n air expands adiabatically (without gaining or losing heat), its pressure Pand volume V are related by the equation PV4 - C, where Cis a constant. Suppose that at a certain instant the volume is 600 cm and the pressure is 80 kPa and is decreasing at a rate of 10 kPa/min. At w is the volume increasing at this instant? (Round your answer to the nearest whole number.) cm?/min

Q: There was a girl in a class studying math with, of course, a math teacher. This girl's name is…

A: Given query is to find the amount converted in two hours.

Q: A tank initially contains 100 gal of pure water. Starting at time t = 0, a brine containing 6lb of…

A: Given: Let us consider a tank holds 100 gallons of pure water at first. A brine containing 6lb of…

Q: le's Law states that when a sample of gas is compressed at a constant temperature, the pressure P…

A:

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

A: We have to find amount and concentration.

Q: 2. The edge of a cube decreases at a rate of 2.5m/s. Find the rate at which the surface area…

A: Application of derivatives.

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A:

Q: Suppose that z = x*y°, where both x and y are changing with time. At a certain instant when x = 1…

A: For the solution of the problem follow the next step.

Q: A boatman is at A which is 4.5 km from the nearest point B on a straight shore BM. He wishes to…

A: topic - application of derivatives

Q: 16.Suppose that the dimensions of a cylinder change at constant rates: the radius of the base is…

A: Use the derivative and substitute the given values.

Q: A rectangular prism with dimensions 6 m x 4 m x 8 m (l x w x h) is shrinking. 8 m 4 m 6 m Answer the…

A:

Q: A 20 m tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: In this question, we find the amount of solt when the takl half full. given that  Initial amount of…

Q: A ball is thrown vertically upward with an initial velocity 15 m/s from an          initial height…

A: Use the kinematics equation to solve the problem and at the highest position the final velocity will…

Q: A cylindrical column is (3m) high and (0.2m) radius, if the radius of the column increases at a rate…

A:

Q: A tank initially holds 80 gal of a brine solution containing - Ib of salt per gallon. At t = 0,…

A: Since you posted a question with multiple parts, we will solve the first three subparts for you. To…

Q: 4. A conical-shaped reservoir has a depth of 20 feet and a radius of 10 feet. Water is leaking out…

A: Given: Depth of the conical reservoir, h = 20 feet Radius of the conical reservoir, r = 10 feet…

Q: 8. The spherical balloon is inflating at the rate of 12,000 cm³/min. How fast is its radius changing…

A: Let  V be the volume of a spherical balloon with radius r at any time tGiven: dVdt=12,000 cm3/min…

Q: a) When a gold plate is heated in order to melt it, initially its area increases at the rate of 67…

A:

Q: 4. A man is walking beside a 30-m street lamp. After walking 25 m away from the street lamp, he sunk…

A: As per our guidelines we can solve only one question at a time. Please repost unsolved question…

Q: 1. A cylindrical tank with radius 5 meters is being filled with water at a rate of 3 m? /min. How…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q: Suppose we have a rectangular aquarium with dimensions of length 8m, width 4m and height 3m.…

A: we are given for rectangular aquarium length l=8 m width w=4 m height h=3 m dVdt=0.4m3/sec

Q: 9) A spherical snowball is melting in such a way that its volume is decreasing at a rate of 3cm /…

A: Let, r=radius  V=volume Given that dV/dt= 3 , we have to find dr/dt=? at r=12 cm Volume and radius…

Q: 5) Suppose a liquid is to be cleared of sediment by pouring it through a cone-shaped filter. Assume…

A:

Q: A triangle with constant base b and height h is changing with time where h(t) = 2t – 3. What is the…

A:

Q: Q-4-A leak in a spherical balloon filled with gas allows the gas to leak at a rate of 3.5 m³ /min .…

A: Given that,       a leak in a spherical balloon filled with gas allows the gas to leak at a rate of…

Q: 1. We are inflating a spherical balloon. At what rate is the volume of the balloon changing when the…

A: Since you have asked multiple question (1&2) we will solve the first question for you. . If you…

Q: The volume, Vm³, of liquid in a container is given by V = (3h² + 4) ³ - 8, where h m is the depth of…

A: Solution

Q: 7. A conical pile is formed by pouring sand at a rate of 30 cm/s. When its base diameter and…

A:

Q: 3. The radius of a cylinder is increasing at a rate of 4cm/sec. The surface area remains constant at…

A: Given

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: 20. The length of a rectangle is increasing at a rate of 5 cm/sec and the width is decreasing at a…

A:

Q: 1. A cylindrical tube expands as its radius r and height h increase at the rate of 2 in/min and 4…

A:

Q: 10. A cylinder is being filled such that the height of its contents is increasing at a rate of 5 cm…

A: Rate of change of height = 5 cm/s Volume, V = πr2h Radius, r = 3

Q: ssume that water is being purified by causing it to flow through a conical filter that has a height…

A: The diagram of a conical filter with given conditions is shown below. From, the figure,…

Q: 3. The radius of a large sphere is increasing at the rate of 8m/ sec. At what rate is the sphere…

A:

Q: A tank initially holds 80 gal of a brine solution containing - Ib of salt per gallon. At t = = 0,…

A: Since you posted a question with multiple parts, we will solve the first three subparts for you. To…

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

A:

Q: A boatman is at A, which is 4.5 km from the nearest point B on a straight shore BM. He wishes to…

A: The given problem is solved below in detail.

Q: A tank initially contains 50 gal of sugar water having a concentration of 2 lb of sugar for each gal…

A: Given:   A tank initially contains 50 gal of sugar water having a concentration of 2 lb of sugar for…

Q: 4. Water is running out of a conical tank 3 m across the top and 4 m deep at the rate of 2 m3 /min.…

A: given  h = 4 m  (Note: measurement of h is always taken from bottom) r = (3 ÷ 2 ) = 1.5 m dVdt = 2…

Q: 3) Water is running from a vertical cylindrical tank 3 m in diameter at the rate of 3ayh , where h…

A: Given, Diameter of the cylindrical tank=3m Radius of the cylindrical tank, r=32=1.5m Volume of the…

Q: A tank initially holds 100 gallons of a brine solution containing 1 1b. of salt. At t = 0 another…

A:

Q: Find the rate of bubble volume increasing when the radus is 4cm if its surface area is increasing at…

A: Given: dSdt=4  cm/secdVdt|r=4 cm=?

Q: When air expands adiabatically (without gaining or losing heat), its pressure Pand volume V are…

A: We have to find the rate at which volume is increasing. We will use product rule of differentiation…

Q: A boatman is at A, which is 4.5 km from the nearest point B on a straight shore BM. He wishes to…

A:

Q: A tank initially holds 10 gal of fresh water. At t = 0, a brine solution containing ¼pounds of salt…

A: Given that , Initially fresh water in tank = 10 gal At t=0 , the solution containing 14 pounds of…

Q: A 14-foot ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate…

A:

Q: When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are…

A: Let's find rate of the increasing the  volume.

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

A:

Q: A ladder 5 m long rests against a vertical wall. If the top of the ladder slides down the wall at a…

A: Given,    Ladder is 5m long.    Therefore,  At any instant    x² + y²= 5² = 25   When y = 4, then x…

Q: A 20 m³ tank is full of brine with 40 kg of dissolved salt. Pure water enters the tank at a rate of…

A: The  given problem we can be formulated as  a differential equation and solve.