Southern New Hampshire University - 7-2 Problem Set_ Module Seven
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School
Southern New Hampshire University *
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Course
140
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
11
Uploaded by brienncaervin
2/22/24, 11:06 PM
Southern New Hampshire University - 7-2 Problem Set: Module Seven
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MAT-140-X3745 Precalculus 24EW3 : MAT-140 : 1466672
, 7-2 Problem Set: Module Seven
Brie Ervin, 2/22/24 at 10:17:19 PM EST
Question1:
Score 6/6
Write an equation describing the relationship of the given variables.
varies directly as the fourth power of and when , .
Your response
Correct response
3x^4
3*x^4
Auto graded
Grade:
1/1.0 Total grade: 1.0×1/1 = 100%
Feedback:
The general formula for direct variation with a fourth power is . The constant can be found
by dividing by the fourth power of .
Now use the constant to write an equation that represents this relationship.
2/22/24, 11:06 PM
Southern New Hampshire University - 7-2 Problem Set: Module Seven
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Question2:
Score 6/6
Write an equation describing the relationship of the given variables.
varies inversely as the cube root of and when , .
Your response
Correct response
28/x^(1/3)
Auto graded
Grade:
1/1.0 Total grade: 1.0×1/1 = 100%
Feedback:
The general formula for inverse variation with a cube root is . The constant can be found
by multiplying by the cube root of .
Now use the constant to write an equation that represents this relationship.
Question3:
Score 6/6
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Use the given information to find the unknown value.
varies directly as the cube of . When , then . Find when .
Enter the exact answer.
Your response
Correct response
13.671875
875/64
Auto graded
Grade:
1/1.0 Total grade: 1.0×1/1 = 100%
Feedback:
The general formula for direct variation with a cube is . The constant can be found by
dividing by the cube of .
Now use the constant to write an equation that represents this relationship.
Substitute and solve for .
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Question4:
Score 6/6
Use the given information to find the unknown value.
varies inversely with the cube of . When , then . Find when .
Enter the exact answer.
Your response
Correct response
8
8
Auto graded
Grade:
1/1.0 Total grade: 1.0×1/1 = 100%
Feedback:
The general formula for inverse variation with a cube is . The constant can be found by
multiplying by the cube of .
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Southern New Hampshire University - 7-2 Problem Set: Module Seven
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Now use the constant to write an equation that represents this relationship.
Substitute and solve for .
Question5:
Score 6/6
Use the given information to answer the question.
The distance that an object falls varies directly with the square of the time, , of the fall. If an
object falls feet in one second, how long will it take for it to fall feet?
Round your answer to two decimal places.
It will take
Your response
Correct response
1.73
1.73±0.01
Auto graded
Grade:
1/1.0 seconds for the object to fall feet.
Total grade: 1.0×1/1 = 100%
Feedback:
The general formula for direct variation with a square is . The constant can be found by
dividing by the square of .
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Now use the constant to write an equation that represents this relationship.
Substitute and solve for .
It will take the object about seconds to to fall feet.
Question6:
Score 6/6
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Use the given information to answer the question.
The weight of an object above the surface of the Earth varies inversely with the square of the
distance from the center of the Earth. If a body weighs pounds when it is miles from
Earth’s center, what would it weigh if it were miles from Earth’s center?
Round your answer to two decimal places.
The body would weigh Your response
Correct response
49.25
49.25±0.01
Auto graded
Grade:
1/1.0 pounds if it were miles from Earth's center.
Total grade: 1.0×1/1 = 100%
Feedback:
Let be the distance of the object from Earth's center and be the weight of the object. The
general formula for inverse variation with a square is . The constant can be found by
multiplying by the square of .
Now use the constant to write an equation that represents this relationship.
Substitute and solve for .
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Southern New Hampshire University - 7-2 Problem Set: Module Seven
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The body would weigh about pounds if the object is miles from the Earth's center.
Question7:
Score 6/6
Use a calculator to evaluate the expression.
Round your answer to the nearest hundredth.
Your response
Correct response
0.284
0.28±0.01
Auto graded
Grade:
1/1.0 radians
Total grade: 1.0×1/1 = 100%
Feedback:
Using a calculator in radian mode, we see .
Question8:
Score 6/6
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Use a calculator to evaluate the expression.
Round your answer to the nearest hundredth.
Your response
Correct response
0.28
0.27±0.01
Auto graded
Grade:
1/1.0 radians
Total grade: 1.0×1/1 = 100%
Feedback:
Using a calculator in radian mode, we see .
Question9:
Score 6/6
Find the angle , in radians, in the given right triangle. The length of the side adjacent to is 16
and the length of the side opposite is 15.
Round your answer to the nearest hundredth.
Your response
Correct response
15
16
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0.75
0.75±0.01
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Grade:
1/1.0 Total grade: 1.0×1/1 = 100%
Feedback:
Because we know the side opposite and the side adjacent to the angle, it makes sense for us to use
the tangent function.
Question10:
Score 6/6
What percentage grade should a road have if the angle of elevation of the road is degrees? (The
percentage grade is defined as the change in the altitude of the road over a -foot horizontal
distance. For example a grade means that the road rises feet for every feet of horizontal
distance.)
Round your answer to two decimal places.
The road should have a(n)
Your response
Correct response
3.49
3.49±0.01
Auto graded
Grade:
1/1.0 grade.
Total grade: 1.0×1/1 = 100%
Feedback:
We know that the elevation of the road is degrees. If the horizontal distance is feet, we want
to know the altitude. See the figure below.
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The trigonometric function relating the side opposite to an angle and the side adjacent to the angle
is the tangent. So we will state our information in terms of the tangent of , letting be the
unknown height.
Since the change in altitude of the road over a -foot horizontal distance is feet, the
percentage grade is .
2º
100