Question 4 (Essay Worth 10 points)
1 answer:
Given
The attached graph
Part A: Is the graph linear or nonlinear
The attached graph has 3 different straight lines, all of which point to different directions. For a graph to be linear, such graph must have just 1 straight line. This means that the graph is nonlinear.
The attached graph is a nonlinear graph
Part B:
<u>(i) The increasing segment</u>
This is the segment that points in the upward direction.
In the attached graph, line segment A [i.e. from (0,0) to (2,16)] represents an upward movement of the ant.
Line segment A is the increasing segment
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<u>(ii) The decreasing segment</u>
This is the segment that points in the downward direction.
In the attached graph, line segment C [i.e. from (4,16) to (6,0)] represents a downward movement of the ant.
Line segment C is the decreasing segment
<u>(ii) The constant segment</u>
This segment is represented by a vertical or a horizontal line.
In the attached graph, line segment B [i.e from (2,16) to (4,16)] represents a horizontal line.
Line segment B is the constant segment
Part C: The movement of the ant
The ant travels at a constant speed through segment A. It then rests for 2 seconds (i.e. segment B) and finally travels at a constant speed through segment C.
In addition, the 2 seconds it rests at segment B is the difference of the x-coordinates of the end points of line segment B
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Let's start with the drawing. (See the drawing at the bottom of this answer.)
Draw a vertical segment.
At the bottom endpoint, draw a horizontal segment to the right.
The angle at the bottom left is a right angle.
So far this should look like an "L" shape.
The vertical segment is the wall, and the horizontal segment is the ground.
Now draw a segment that connects the right endpoint of the horizontal segment and the top endpoint of the vertical segment. Now you have a right triangle. The diagonal segment represents the ladder. The diagonal segment is the hypotenuse. Label the diagonal segment, the hypotenuse, 12 ft.
Label the vertical segment, the wall, 11.8 ft.
The angle at the bottom right is A. It is the angle the ladder makes with the ground. This angle cannot be greater than 75 degrees.
Now we use trigonometry to find the measure of angle A.
For this right triangle, and its angle A, you have a hypotenuse that measures 12 ft, and an opposite leg that measures 11.8 ft.
We need to find angle A.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.
Since the sine of angle A equals 0.98333, we use the inverse sine function to find the measure of angle A.
Answer:
The angle the ladder makes with the ground is 79.5 degrees which is greater than 75 degrees, so the ladder it will be unsafe in this position.
|\
| \
| \
| \
opp = | \ hyp = 12
= 11.8 | \
| \
|_______\ A
Draw a vertical segment.
At the bottom endpoint, draw a horizontal segment to the right.
The angle at the bottom left is a right angle.
So far this should look like an "L" shape.
The vertical segment is the wall, and the horizontal segment is the ground.
Now draw a segment that connects the right endpoint of the horizontal segment and the top endpoint of the vertical segment. Now you have a right triangle. The diagonal segment represents the ladder. The diagonal segment is the hypotenuse. Label the diagonal segment, the hypotenuse, 12 ft.
Label the vertical segment, the wall, 11.8 ft.
The angle at the bottom right is A. It is the angle the ladder makes with the ground. This angle cannot be greater than 75 degrees.
Now we use trigonometry to find the measure of angle A.
For this right triangle, and its angle A, you have a hypotenuse that measures 12 ft, and an opposite leg that measures 11.8 ft.
We need to find angle A.
The trig ratio that relates the opposite leg and the hypotenuse is the sine.
Since the sine of angle A equals 0.98333, we use the inverse sine function to find the measure of angle A.
Answer:
The angle the ladder makes with the ground is 79.5 degrees which is greater than 75 degrees, so the ladder it will be unsafe in this position.
|\
| \
| \
| \
opp = | \ hyp = 12
= 11.8 | \
| \
|_______\ A