Question 1

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.) A)208 lb B)1040 lb C)104 lb D)520 lb

Accepted Answer

B

Question 2

Solve the initial-value problem.

Accepted Answer

The answer of Solve the initial-value problem. ...

Question 3

One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people. In an isolated town of  inhabitants,  people have a disease at the beginning of the week and  have it at the end of the week. How long does it take for  of the population to be infected?
A) 
B) 
C) 
D) 
E)

Accepted Answer

A

Question 4

A trough has vertical ends that are equilateral triangles with sides of length 2 ft. If the trough is filled with water to a depth of 1 ft, find the force exerted by the water on one end of the trough. Round to one decimal place. (The weight density of water is 62.4 lb/ft³.) A)31.2 lb B)62.4 lb C)12.0 lb D)6.0 lb

Accepted Answer

The answer of A trough has vertical ends that are...

Question 5

Find the centroid of the region bounded by the given curves. 
A) 
B) 
C) 
D) 
E)None of these

Accepted Answer

The answer of Find the centroid of the region bounded...

Question 6

A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane, the shallow end having a depth of  ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/  .)

Accepted Answer

The answer of A swimming pool is 10 ft wide...

Question 7

The Pacific halibut fishery has been modeled by the differential equation  where  is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be  and  per year. If  , find the biomass a year later.

Accepted Answer

The answer of The Pacific halibut fishery has been modeled...

Question 8

Find the solution of the differential equation  that satisfies the initial condition  .

Accepted Answer

The answer of Find the solution of the differential equation...

Question 9

Find the centroid of the region bounded by the graphs of the given equations. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the centroid of the region bounded...

Question 10

Solve the differential equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the differential equation. 
A) 
B) 
C)...

Question 11

Choose the differential equation corresponding to this direction field. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Choose the differential equation corresponding to this...

Question 12

A tank contains  L of brine with  kg of dissolved salt. Pure water enters the tank at a rate of  L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after  minutes?

Accepted Answer

The answer of A tank contains  L of brine...

Question 13

A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft³.) (ft) A)62.4 lb B)436.8 lb C)873.6 lb D)124.8 lb

Accepted Answer

The answer of A vertical plate is submerged in water...

Question 14

A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Let  denote the amount of new currency in circulation at time t with  . Formulate and solve a mathematical model in the form of an initial-value problem that represents the "flow" of the new currency into circulation (in billions per day).

Accepted Answer

The answer of A certain small country has $20 billion...

Question 15

The masses  are located at the point  . Find the moments  and  and the center of mass of the system.  ; 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The masses  are located at the...

Question 16

Solve the differential equation. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the differential equation. 
A) 
B) 
C)...

Question 17

Find the coordinates of the centroid for the region bounded by the curves  , x = 0,
and y =  .

Accepted Answer

The answer of Find the coordinates of the centroid for...

Question 18

Find the centroid of the region bounded by the given curves. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the centroid of the region bounded...

Question 19

Biologists stocked a lake with  fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be  . The number of fish tripled in the first year. Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.

Accepted Answer

The answer of Biologists stocked a lake with  fish...

Question 20

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.) A)332.8 lb B)1331.2 lb C)2662.4 lb D)665.6 lb

Accepted Answer

The answer of You are given the shape of the...

Quiz 7: Applications of Integration

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)

Solve the initial-value problem.

A trough has vertical ends that are equilateral triangles with sides of length 2 ft. If the trough is filled with water to a depth of 1 ft, find the force exerted by the water on one end of the trough. Round to one decimal place. (The weight density of water is 62.4 lb/ft³.)

Find the centroid of the region bounded by the given curves.

A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane, the shallow end having a depth of ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/ .)

The Pacific halibut fishery has been modeled by the differential equation where is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be and per year. If , find the biomass a year later.

Find the solution of the differential equation that satisfies the initial condition .

Find the centroid of the region bounded by the graphs of the given equations.

Solve the differential equation.

Choose the differential equation corresponding to this direction field.

A tank contains L of brine with kg of dissolved salt. Pure water enters the tank at a rate of L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after minutes?

A vertical plate is submerged in water (the surface of the water coincides with the x-axis) . Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft³.) (ft)

The masses are located at the point . Find the moments and and the center of mass of the system. ;

Solve the differential equation.

Find the coordinates of the centroid for the region bounded by the curves , x = 0, and y = .

Find the centroid of the region bounded by the given curves.

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)

Quiz 7: Applications of Integration

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)

Solve the initial-value problem.

A trough has vertical ends that are equilateral triangles with sides of length 2 ft. If the trough is filled with water to a depth of 1 ft, find the force exerted by the water on one end of the trough. Round to one decimal place. (The weight density of water is 62.4 lb/ft3.)

Find the centroid of the region bounded by the given curves.

A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane, the shallow end having a depth of ft and the deep end, 12 ft. If the pool is full of water, find the hydrostatic force on the shallow end. (Use the fact that water weighs 62.5 lb/ .)

The Pacific halibut fishery has been modeled by the differential equation where is the biomass (the total mass of the members of the population) in kilograms at time t (measured in years), the carrying capacity is estimated to be and per year. If , find the biomass a year later.

Find the solution of the differential equation that satisfies the initial condition .

Find the centroid of the region bounded by the graphs of the given equations.

Solve the differential equation.

Choose the differential equation corresponding to this direction field.

A tank contains L of brine with kg of dissolved salt. Pure water enters the tank at a rate of L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after minutes?

A vertical plate is submerged in water (the surface of the water coincides with the x-axis) . Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.) (ft)

The masses are located at the point . Find the moments and and the center of mass of the system. ;

Solve the differential equation.

Find the coordinates of the centroid for the region bounded by the curves , x = 0, and y = .

Find the centroid of the region bounded by the given curves.

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)

A trough has vertical ends that are equilateral triangles with sides of length 2 ft. If the trough is filled with water to a depth of 1 ft, find the force exerted by the water on one end of the trough. Round to one decimal place. (The weight density of water is 62.4 lb/ft³.)

A vertical plate is submerged in water (the surface of the water coincides with the x-axis) . Find the force exerted by the water on the plate. (The weight density of water is 62.4 lb/ft³.) (ft)

You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft³.)