When air expands adiabatically (without gaining or losing heat), its pre and volume V are related by the equation PV 14 = C where C is a consta uppose that at a certain instant the volume is 390 cubic centimeters and the essure is 85 kPa and is decreasing at a rate of 15 kPa/minute. At what rate i bic centimeters per minute is the volume increasing at this instant?

Q: 1. The side of a cube decreases at a rate of 2.5m/s. Find the rate at which the surfacearea…

A:

Q: We found that salt is added to the tank at a constant rate and it is removed from the tank at a rate…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

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

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

A: given that pressure and volume are related by the equation PV1.4=C and a certain instant of time…

Q: 4. The area of a semicircle is given by A = 0.5r, where r is the radius in inches. The semicircle,…

A: We need to find rate of change.

Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

A:

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

A:

Q: A 80-kg cyclist on a 19-kg bicycle starts coasting on level ground at 30 m/sec. Use v = vo e (-k/m)t…

A:

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A:

Q: The pressure in newtons per square meter (N/m²) of a gas in a cylinder is given by P = 307 - with…

A: Here we use the derivative the both parts.

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

A: Here volume of the prism will be V=lbh So the change in volume in time t will be given by…

Q: 1. How fast is the volume of a cube changing when the edge is 15 cm if the edge is changing at the…

A:

Q: A culture initially has P number of bacteria. At t = 3hour the number of bacteria is measured to be…

A:

Q: A right trianglewith dimensions of X = 3 cm and y =4cm.if Cx) is increasing at arate of 2 cml sec…

A: We will find the rate of change in z

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

A: Given expression is PV1.4=C   ......1 Where P is pressure, V is volume and C is constant.  Pressure…

Q: Because a new employee must learn an assigned task, production will increase with time. Suppose that…

A: To find the number of units completed in t hours by the new employee, integrate the rate of…

Q: A population of bacteria is growing according to the equation P(t) = 1800e.16t. Estimate when the…

A: A population of bacteria growing according to the equation Pt=1800e0.16t.

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

A:

Q: A tank contains 10m^3 of free water, brine having a concentration of 15kgsalt/m^3 is sent into the…

A:

Q: a cylindrical tank is filled with 31.4 m3 of water at t = 0. The radius of the tank is 1 m and its…

A: Given that, the volume of the cylindrical tank is 31.4 m3 Radius of the tank =1 m Height = 10 m

Q: If the radius r of a sphere is expanding at a rate of 15 cm/min, find the rate at which the volume…

A: We have given radius of a sphere is expanding at a rate of 15 cm/min. So drdt=15 cm/min As Volume of…

Q: (c) Suppose instead that we have a rectangular tank containing the same volume of water (pictured…

A: c Volume of cube =8m×1.5m×3m=36m3 volume of water =12×3×3×8=36m3 Volume of water is equal to volume…

Q: Q2 The rate of heat transfer of a body can be express as: dT -k(T – Ta) dt where T= temperature of…

A:

Q: b) The mass (in kg) of a product from a chemical reaction is denoted by 'y'. The dy rate at which…

A: b Separate the terms of both the variables Then let 1+y2=z2ydy=dzand 1+t2=u22tdt=2udu

Q: The volume of a cube decreases at the rate of 74 m³/ sec. The rate at which the side of the cube…

A:

Q: Jim is driving at a constant 75.0 mi/hr (33.5 m/s) along a straight section of Route 3 North. The…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.15 m/s . At the moment when the…

A: Solve for the length of ladder

Q: A traffic engineer monitors the rate at which cars enter a freeway during rush hour. From the data…

A:

Q: Solve parts a,b, and c.

A: Here we need to apply some basic concepts of derivatives to find the answers

Q: Solve the following problems completely. A solid cylindrical cord of elastic material has length 32…

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

Q: The air in a small room 12 ft by 8 ft by 8 ft is 5% carbon monoxide. Starting at t = 0, fresh air…

A: Let v(t) be the volume of CO in the room at time t, and let V be the total volume of the room.The…

Q: Q2 The rate of heat transfer of a body can be express as: dT = -k(T – Ta) dt where T= temperature of…

A: Using Euler's method we can find the solution, the initial values are t0 = 0 and T0 = 90°C The…

Q: The radius r and height h of a cylinder are changing with time. At the instant in question, r = 4…

A: Given problem:- The radius r and height h of a cylinder are changing with time. At the instant in…

Q: The kinetic energy K of a mass is proportional to the square of its velocity y. If K = 12,960 joules…

A: To determine the kinetic energy.

Q: The volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t =…

A: Given that the volume of sphere is increasing at a rate proportional to the reciprocal of its…

Q: The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of…

A: Here we will use the chain rule i.e., if u and v are function of t with f=uv then…

Q: A tank holds 59 gallons of water. Initially, at t=0, a solution containing 1/8 lb/gal of a chemical…

A: This is a mixing problem and at any time the amount of salt in in tank is (total salt in - total…

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 velocity function of a particle moving along a horizontal line is given by v(t) = ln 2 · 23t,…

A: The Velocity function of the particle moving along a horizontal line is given by v(t)=ln2·23t…

Q: A cement mixer is pouring concrete in a conical pile. At the time when the height and base radius of…

A:

Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

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:

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

A:

Q: A pitcher of buttermilk initially at 27°C is to be cooled by settling in on a place where the…

A: At time t=0 minutes, temperature of buttermilk = 270C   At time t=20 minutes, temperature of…

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

A:

Q: 28. The volume of a cone of radius r and height h is given by V=1/3 ttr^2 h. If the radius and the…

A: