Difeientiation Rules CHAPTER 3 250 the sape of a cone whose hae diame dhe always equl How fast is the height of dhe pile incrca when the poe is 10 t big 21 The altinke of a triangie is increasing ar a rate of 1 cm/min while the area of the triangle is increasing ar a rate of Zcmmin A what cate is the hase of the triangie changing when the altitude n 10 cm and the area is 100 cm 22 A boot is pulled into a dock by a rope aitached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat II the rope is pulied in at a ate of I m/s how fast is the boar approsching the dock when it is 8 mn from the dock? 30. A kite 10 ft above the ground moves horizontally at a speed of8 n/s Al what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out? 23. At noon ship A is 100 km west of ship B. Ship A is sading sath at 35 km/h and ship B is sailing north at 25 km/h How fast is the distance berween the stups changing at 4.00 PM 31. The sides of an equilateral triangle are increasing at a rate of 10 cm/min At what rate is the area of the trangle increasing when the sides are 30 cm long? 2 sunfx/2) As the 24. A particle moves along the curve y particle passes through the point (1,ts rcoordinate increases at a nte ofy 10 cm/s How fast is the distance from the particle to the origin changing ut this instant 32. How fast is changing in Example 2 when the bottom of the ladder is 6 ft from the wall? angle between the ladder and the ground 25. Water is leaking out of an inverted.conical tank at a rale of 10.000 cm min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. Jf the water level is nising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at whoch water is being pumped into the tank 33. The top of a ladder slides down a vertical wall at a rale of 0.15 m/s At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 02 m/s How long is the ladder? 26. A tough is 10 h long and its ends have the shape of isos celes triangles that are 3 ft acrosS at the top and have a height of I ft.If the trough is being filled with water at a rate of 12 ftmn,how fast is the water level nising when the water is 6 inches deep 34. According to the model we used to solve Example 2 what happens as the top of the ladder approaches the ground? ts the model appropriate for small values of y? 35. If the minute hand of a clock has leneth c in cet
Difeientiation Rules CHAPTER 3 250 the sape of a cone whose hae diame dhe always equl How fast is the height of dhe pile incrca when the poe is 10 t big 21 The altinke of a triangie is increasing ar a rate of 1 cm/min while the area of the triangle is increasing ar a rate of Zcmmin A what cate is the hase of the triangie changing when the altitude n 10 cm and the area is 100 cm 22 A boot is pulled into a dock by a rope aitached to the bow of the boat and passing through a pulley on the dock that is 1 m higher than the bow of the boat II the rope is pulied in at a ate of I m/s how fast is the boar approsching the dock when it is 8 mn from the dock? 30. A kite 10 ft above the ground moves horizontally at a speed of8 n/s Al what rate is the angle between the string and the horizontal decreasing when 200 ft of string has been let out? 23. At noon ship A is 100 km west of ship B. Ship A is sading sath at 35 km/h and ship B is sailing north at 25 km/h How fast is the distance berween the stups changing at 4.00 PM 31. The sides of an equilateral triangle are increasing at a rate of 10 cm/min At what rate is the area of the trangle increasing when the sides are 30 cm long? 2 sunfx/2) As the 24. A particle moves along the curve y particle passes through the point (1,ts rcoordinate increases at a nte ofy 10 cm/s How fast is the distance from the particle to the origin changing ut this instant 32. How fast is changing in Example 2 when the bottom of the ladder is 6 ft from the wall? angle between the ladder and the ground 25. Water is leaking out of an inverted.conical tank at a rale of 10.000 cm min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. Jf the water level is nising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at whoch water is being pumped into the tank 33. The top of a ladder slides down a vertical wall at a rale of 0.15 m/s At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 02 m/s How long is the ladder? 26. A tough is 10 h long and its ends have the shape of isos celes triangles that are 3 ft acrosS at the top and have a height of I ft.If the trough is being filled with water at a rate of 12 ftmn,how fast is the water level nising when the water is 6 inches deep 34. According to the model we used to solve Example 2 what happens as the top of the ladder approaches the ground? ts the model appropriate for small values of y? 35. If the minute hand of a clock has leneth c in cet
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I need help with question 23 in Section 3.9, page 250, of the James Stewart Calculus Eighth Edition textbook.
Transcribed Image Text:Difeientiation Rules
CHAPTER 3
250
the sape of a cone whose hae diame dhe
always equl How fast is the height of dhe pile incrca
when the poe is 10 t big
21 The altinke of a triangie is increasing ar a rate of 1 cm/min
while the area of the triangle is increasing ar a rate of
Zcmmin A what cate is the hase of the triangie changing
when the altitude n 10 cm and the area is 100 cm
22 A boot is pulled into a dock by a rope aitached to the bow of
the boat and passing through a pulley on the dock that is 1 m
higher than the bow of the boat II the rope is pulied in at a
ate of I m/s how fast is the boar approsching the dock
when it is 8 mn from the dock?
30. A kite 10 ft above the ground moves horizontally at a speed
of8 n/s Al what rate is the angle between the string and the
horizontal decreasing when 200 ft of string has been let out?
23. At noon ship A is 100 km west of ship B. Ship A is sading
sath at 35 km/h and ship B is sailing north at 25 km/h
How fast is the distance berween the stups changing at
4.00 PM
31. The sides of an equilateral triangle are increasing at a rate of
10 cm/min At what rate is the area of the trangle increasing
when the sides are 30 cm long?
2 sunfx/2) As the
24. A particle moves along the curve y
particle passes through the point (1,ts rcoordinate
increases at a nte ofy 10 cm/s How fast is the distance
from the particle to the origin changing ut this instant
32. How fast is
changing in Example 2 when the bottom of the ladder is 6 ft
from the wall?
angle between the ladder and the ground
25. Water is leaking out of an inverted.conical tank at a rale of
10.000 cm min at the same time that water is being pumped
into the tank at a constant rate. The tank has height 6 m and
the diameter at the top is 4 m. Jf the water level is nising at a
rate of 20 cm/min when the height of the water is 2 m, find
the rate at whoch water is being pumped into the tank
33. The top of a ladder slides down a vertical wall at a rale of
0.15 m/s At the moment when the bottom of the ladder is
3 m from the wall, it slides away from the wall at a rate of
02 m/s How long is the ladder?
26. A tough is 10 h long and its ends have the shape of isos
celes triangles that are 3 ft acrosS at the top and have a height
of I ft.If the trough is being filled with water at a rate of
12 ftmn,how fast is the water level nising when the water
is 6 inches deep
34. According to the model we used to solve Example 2 what
happens as the top of the ladder approaches the ground? ts
the model appropriate for small values of y?
35. If the minute hand of a clock has leneth c in cet
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