression with respect to m and setting it equal to zero yields m = -x/y = 0 since the line is horizontal. Substituting m = 0 back into the equation of the line gives y = 5. Therefore, the maximum distance occurs when the slope is 0 and the line is horizontal. The distance between the origin and the point (0,5) is 5, so the answer is B.

Question 7

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The Falls Incline Railway in Niagara Falls,...

Question 8

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)​

Accepted Answer

The answer of Consider a line with slope m and...

Question 9

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

Accepted Answer

Choice B shows a slope with a rise of 7 meters for every 9 meters of horizontal travel. The other choices either do not show the correct slope or do not include both horizontal and vertical dimensions.

Question 10

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Consider a line with slope m and...

Question 11

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  of the railway.Round your answer to four decimal places for radians and round your answer to one decimal places for degree. ​  ​  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The Falls Incline Railway in Niagara Falls,...

Question 12

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Consider a line with slope m and...

Question 13

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A roof has a rise of 9...

Question 14

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) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Consider a line with slope m and...

Quiz 6: Topics-In-Analytic-Geometry

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 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 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.

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.

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

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.

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.

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 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.

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.

Quiz 6: Topics-In-Analytic-Geometry

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 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 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. ​

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. ​

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

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. ​

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. ​

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 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. ​ ​ ​

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. ​

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 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 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.

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.

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

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.

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.

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 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.

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.