Practice Quiz 12_ Attempt review
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School
Thompson Rivers University *
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Course
1901
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
7
Uploaded by CaptainArt11246
Started on
Thursday, 27 July 2023, 4:01 PM
State
Finished
Completed on
Thursday, 27 July 2023, 4:27 PM
Time taken
25 mins 47 secs
Question 1
Correct
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Question 2
Correct
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A garden gate that is 3 feet wide and 4 feet tall needs a diagonal brace to make it stable. A piece of wood for this diagonal brace will
need to be
5
feet long. (Write a whole number; do not include words or calculations.)
If we let be the length in feet of the diagonal brace, then, according to the Pythagorean theorem, . Therefore, , so , which means that the diagonal brace is 5 feet long. Tim knows the area of a circle is “pi r squared,” so to calculate the area of a circle with radius 2 cm, he calculates cm .
Select one:
True
False
2
The area should be cm . The correct answer is 'False'.
2
Question 3
Incorrect
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The next three questions work towards calculating the area of the track shown in the following diagram:
First, assuming that the two ends are semi-circles, what is the correct calculation for the diameter of each semi-circle (i.e., the lengths
of each vertical line in the diagram)?
Select one:
a.
Diameter m
b.
Diameter m
c.
Diameter m
d.
Diameter m
e.
None of answers a-d are correct
Your answer is incorrect.
For the semi-circular ends, circumference, , so diameter, m
The correct answer is: Diameter m
Question 4
Incorrect
Mark 0.00 out of 1.00
Consider the track shown in the following diagram:
Next, what is the correct calculation for the sum of the areas of each semi-circular end?
Select one:
a.
Area m
b.
Area \( = 20,000/\pi \) m
c.
Area \( = 40,000/\pi \) m
d.
Area \( = 80,000/\pi \) m
e.
None of answers a-d are correct.
2
2
2
2
Your answer is incorrect.
For the semi-circular ends, circumference, \(c = 2\pi r\), so \(r = c/2\pi \). Sum of areas of semi-circular ends, \(a = \pi {r^2} = \pi {\left(
{c/2\pi } \right)^2} = {c^2}/4\pi = {400^2}/4\pi = 40,000/\pi \) m
.
The correct answer is: Area \( = 40,000/\pi \) m
2
2
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Question 5
Incorrect
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Question 6
Incorrect
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Consider the track shown in the following diagram:
Finally, what is the correct calculation for the area of the rectangular section in the middle?
Select one:
a.
Area \( = 60,000/\pi \) m
b.
Area \( = 120,000/\pi \) m
c.
Area \( = 180,000/\pi \) m
d.
Area \( = 240,000/\pi \) m
e.
None of answers a-d are correct.
2
2
2
2
Your answer is incorrect.
Area of rectangular middle, \(a = lw = 300 \times 2r = 300 \times \left( {c/\pi } \right) = 120,000/\pi \) m
. The total area is therefore \
(\left( {40,000 + 120,000} \right)/\pi = 160,000/\pi = 50,930\) m
The correct answer is: Area \( = 120,000/\pi \) m
2
2
2
Calculate the area of the polygon below.
The area is
157
m
. (Write a whole number; do not include words or calculations.)
2
Create two triangles by drawing a diagonal line from the top left corner to the bottom right corner. The base of the lower left triangle is
20 m and the heights is 6 m so, \({\rm{area}} = \frac{1}{2}\left( {20 \times 6} \right) = 60\) m
. The base of the upper right triangle is 17
m and the height is 12 m so, a\({\rm{rea}} = \frac{1}{2}\left( {17 \times 12} \right) = 102\) m
. So, the total area is 162 m
.
2
2
2
Question 7
Correct
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Question 8
Correct
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Consider the following diagram.
The next three questions work towards calculating the perimeter of the large triangle. First, calculate the length marked \(x\) in the
right triangle below.
The length \(x\) is
12
m. (Write a whole number; do not include words or calculations.)
According to the Pythagorean theorem, \({x^2} + {5^2} = {13^2}\). Therefore, \({x^2} = {13^2} - {5^2} = 169 - 25 = 144\), so \(x = 12\) m.
Next, calculate the length marked \(y\) in the right triangle below.
The length \(y\) is
9
m. (Write a whole number; do not include words or calculations.)
According to the Pythagorean theorem, \({y^2} + {12^2} = {15^2}\). Therefore, \({y^2} = {15^2} - {12^2} = 225 - 144 = 81\), so \(y = 9\)
m.
Question 9
Correct
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Question 10
Correct
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Finally, use the answers to the previous two questions to calculate the perimeter of the large triangle below.
The perimeter is
36
m. (Write a whole number; do not include words or calculations.)
The perimeter of the larger triangle is 12 m + 9 m + 15 m = 36 m.
What is the largest possible area for a forest with a perimeter of 200 km?
Select one:
a.
200 km
b.
2,500 km
c.
3,183 km
d.
40,000 km
e.
None of answers a-d are correct.
2
2
2
2
Your answer is correct.
The largest possible area that can occur is a circle of circumference 200 km, whose area is \(a = \pi {r^2} = \pi {\left( {c/2\pi } \right)^2}
= {c^2}/4\pi = {200^2}/4\pi = 10,000/\pi = 3,183\) km
.
The correct answer is: 3,183 km
2
2
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