MATH 101 Webwork 4 Homework Questions and Answers PDF from 2020
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Course
MATH 101 (MATH101)
Institution
University Of British Columbia (UBC
)
This is a pdf copy of the webwork 4 questions for MATH 101 at UBC with answers attached. Note that the exact numbers in your question will differ but the answer key here will provide insight for you to tackle the problems nonetheless.
Nikita Sharma 2019W2 MATH 101 209
Assignment Homework 4 due 9/12/14 at 9pm
1. (1 point)
The volume of the solid obtained by rotating the region en- Hint
closed by Correct Answers:
y = x3 , y = 36x, x ≥ 0
• pi*pi/(4*1) + 2*8*pi/1
about the line y = 0 can be computed using vertical slices via an
integral
5. (1 point) Find the volume of the√
solid obtained by rotating
Z b the region bounded by y = x and y = x about the line x = 3.
V= ? Volume =
a
Correct Answers:
with limits of integration a = and b = . • pi*(3/3-2/15)
The volume is V = cubic units.
Note: You can earn full credit if the last question is correct 6. (1 point)
and all other questions are either blank or correct. A spring has a natural length of 20 cm. If a 25-N force is re-
Correct Answers: quired to keep it stretched to a length of 30 cm, how much work
• pi*((36*x)**2) - pi*((x**3)**2) (in J) is required to stretch it from 20 cm to 25 cm?
• DX Work done = J
• 0 Correct Answers:
• 6
• 0.3125
• 167513.310681012
2. (1 point)
7. (1 point)
Using vertical slices, find the volume of the √
solid obtained
If 6 J of work are needed to stretch a spring from 10 cm to 12
by rotating the region bounded by the curves y = x − 1, y = 0,
cm and another 10 J are needed to stretch it from 12 cm to 14
x = 2, and x = 6 about the x-axis.
cm, what is the natural length (in cm) of the spring?
Volume =
Correct Answers:
Natural length of the spring = cm
Correct Answers:
• pi*((6)ˆ2/2-6)
• 8
3. (1 point)
Using horizontal slices, find the volume of the solid obtained
by rotating the region bounded by 8. (1 point)
A particle is moved along the x-axis by a force that measures
x = 8y2 , y = 1, x = 0 10/(1 + x)2 N at a point x metres from the origin. Find the work
(in joules) done in moving the particle from the origin to a dis-
about the y-axis.
tance of 9 metres.
Work done = joules
Answer: Correct Answers:
Correct Answers:
• 8*8*pi/5 • 9
4. (1 point)
Find the volume of the solid obtained by rotating the region 9. (1 point)
bounded by A cable that weighs 2 kg/m is used to lift 800 kg of coal up a
mineshaft 500 m deep. Find the work done (in joules). Use the
value 9.8 m/s2 for the acceleration due to gravity.
y = 0, y = cos(1x), x = π/2, x = 0
Work done = joules
about the line y = −8 Correct Answers:
• 650000*9.8
Answer:
1
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