1) The radius of a spherical balloon increases at a rate of 1 mm/sec. How fast is the surface 1) area increasing when the radius is 10mm? (Note: The surface area S of a sphere of radius r is S = 47r².) Enter just a real number (no approximations, no units or words). 2) Mr. Smith is 6 ft tall and walks at a constant rate of 2 ft/sec toward a street light that is 10 ft 2) above the ground. At what rate is the length of his shadow changing when he is 6 ft from the base of the pole that supports the light? Enter just an integer (no units). Solve the problem. 3) Given the revenue and cost functions R(x) = 34x - 0.7x2 and C(x) = 3x + 13, where x is the daily production, find the rate of change of profit with respect to time when x = 15 units and dx -= 4 units per day. dt B) $118.4/day C) $40/day D) $52/day 4) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at 3 m²/sec, how fast are the people moving when they are 3 m from the right angle? (Round A) $103/day approximations to two decimal places.) A) 3.00 m/sec B) 2.00 m/sec C) 0.50 m/sec 5) A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping at the constant rate of 4 ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 5 ft from the wall? A) 9.6 ft/s B) 10.4 ft/s C) 2.4 ft/s D) 0.80 ft/s D) 1.00 m/sec 3) 4) 5)
1) The radius of a spherical balloon increases at a rate of 1 mm/sec. How fast is the surface 1) area increasing when the radius is 10mm? (Note: The surface area S of a sphere of radius r is S = 47r².) Enter just a real number (no approximations, no units or words). 2) Mr. Smith is 6 ft tall and walks at a constant rate of 2 ft/sec toward a street light that is 10 ft 2) above the ground. At what rate is the length of his shadow changing when he is 6 ft from the base of the pole that supports the light? Enter just an integer (no units). Solve the problem. 3) Given the revenue and cost functions R(x) = 34x - 0.7x2 and C(x) = 3x + 13, where x is the daily production, find the rate of change of profit with respect to time when x = 15 units and dx -= 4 units per day. dt B) $118.4/day C) $40/day D) $52/day 4) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time, and walk at the same speed along different legs of the triangle while spraying the land. If the area covered is changing at 3 m²/sec, how fast are the people moving when they are 3 m from the right angle? (Round A) $103/day approximations to two decimal places.) A) 3.00 m/sec B) 2.00 m/sec C) 0.50 m/sec 5) A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping at the constant rate of 4 ft/s, how fast is the bottom of the ladder moving along the ground when the bottom is 5 ft from the wall? A) 9.6 ft/s B) 10.4 ft/s C) 2.4 ft/s D) 0.80 ft/s D) 1.00 m/sec 3) 4) 5)
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter65: Achievement Review—section Six
Section: Chapter Questions
Problem 57AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...
Related questions
Question
Need 9’10
![1)
1) The radius of a spherical balloon increases at a rate of 1 mm/sec. How fast is the surface
area increasing when the radius is 10mm? (Note: The surface area S of a sphere of radius r
is S = 47tr2.) Enter just a real number (no approximations, no units or words).
2)
2) Mr. Smith is 6 ft tall and walks at a constant rate of 2 ft/sec toward a street light that is 10 ft
above the ground. At what rate is the length of his shadow changing when he is 6 ft from
the base of the pole that supports the light? Enter just an integer (no units).
Solve the problem.
3) Given the revenue and cost functions R(x) = 34x - 0.7x2 and C(x) = 3x + 13, where x is the daily
production, find the rate of change of profit with respect to time when x = 15 units and
dx = 4 units per day.
dt
C) $40/day
D) $52/day
4) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time,
and walk at the same speed along different legs of the triangle while spraying the land. If the area
covered is changing at 3 m²/sec, how fast are the people moving when they are 3 m from the right
angle? (Round
A) $103/day
approximations to two decimal places.)
A) 3.00 m/sec
B) 2.00 m/sec
B) $118.4/day
C) 0.50 m/sec
5) A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping at
the constant rate of 4 ft/s, how fast is the bottom of the ladder moving along the ground when the
bottom is 5 ft from the wall?
A) 9.6 ft/s
B) 10.4 ft/s
C) 2.4 ft/s
D) 0.80 ft/s
Solve the problem. Round your answer, if appropriate.
6) One airplane is approaching an airport from the north at 151 km/hr. A second airplane approaches
from the east at 203 km/hr. Find the rate at which the distance between the planes changes when
the southbound plane is 26 km away from the airport and the westbound plane is 15 km from the
airport.
A) -232 km/hr
B)-116 km/hr
C) -464 km/hr
D) -348 km/hr
D) 1.00 m/sec
7) The radius of a right circular cylinder is increasing at the rate of 10 in./sec, while the height is
decreasing at the rate of 5 in./sec. At what rate is the volume of the cylinder changing when the
radius is 6 in. and the height is 12 in.?
D) 540 in.3/sec
A) 12607 in.3/sec
B) 540 in.3/sec
C) -210 in.3/sec
A)
8) The volume of a sphere is increasing at a rate of 2 cm³/sec. Find the rate of change of its surface
area when its volume is 2567 cm3. (Do not round your answer.)
3
cm²/sec
B) cm²/sec
C) 47 cm²/sec
3
D) 1 cm2/sec
9) Water is being drained from a container which has the shape of an inverted right circular cone. The
container has a radius of 3.00 inches at the top and a height of 5.00 inches. At the instant when the
water in the container is 3.00 inches deep, the surface level is falling at a rate of 1.7 in./sec. Find the
rate at which water is being drained from the container.
A) 22.4 in.3s
B) 25.0 in.3/s
C) 17.3 in.3/s
D) 16.5 in.3/s
C)
c) ft/sec
2
10) A man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 18 ft high. At what rate is the
length of his shadow changing when he is 30 ft away from the lamppost? (Do not round your
answer)
A) 3 ft/sec
B) ft/sec
D) 30 ft/sec
3)
4)
5)
6)
7)
8)
9)
10)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2189dbeb-fa6a-4493-ae73-344162cd8723%2F671e6eb1-ade5-4976-9894-51fc1382c349%2Fz4uf7wo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1)
1) The radius of a spherical balloon increases at a rate of 1 mm/sec. How fast is the surface
area increasing when the radius is 10mm? (Note: The surface area S of a sphere of radius r
is S = 47tr2.) Enter just a real number (no approximations, no units or words).
2)
2) Mr. Smith is 6 ft tall and walks at a constant rate of 2 ft/sec toward a street light that is 10 ft
above the ground. At what rate is the length of his shadow changing when he is 6 ft from
the base of the pole that supports the light? Enter just an integer (no units).
Solve the problem.
3) Given the revenue and cost functions R(x) = 34x - 0.7x2 and C(x) = 3x + 13, where x is the daily
production, find the rate of change of profit with respect to time when x = 15 units and
dx = 4 units per day.
dt
C) $40/day
D) $52/day
4) A piece of land is shaped like a right triangle. Two people start at the right angle at the same time,
and walk at the same speed along different legs of the triangle while spraying the land. If the area
covered is changing at 3 m²/sec, how fast are the people moving when they are 3 m from the right
angle? (Round
A) $103/day
approximations to two decimal places.)
A) 3.00 m/sec
B) 2.00 m/sec
B) $118.4/day
C) 0.50 m/sec
5) A ladder is slipping down a vertical wall. If the ladder is 13 ft long and the top of it is slipping at
the constant rate of 4 ft/s, how fast is the bottom of the ladder moving along the ground when the
bottom is 5 ft from the wall?
A) 9.6 ft/s
B) 10.4 ft/s
C) 2.4 ft/s
D) 0.80 ft/s
Solve the problem. Round your answer, if appropriate.
6) One airplane is approaching an airport from the north at 151 km/hr. A second airplane approaches
from the east at 203 km/hr. Find the rate at which the distance between the planes changes when
the southbound plane is 26 km away from the airport and the westbound plane is 15 km from the
airport.
A) -232 km/hr
B)-116 km/hr
C) -464 km/hr
D) -348 km/hr
D) 1.00 m/sec
7) The radius of a right circular cylinder is increasing at the rate of 10 in./sec, while the height is
decreasing at the rate of 5 in./sec. At what rate is the volume of the cylinder changing when the
radius is 6 in. and the height is 12 in.?
D) 540 in.3/sec
A) 12607 in.3/sec
B) 540 in.3/sec
C) -210 in.3/sec
A)
8) The volume of a sphere is increasing at a rate of 2 cm³/sec. Find the rate of change of its surface
area when its volume is 2567 cm3. (Do not round your answer.)
3
cm²/sec
B) cm²/sec
C) 47 cm²/sec
3
D) 1 cm2/sec
9) Water is being drained from a container which has the shape of an inverted right circular cone. The
container has a radius of 3.00 inches at the top and a height of 5.00 inches. At the instant when the
water in the container is 3.00 inches deep, the surface level is falling at a rate of 1.7 in./sec. Find the
rate at which water is being drained from the container.
A) 22.4 in.3s
B) 25.0 in.3/s
C) 17.3 in.3/s
D) 16.5 in.3/s
C)
c) ft/sec
2
10) A man 6 ft tall walks at a rate of 6 ft/sec away from a lamppost that is 18 ft high. At what rate is the
length of his shadow changing when he is 30 ft away from the lamppost? (Do not round your
answer)
A) 3 ft/sec
B) ft/sec
D) 30 ft/sec
3)
4)
5)
6)
7)
8)
9)
10)
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