4. p = pRT is the perfect gas equation where p is pressure, p is density T is temperature and R is constant. Solve for the rate of change in pressure if the rate of change in density and temperature are 12 and 5, respectively. (Disregard the units)

Q: f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph are…

A:

Q: Suppose x and y are functions of third variable t. In the equation x+y=45, what are the values of…

A: The given equation is: x2+y2=45   .....(1) When x = 3, 32+y2=45y2=45-9y2=36y=±6

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: How do you solve question 3?

A:

Q: The Ideal Gas Law is PV = mRT where P is the pressure, V is the volume, m is the constant mass, R is…

A:

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

A:

Q: If the brakes on a car give the car a constant negative acceleration of 2k m/s?, where k is a…

A: The given question has been solved in detail.

Q: A 50 – gallon tank of pure water has a brine mixture with concentration of 2 pounds per gallon…

A: Form the first order differential equation then find its solution to get amount of salt at any time…

Q: Suppose x and y are functions of third variable t. In the equation x2+y²=45, what are the values of…

A: This question is related to application of derivatives.

Q: 7. A 6ft tall human is walking away from a 20ft lamppost. Given that the length of the shadow of the…

A: Let the distance of the person from the bottom of the light post be x. Let the length of the shadow…

Q: A substance cools in moving air at a rate proportional to the difference between the temperature of…

A:

Q: 15 Suppose that y is directly proportional to x. When x = 8, y = 4. Find y when x = 30. %3D

A:

Q: 8. Given that y=/2x +7 and y is increasing at a rate of 5 units s. Find the rate of change in X,…

A:

Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°,…

A:

Q: 1 If a spherical drop of liquid evaporates at a rate proportional to its area, if initially its…

A: Let the surface area be A So rate of evaporates is dA/dt, According to the question, dVdtαAdVdt=-kA…

Q: Suppose y varies at a constant rate of change of 4 with respect to x (so that Δy=4⋅Δx ), and when…

A: topic - linear equation in two variables

Q: 2. A street lamp is 5m tall and located 6m from a brick wall. A person who is 2m tall walks away…

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given that,  At time, t=0, the amount of cane sugar in water =75kg At time, t=30minutes, the amount…

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A:

Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

Q: If the demand for q units of a product priced at $p per unit is described by the equation 200 V29 +…

A:

Q: 8. An express train reducing its velocity to 40 km./h. , has to apply the brakes for 50 sec. . If…

A: Given that  Velocity of express train =40km/hr  Breaks apply at 50sec Retardation =0.5m/sec^2 To…

Q: Suppose the constant rate of change y with respect to x is -2.5 and we know that y=-6.75 when x=1.5…

A: Given,The constant rate of change of y with respect to x = -2.5.We know that,Slope = rate of change…

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: This question can be solved using the concept of rate of change of physical quantities.

Q: Suppose x and y are functions of third variable t. In the equation +y²=45, what are the values of…

A: First we will differentiate the given equation with respect to t using the chain rule of…

Q: What will be the rate of change of the surface of the sphere when the radius of the sphere is 5.00…

A: Given; Radius= 5cm And time rate of change in Radius is= π/2.

Q: The length l of a rectangle is decreasing at a rate of 2 cm divided by sec while the width w is…

A: Given,           dldt=-2cm/s           dwdt=+2cm/s(a) Area, A=lw              dAdt=ddt(lw)…

Q: (4) The temperature at a point (x, y) is given by T(x, y) = xy + x². (a) (2, –1)? What is the rate…

A: (1) The rate of change in temperature can be determined by finding the gradient,…

Q: b) Suppose a ball is thrown downward with a speed of 8 meters per second from a height of 75 meters.…

A: Given: Suppose a ball is thrown downward with a speed of 8 meters per second from a height of 75…

Q: A point moves along the curve y = x ^ 3−3x + 5 so that x = 1/2√t + 3, where t is time. At what rate…

A: Given- y=x3-3x+5 and x=12t+3 To find- The rate of changing when t=4. Concept Used- dydt=dydx·dxdt

Q: At time t = 0, Car A passes through an intersection and goes east at a speed of 40 feet per second.…

A:

Q: If the brakes on a car can give the car a constant negative acceleration of 2k m/2, where k is a…

A: Use simple velocity, distance, acceleration formula.

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: 1. Suppose the length of the diagonal of a square is increasing at the rate of 2 inches per second.…

A:

Q: 6. Train E travels west toward Chicago station at 120 miles per hour while a second train N travels…

A: Train E =120 miles per hour  Train N=90 miles per hour

Q: What is the rate of change of y with respect to x for 9x-11y+2=0

A: Given that 9x-11y+2=0 We need to find the rate of change of y with respect to x that is dy/dx.

Q: here is a constant inflow of a liquid into a conical vessel 15 feet deep and 7.5 feet in diameter at…

A: The height of the conical vessel h = 15 feet.  Diameter of the lop d = 7.5 feet,  The radius of the…

Q: Suppose x and y are functions of third variable t. In the equation +y=45, what are the values of the…

A:

Q: Suppose a and y are related by a constant rate of change Ay and = 2, and y 4 when x = 3. Ax

A: Suppose x and y are related to the constant rate of change and ∆y∆x=2and y = 4 when x= 3

Q: Suppose yy varies at a constant rate of change of -0.6 with respect to xx (so that…

A:

Q: A body weighing 64 Ib is dropped from a height of 100 ft with an initial velocity of 10 ft/sec.…

A:

Q: For the given curve y = 5x – 2x', when x increases at the rate of 2 units / sec, then how fast is…

A:

Q: Suppose that a rocket is launched vertically and it is known that the exaust gases are emitted at a…

A: Given Constant Velocity u=19.5 m/sInitial mass mo=0.7kgGravity g=9.81 ms-2Time t=0.3 second,…

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

A:

Q: 4. A lizard accelerates from 2 m/s to 10 m/s in 4 seconds. What is the lizard's average…

A: Given: a) A lizard accelerates from 2 m/s to 10m/s in 4 seconds. What is lizards average…

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A:

Q: Suppose the cost incurred in operating a cruise ship per hour is a+bv^33 dollars, where a and b are…

A: ANSWER :

Q: If the rate of change of y with respect to x is equals to 2-y and y=8 and x=0. Find y when x=ln(2).

A: Given: The rate of change of y with respect to x  is equal to 2-y. That is, dydx=2-y

Q: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

A: Given: A solution with 35% ammonia is added at a rate of 5 liters per minute to a vat that initially…

Q: 1. After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is…

A: