For questions 10-12 consider: The volume of a frustum of a cone is given by the formula v=r2(x² + y? + xy) where x is the radius of the smaller circle, y is the radius of the larger circle, and z is the height of the frustum (see figure) 10. The rate of change of the volume is determined using av (i) AV = Ax+ ôx av -Ay+Az av dV av dx av dy av dz (ii) dt ôx dt oy dt oz dt 11. The rate of change of the volume of this frustum when x increases at a rate of a cm/s, y decreases at a rate of b cm/s and z remains constant is 12. The rate of change of the volume of this frustum in terms of n, a and b when x = 2 cm, y = 2 cm and z=3 cm is
For questions 10-12 consider: The volume of a frustum of a cone is given by the formula v=r2(x² + y? + xy) where x is the radius of the smaller circle, y is the radius of the larger circle, and z is the height of the frustum (see figure) 10. The rate of change of the volume is determined using av (i) AV = Ax+ ôx av -Ay+Az av dV av dx av dy av dz (ii) dt ôx dt oy dt oz dt 11. The rate of change of the volume of this frustum when x increases at a rate of a cm/s, y decreases at a rate of b cm/s and z remains constant is 12. The rate of change of the volume of this frustum in terms of n, a and b when x = 2 cm, y = 2 cm and z=3 cm is
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter47: Applications Of Formulas To Cutting Speed, Revolutions Per Minute, And Cutting Time
Section: Chapter Questions
Problem 43A
Related questions
Question
![For questions 10-12 consider:
The volume of a frustum of a cone is given by the formula
v==R={x² + v² + xv)
3
where x is the radius of the smaller circle, y is the radius of the larger circle, and z is the
height of the frustum (see figure)
10. The rate of change of the volume is determined using
av
-Ay +Az
ду
av
(i) AV=Ax+
av
dV av dx av dy ôV dz
(ii)
dt ôx dt ay dt ôz dt
11. The rate of change of the volume of this frustum when x increases at a rate of
a cm/s, y decreases at a rate of b cm/s and z remains constant is
12. The rate of change of the volume of this frustum in terms of n, a and b when
x= 2 cm, y= 2 cm and z=3 cm is
1
13. Consider the integral -
dx then (which statement(s) is/are correct):
2
4x
X
(i) 2-4x
1
dx ==[In(x-4)-Inx]+C when using partial fractions
1
1
dx =tanh 1(x- 2)
+C when completing the square
(ii)
x- 4x
v2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28e9706d-e7c3-4a84-9003-21b20b919a0a%2F204e9b2d-f3d7-4828-870a-c10bc18e2c62%2Fozjuod2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For questions 10-12 consider:
The volume of a frustum of a cone is given by the formula
v==R={x² + v² + xv)
3
where x is the radius of the smaller circle, y is the radius of the larger circle, and z is the
height of the frustum (see figure)
10. The rate of change of the volume is determined using
av
-Ay +Az
ду
av
(i) AV=Ax+
av
dV av dx av dy ôV dz
(ii)
dt ôx dt ay dt ôz dt
11. The rate of change of the volume of this frustum when x increases at a rate of
a cm/s, y decreases at a rate of b cm/s and z remains constant is
12. The rate of change of the volume of this frustum in terms of n, a and b when
x= 2 cm, y= 2 cm and z=3 cm is
1
13. Consider the integral -
dx then (which statement(s) is/are correct):
2
4x
X
(i) 2-4x
1
dx ==[In(x-4)-Inx]+C when using partial fractions
1
1
dx =tanh 1(x- 2)
+C when completing the square
(ii)
x- 4x
v2
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