Estimate how fast the total force on the dam is increasing at t = 2 days.

Q: Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x…

A: Given Data The length of the rectangle is y=9 ft. The width of the rectangle is x=7 ft. The rate of…

Q: A tank initially holds 100 gallons of a brine solution containing 20 lb of salt. At t = 0, fresh…

A:

Q: 2. Oil leaks from a damaged, stationary oil tanker at the rate of 30 m3/hr, forming a circular oil…

A: The instantaneous rate of change is the differential of the variable. The rate of change of one…

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 60cm³/s. How…

A: To find the rate at which surface area is changing

Q: An object with an initial velocity of – 85 m/s undergoes an acceleration of a(t) = 6t + 18 m/s“, t…

A: Given, v=-85 at t=0. a=6t+18

Q: The volume of a cylinder of height 12 inches and radius r inches is given by the formula V = 12². dV…

A: Given query is to find rate of change of volume.

Q: dA dr in terms of dt (a) If A is the area of a circle with radius r and the circle expands as time…

A:

Q: (85 pts) 1. The length of a rectangle is decreasing at a rate of 8 cm/sec and its area is increasing…

A:

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the…

A: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the…

Q: The volume of a cylinder of height 12 inches and radius r inches is given by the formula 12πr. V dV…

A:

Q: Air is being pumped out of a spherical balloon at the rate of 25 cm3/s. How fast is the radius…

A:

Q: The length, x, of the edge of a cube is increasing. (a) Write the chain rule fordV/dt, the time rate…

A: The length, x, of the edge of a cube is increasing. a). Consider the volume of a cube, V=x3…

Q: Assume that the radius r of the cylinder below is decreasing at a rate of 2 m/s, and that its height…

A:

Q: The cumulative number of jobs outsourced overseas by U.S.-based multinational companies in year t…

A:

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm3/s. How…

A: Air is being pumped into a spherical balloon so that its volume increases at a rate of 80cm3/s. To…

Q: Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile…

A: Given Information - Rate at which the gravel is being dumped = 10 ft3/min the pile is in shape of a…

Q: A ball is being inflated such that the volume is increasing at a constant rate of 100cm3/s How fast…

A: Given  and

Q: 4. A ladder 25 feet long is leaning against a vertical wall. The base of the ladder slides away from…

A:

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

A:

Q: Let l be the length of a diagonal of a rectangle whose sides have lengths a and y, and assume that a…

A: let l be the diagonal of a rectangle and x and y are the length and breadth of a rectangle  as we…

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

A:

Q: Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile…

A: The rate of change of volume with respect to time is 50 ft3/min, that is, dVdt=50 ft3/min. Since the…

Q: A tank initially holds 10 gal of fresh water. at t=0, a brine solution containing 1/2 lb of salt per…

A:

Q: Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile…

A: Here given , h=18 feet

Q: (a) If A is the area of a circle with radius r and the circle expands as time passes, find in terms…

A:

Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

A:

Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A: Here, given that the volume is constant. So, dVdt=0⇒ddtπr2h=0⇒πh 2rdrdt+r2dhdt=0⇒h 2rdrdt+r2dhdt=0…

Q: Suppose you hang a bucket from a spring that stretches it 15 mm from its natural length. You then…

A: Given:The difference in spring length when the bucket is attached = 15 mmData of length of spring…

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 70cm³ /s. How…

A: Volume of the sphere , V =43πr3 ; where , 'r' is the radius of the sphere. Surface Area of the…

Q: The altitude h [ft] attained by an aircraft climbing from sea level at its maximum rate of climb…

A: The complete solutions are given below

Q: * A 5 m pole, leaning against a wall s1ips in such a way that its base is vdun moving away from the…

A:

Q: Sand is leaking from a bag in such a way that after t seconds, there are S(t) = 50 (1 − t 2 15 ) 3…

A: Put t=0 for amount of sand originally than take derivative at t=1 to get rate of leaking of sand.

Q: dr dA in terms of dt (a) If A is the area of a circle with radius r and the circle expands as time…

A:

Q: 3. A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At…

A: Diagonal of Square = √2 * Side Perimeter of Square = 4* Side Area of Square = (Side)^ 2

Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile…

A: Given that  Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute.  It…

Q: A cancer tissue is in the shape of a sphere whose radius is increasing at the rate of 2 mm per day.…

A: we know that surface area of sphere is S=4πr2   As per our guideline, we supposed to answer only the…

Q: The following table shows the rate of water flow (in L/min) through a dam. t (min) 1 5 9. 13 17 21…

A:

Q: If water is being drained from a swimming pool and V(t) liters is the volume of water in the pool t…

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Q: The rate (in liters per minute) at which water drains from a tank is recorded at half-minute…

A:

Q: The volume of a cylinder of height 12 inches and radius 7 inches is given by the formula V = 12π².…

A: We have to slove the derivative

Q: The table below gives the result of an observation, is the observed temperature in degrees…

A: We have to solve the given problem by Newton's forward differential equation.

Q: l edges of a cube are expanding at a rate of 4 centimeters per second. (a) How fast is the surface…

A:

Q: Sand is dumped in such a way that the shape of the sand pile is always a cone with its height, h…

A: Let, h be the height of the cone, r be the radius of the cone. Also, the sand is dumped at a…

Q: The following table shows the rate of water flow (in L/min) through a dam. t (min) V'(t) (L/min) 1 3…

A: We will use the following Simpson's rule for n=6 ∫113vdt=h3[(v0+v6)+4(v1+v3+v5)+2(v2+v4)] here…

Q: The volume of a cylinder of height 12 inches and radius 7 inches is given by the formula V = 12π².…

A:

Q: If a tank holds 3000 gallons of water, which drains from the bottom of the tank in 20 minutes, then…

A:

Q: 6. At noon, ship A is 150 km west of ship B. Ship A is sailing east at 40 km/hr and ship B is…

A: Given query is to find the rate of change of distance.

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 40 m s1. How…

A:

Q: How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the rate…

A:

Q: A rectangle is growing such that the length of a rectangle is 5t + 4 and its height is t, where t is…

A: Given:- A rectangle is growing such that the length of a rectangle is 5t + 4 and its height is t4 ,…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.