4 1 21 &lr1B &/1414 44 414411W0wden2when cach edge is (16. Surface Area All edges of a cube are exrate of 6 centimeters per second. How fast is tearea changing when each edge is (a) 2 centime(b) Consider the trianladder, and theof the triangle7 feet from thewdee r S(c) Find the rate awall of the ho(b)aden a 1(b) 10 centimeters?dewhena3y417. Height At a sand and gravel plant, sand is fallinis 7 feet from(a)conveyor and onto a conical pile at a rate of 10 cubicminute. The diameter of the base of the cone is apprthree times the altitude. At what rate is the height of tchanging when the pile is 15 feet high? (Hint: The fomthe volume of a cone is V = nrh.)18. Height The volume of oil in a cylindrical comuincreasing at a rate of 150 cubic inches per second. Theof the cylinder is approximately ten times the radius. Arate is the height of the oil changing when the oil is 35 mhigh? (Hint: The formula for the volume of a cylneV= nr?h.)-2(b)whenx = 4y3Point In Exercises 7-10, a point isalong the graph of the given function atrd. Find dy dt for the given values of x.2 centimeters per second)r0(c) x = 1Figure for 215 inches per secondFOR FUon the mathex 0(c) x 2(c) x=2Ladder Para19. Depth A swimming pool is 12 meters long, 6 metersI meter deep at the shallow end, and 3 meters depdeep end (see figure). Water is being pumped into the pcubic meter per minute, and there is 1 meter of waterThe Colleget per secondMathArticle22. Consplankof a r*4(c) x 0deep end.mtimeters per secondoppowall(c)1 m0.1Salo

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Asked Oct 14, 2019
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number 18 please 

4 1 2
1 &l
r1B &/
1
414 44 41441
1W
0
wden2
when cach edge is (
16. Surface Area All edges of a cube are ex
rate of 6 centimeters per second. How fast is te
area changing when each edge is (a) 2 centime
(b) Consider the trian
ladder, and the
of the triangle
7 feet from the
wdee r S
(c) Find the rate a
wall of the ho
(b)
aden a 1
(b) 10 centimeters?
de
whena3y4
17. Height At a sand and gravel plant, sand is fallin
is 7 feet from
(a)
conveyor and onto a conical pile at a rate of 10 cubic
minute. The diameter of the base of the cone is appr
three times the altitude. At what rate is the height of t
changing when the pile is 15 feet high? (Hint: The fom
the volume of a cone is V = nrh.)
18. Height The volume of oil in a cylindrical comu
increasing at a rate of 150 cubic inches per second. The
of the cylinder is approximately ten times the radius. A
rate is the height of the oil changing when the oil is 35 m
high? (Hint: The formula for the volume of a cylne
V= nr?h.)
-2
(b)
whenx = 4y3
Point In Exercises 7-10, a point is
along the graph of the given function at
rd. Find dy dt for the given values of x.
2 centimeters per second
)r0
(c) x = 1
Figure for 21
5 inches per second
FOR FU
on the mathe
x 0
(c) x 2
(c) x=2
Ladder Para
19. Depth A swimming pool is 12 meters long, 6 meters
I meter deep at the shallow end, and 3 meters dep
deep end (see figure). Water is being pumped into the p
cubic meter per minute, and there is 1 meter of water
The Colleg
et per second
MathArticle
22. Cons
plank
of a r
*
4
(c) x 0
deep end.
mtimeters per second
oppo
wall
(c)
1 m
0.1S
alo
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4 1 2 1 &l r1B &/ 1 414 44 41441 1W 0 wden2 when cach edge is ( 16. Surface Area All edges of a cube are ex rate of 6 centimeters per second. How fast is te area changing when each edge is (a) 2 centime (b) Consider the trian ladder, and the of the triangle 7 feet from the wdee r S (c) Find the rate a wall of the ho (b) aden a 1 (b) 10 centimeters? de whena3y4 17. Height At a sand and gravel plant, sand is fallin is 7 feet from (a) conveyor and onto a conical pile at a rate of 10 cubic minute. The diameter of the base of the cone is appr three times the altitude. At what rate is the height of t changing when the pile is 15 feet high? (Hint: The fom the volume of a cone is V = nrh.) 18. Height The volume of oil in a cylindrical comu increasing at a rate of 150 cubic inches per second. The of the cylinder is approximately ten times the radius. A rate is the height of the oil changing when the oil is 35 m high? (Hint: The formula for the volume of a cylne V= nr?h.) -2 (b) whenx = 4y3 Point In Exercises 7-10, a point is along the graph of the given function at rd. Find dy dt for the given values of x. 2 centimeters per second )r0 (c) x = 1 Figure for 21 5 inches per second FOR FU on the mathe x 0 (c) x 2 (c) x=2 Ladder Para 19. Depth A swimming pool is 12 meters long, 6 meters I meter deep at the shallow end, and 3 meters dep deep end (see figure). Water is being pumped into the p cubic meter per minute, and there is 1 meter of water The Colleg et per second MathArticle 22. Cons plank of a r * 4 (c) x 0 deep end. mtimeters per second oppo wall (c) 1 m 0.1S alo

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Expert Answer

Step 1

Given,

 

dV
150 cubic inches per second
dt
h=10r
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Image Transcriptionclose

dV 150 cubic inches per second dt h=10r

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Step 2

Consider the volume of the cylinger,

V Trh
h
hh=10r]
10
V = 7
V =
100
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Image Transcriptionclose

V Trh h hh=10r] 10 V = 7 V = 100

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Step 3

Now differentiating with r...

dV
dh
-.3h2
dt
dt 100
Злh dh
150
dV
=150
dt
100 dt
When h 35 inches, we get
Зл (35)
dh
= 150
dt
100
dh 150x100
di 3л-(35)*
1.2992 inches per second.
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Image Transcriptionclose

dV dh -.3h2 dt dt 100 Злh dh 150 dV =150 dt 100 dt When h 35 inches, we get Зл (35) dh = 150 dt 100 dh 150x100 di 3л-(35)* 1.2992 inches per second.

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