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Calc 1 2.7

 

<== Calculus 1
Number Question Answer
See the work

1.

 

 

Suppose xy=-3 and dy/dt=1. Find dx/dt when x=-4

dx/dt=______

 

dx/dt= 16/3

 

The work

Point Cost: 3

 

2.

 

 

Suppose that x= x(t) and y=y(t) are both functions of t.
If
y=6x^(.5)+3,
and dx/dt=6 when x=9, what is dy/dt?

 

dy/dt= 6

 

The work

Point Cost: 2

3.

 

 

Suppose that x= x(t) and y=y(t) are both functions of t.
If
x^2+y^2=26
and dx/dt=-1 when x=1 and y=5, what is dy/dt?

 

dy/dt= 0.2

 

The work

Point Cost: 2

4.

 

 

Suppose that x= x(t) and y=y(t) are both functions of t.
If
y^2+x=8,
and dy/dt=-4 when x=-1 and y=-3, what is dx/dt?

 

dx/dt= -24

 

The work

Point Cost: 2

 

5.

 

 

Suppose that x= x(t) and y=y(t) are both functions of t.

If
y^2+xy-3x=1,
and dy/dt=4 when x=3 and y=2, what is dx/dt?

 

dx/dt= 28

 

The work

Point Cost: 3

 

6.

 

 

 

A particle is moving along the curve
 y=5sqrt(2x+3).
As the particle passes through the point (3,15), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this instant.

 

9.15208630644859

 

The work

Point Cost: 3

7.

 

 

 

The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the volume changing when the radius is 14 centimeters?
The volume of a sphere is given by V= (4/3)πr^3.
Rate of change of volume=____

 

Change of volume= 4926.01728083      

 

The work

Point Cost: 2

 

8.

 

 

 

Helium is pumped into a spherical balloon at a rate of 4 cubic feet per second. How fast is the radius increasing after 2 minutes?
The volume of a sphere is given by V=(4/3)πr^3.
Rate of change of radius=_______ (feet per second)

 

change of R= 0.0134921670167 ft/sec

 

The work

Point Cost: 3

 

9.

 

 

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 16cm.

 

160.84954368

 

The work

Point Cost: 2

 

10.

 

 

At noon, ship A is 20 nautical miles due west of ship B. Ship A is sailing west at 23 knots and ship B is sailing north at 15 knots. How fast (in knots) is the distance between the ships changing at 5 PM?

 

27.3902613184749 knots

 

The work

Point Cost: 4

 

11.

 

 

 

A street light is at the top of a 12 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole?

 

12

 

The work

Point Cost: 4

12.

 

 

 

 

The altitude of a triangle is increasing at a rate of 2.500 centimeters/minute while the area of the triangle is increasing at a rate of 4.000 square centimeters/minute. At what rate is the base of the triangle changing when the altitude is 11.000 centimeters and the area is 88.000 square centimeters?

 

-2.90909090909091

 

The work

Point Cost: 3

 

13.

 

 

 

A boat is pulled into a dock by a rope attached 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. If the rope is pulled in at a rate of 1 m/s, how fast is the boat approaching the dock when it is 8 m from the dock? Rate=_____

 

Rate= 1.00778221853732

 

The work

Point Cost: 4

 

14.

 

 

 

 

Water is leaking out of an inverted conical tank at a rate of 2500.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top is 4.0 meters. If the water level is rising at a rate of 27.0 centimeters per minute when the height of the water is 5.0 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.____

 

379491.112
The work

Point Cost: 4

15.

 

 

 

Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 12 feet high?

 

0.26525823
The work

Point Cost: 4

16.

 

 

 

 

When air expands adiabatically its pressure P and volume V are related by the equation PV^(1.4)=C where C is a constant. Suppose that at a certain instant the volume is 700 cubic centimeters and the pressure is 79 kPa and is decreasing at a rateof 7 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

 

44.3038
The work

Point Cost: 3

17.

 

 

 

A plane flying with a constant speed of 14 km/min passes over a ground radar station at an altitude of 7 km and climbs at an angle of 20 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 4 minutes later?

 

13.9120131086325
The work

Point Cost: 5