3.9 EXERCIir es ra e lh lerth13ra)What quall(b) What is the unkmDraw a picture of the situalil(d) Write an eqution that relates the quile) Finish solving the problem2 4 eanea ncle wth nds ad the cinleds as in nsofh Sp a aptured ranker and sprends inac ar rhe radis of the oil spull ncreases ate e how fastis the ansa of the spillng he e raius s 013, A plane tving horizontally at an altitude of TI and a spS00 mi/h passes directly over a radar station Find the rate atwhich the distance from the plane to the station is increasingwhen it is 2 mi away from the stationchse of aneis increasing at a rate alo em/s A whatr e an f the sare increasng when the area of the14. Ir a snowball melts so that its surfnce area decreases at a rate ofI cm/min, find the rate at which the diameter decreases whCnthe diameter is 10 cmgoire te cor4The ogh of a recangle is increasang at a rate of 8 cms andh is acreag ar a rate of 3 cms When the length is20 c and the width is 10 cm. bow fast is the arca of the15. A street light is mounted at the top of a 15-ft-tall pole. A 1man6 tall walks away from the pole with a speed of 5 ft/s along astraight path How fast is the tip of his shadow moving when heis 40 fi from the pole?5. A rlindncal tank wth radius 5 m is being tilled with watcra rate of 3 m nincreasingHow fast is the beight of the waterThe radius of a sphere is mereasing a a rate of 4 mnm/s Howst is the volume increasing when the diameter is 80 mm?16. At noon, ship A is 150 km west of ship B. Ship A is sailing eastat 35 km/h and ship B is sailing north at 25 km/h. How fast isthe distance between the ships changing at 4:00 PM?radrus of a spherical ball is increasing at a rate ofmin Ar what rate is the surface area of the balltsing when the radius is 8 cm?of a triangle with sides of lengths a and b andl angle & is17. Two cars start moving from the same point. One travels southat 60 mi/h and the other travels west at 25 mi /h. At what rateis the distance between the cars increasing two hours later?18. A spotlight on the ground shines on a wall 12 m away. If a man2 m tall walks from the spotlight toward the building at a speedof 1.6 m/s. how fast is the length of his shadow on the build-ing decreasing when he is 4 m from the building?A=ab sinCm. b 3 cm, and 0 increases at a rate ofin, how fast is the area increasing whenncreases at a rate of 1 5 cm/min md10

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Asked Oct 25, 2019
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I need help with problem 17 in Section 3.9, page 249, of the the James Stewart Calculus Eighth Edition textbook.

3.9 EXERCI
ir es ra e lh lerth
13
ra)What quall
(b) What is the unkm
Draw a picture of the situalil
(d) Write an eqution that relates the quil
e) Finish solving the problem
2 4 eanea ncle wth nds ad the cinle
ds as in nsof
h Sp a aptured ranker and sprends in
ac ar rhe radis of the oil spull ncreases at
e e how fastis the ansa of the spill
ng he e raius s 0
13, A plane tving horizontally at an altitude of TI and a sp
S00 mi/h passes directly over a radar station Find the rate at
which the distance from the plane to the station is increasing
when it is 2 mi away from the station
chse of aneis increasing at a rate alo em/s A what
r e an f the sare increasng when the area of the
14. Ir a snowball melts so that its surfnce area decreases at a rate of
I cm/min, find the rate at which the diameter decreases whCn
the diameter is 10 cm
goire te cor
4The ogh of a recangle is increasang at a rate of 8 cms and
h is acreag ar a rate of 3 cms When the length is
20 c and the width is 10 cm. bow fast is the arca of the
15. A street light is mounted at the top of a 15-ft-tall pole. A 1man
6 tall walks away from the pole with a speed of 5 ft/s along a
straight path How fast is the tip of his shadow moving when he
is 40 fi from the pole?
5. A rlindncal tank wth radius 5 m is being tilled with watcr
a rate of 3 m n
increasing
How fast is the beight of the water
The radius of a sphere is mereasing a a rate of 4 mnm/s How
st is the volume increasing when the diameter is 80 mm?
16. At noon, ship A is 150 km west of ship B. Ship A is sailing east
at 35 km/h and ship B is sailing north at 25 km/h. How fast is
the distance between the ships changing at 4:00 PM?
radrus of a spherical ball is increasing at a rate of
min Ar what rate is the surface area of the ball
tsing when the radius is 8 cm?
of a triangle with sides of lengths a and b and
l angle & is
17. Two cars start moving from the same point. One travels south
at 60 mi/h and the other travels west at 25 mi /h. At what rate
is the distance between the cars increasing two hours later?
18. A spotlight on the ground shines on a wall 12 m away. If a man
2 m tall walks from the spotlight toward the building at a speed
of 1.6 m/s. how fast is the length of his shadow on the build-
ing decreasing when he is 4 m from the building?
A=ab sin
Cm. b 3 cm, and 0 increases at a rate of
in, how fast is the area increasing when
ncreases at a rate of 1 5 cm/min md
10
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3.9 EXERCI ir es ra e lh lerth 13 ra)What quall (b) What is the unkm Draw a picture of the situalil (d) Write an eqution that relates the quil e) Finish solving the problem 2 4 eanea ncle wth nds ad the cinle ds as in nsof h Sp a aptured ranker and sprends in ac ar rhe radis of the oil spull ncreases at e e how fastis the ansa of the spill ng he e raius s 0 13, A plane tving horizontally at an altitude of TI and a sp S00 mi/h passes directly over a radar station Find the rate at which the distance from the plane to the station is increasing when it is 2 mi away from the station chse of aneis increasing at a rate alo em/s A what r e an f the sare increasng when the area of the 14. Ir a snowball melts so that its surfnce area decreases at a rate of I cm/min, find the rate at which the diameter decreases whCn the diameter is 10 cm goire te cor 4The ogh of a recangle is increasang at a rate of 8 cms and h is acreag ar a rate of 3 cms When the length is 20 c and the width is 10 cm. bow fast is the arca of the 15. A street light is mounted at the top of a 15-ft-tall pole. A 1man 6 tall walks away from the pole with a speed of 5 ft/s along a straight path How fast is the tip of his shadow moving when he is 40 fi from the pole? 5. A rlindncal tank wth radius 5 m is being tilled with watcr a rate of 3 m n increasing How fast is the beight of the water The radius of a sphere is mereasing a a rate of 4 mnm/s How st is the volume increasing when the diameter is 80 mm? 16. At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 4:00 PM? radrus of a spherical ball is increasing at a rate of min Ar what rate is the surface area of the ball tsing when the radius is 8 cm? of a triangle with sides of lengths a and b and l angle & is 17. Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi /h. At what rate is the distance between the cars increasing two hours later? 18. A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s. how fast is the length of his shadow on the build- ing decreasing when he is 4 m from the building? A=ab sin Cm. b 3 cm, and 0 increases at a rate of in, how fast is the area increasing when ncreases at a rate of 1 5 cm/min md 10

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Expert Answer

Step 1

Given:

Two cars start moving from the point. One car travel towards south at 60 mi/h and another travel towards west at 25 mi/h.

Let x be the distance covered by the car that travel towards south and y be the distance covered by the car that travel towards west.

Then,

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Step 2

Sketch the given situation as shown below

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Step 3

Here z is the distance between the cars aft...

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