39. Water flows into the tank at a rate of R L/min, is mixed instantaneously with the dye solution, and flows out through the bottom at the same rate R. Let c1 (t) be the dye concentration in the tank at time t. Tank 1 in Figure 5 is filled with Vị liters of water containing blue dye at an initial concentration of co g/L. dc, R V1 = 300 L, R = 50, and co = 10 g/L. (a) Explain why cj satisfies the differential equation dt (b) Solve for c1 (t) with V1 %3D %3D R(L/min) Tank I R (L/min) Tank 2 R (L/min) FIGURE 5

Q: 2. The rate at which a phase transformation proceeds depends on the time t and the dt transformed…

A: Rate of Phase transformation is gievn bydydt=4kt3(1-y)We need to find y as function of t.

Q: A stone is tossed vertically in the air from ground level with an initial velocity of 30 m/s. It's…

A:

Q: A stone is tossed vertically into the air from ground level with an initial velocity of 15 m/s. Its…

A: Given, A stone is tossed vertically into the air from ground level with an initial velocity of 15…

Q: A 100 gal-tank initially contains 50 gal of fresh water. At t = 0, a salt solution containing 1 Ib…

A: Given: A 100 gal-tank initially contains 50 gal of fresh water. At t=0, a salt solution containing 1…

Q: 17. The displacement (in meters) of a particle in motion is given by a= dt -t², where t is measured…

A: The displacement function is provided. And, we know that velocity is the derivative of time. So,…

Q: A tank has 25 liters of water in it at time t = 0 minutes. Water begins to be pumped into the tank…

A:

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given: Ah-area of hole, dVdt=-cAh2gh, where c is an impirical constant and radius of hole = 8 in. To…

Q: 39. The conical watering pail in Figure 17 has a grid of holes. Water flows out through the holes at…

A:

Q: The height (in centimeters) at time t (in seconds) of a small mass oscillating at the end of a…

A:

Q: A bug is moving along the right side of the parabola y = x^2 at a rate such that its distance from…

A: Let (x,y) be a point on the parabola y=x^2. Then (x,y)=(x,x^2).Let, distance from origin= p. Given,…

Q: 3. A lady 1.65 m tall walks towards a lamp post 2.65 m high at a speed of 1.5 m/s. How fast does her…

A:

Q: 9) A 120 V potential difference is applied to a space heater that dissipates 1000 W during…

A:

Q: a) A particle is moving along the curve y lIn x, in the upward direction and heading to the right.…

A:

Q: 1 6) The volume V of a right circular cone of radius r and height h is V =-ar²h. Suppose the radius…

A: We have to find the change in the volume of cone using total differential.

Q: The quantity of a substance can be modeled by the function N(t) that satisfies the differential…

A: We have to find the quantity of substance at t=1.8.

Q: Consider the ideal gas law PV = kT, where k > 0 is a constant. av a.) Determine the rate of change…

A:

Q: Water flows from an inverted conical tank with circular orifice at the rate dx *= -0.6zr*/29 where r…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Some diseases (such as typhoid fever) are spread largely by carriers, individuals who can transmit…

A:

Q: A cylindrical tank with radius 4 m is being filled with water at a rate of 2 m³/min. How fast is the…

A:

Q: A stone is tossed vertically into the air from ground level with an initial velocity of 15 m/s. Its…

A: Given :               h(t) = 15 - 4.9t2v(0) = 15 m/sAverage velocity = area under velocitytime…

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

A: Given: Let A is the area of a circle with radius r Then we have A = πr2

Q: EXAMPLE 5 In an oil refinery, a storage tank contains 2000 gal of gasoline that ini- tially has 100…

A:

Q: A type of sugar in the blood, also known as glucose, which is one of the major sources of energy, is…

A:

Q: A cylindrical tank initially contains 400 liters of fluid with 90 grams of salt dissolved in it.…

A:

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given- Suppose water is leaking from a tank through a circular hole of area Ah at its bottom. When…

Q: Suppose that a population grows according to the unlimited growth model described by the…

A: Question: Suppose that size of the population grows according to the unlimited growth model…

Q: A 3 kg mass is attached to a spring with stiffness k = 48N / m. The mass moves 1/2 m to the left of…

A: The equation can be given as; y" + (k/m)y =0,   The mass moves 1/2 m to the left of the equilibrium…

Q: 28. Water flows from an inverted conical tank with circular orifice at the rate dx -0.6r² /2g- dt…

A: Given, water flows from an inverted conical tank with circular orifice at the rate dxdt=-0.6πr22gxAx…

Q: The temperature (in degree Celsius) at a point (x, y) on a metal plate is given by a function T(x,…

A: T=Tx-yTyTo Find:a. Suppose T(4, 6)=320C and Tx(4, 6)=20C. Use the linearization of T at (4, 6)  to…

Q: 1. The surface area of a sphere of radius r is S = 4t r2 and the volume is V = ar. A spherical…

A: Given,

Q: í Cardiac output is the rate R of volume of blood pumped by the heart per unit time (in liters per…

A: Over a short time interval,c(t)is nearly constant. Rc(t) is the rate of volume of dye (amount of…

Q: dV = 0.6t · cos(0.08t² – 1) , where V(t) is in dt 10) The rate of change in the volume of a tank is…

A:

Q: A bar is insulated at end x =0, and open to the ambient temperature at end x =2L. There is a heat…

A: The solution to the above question is in the images below.

Q: 20 grams of salt are dissolved into a beaker containing 1 litre of certain chemical. The mass of…

A: The differential equation is dMdt+2M10-t+1=0. We need to prove that: M=11010-t20-t.

Q: A stone is tossed vertically into the air from ground level with an initial velocity of 15 m/s. Its…

A: We use the average velocity formula

Q: A stone is tossed vertically into the air from ground level with an initial velocity of 15 mis. Its…

A:

Q: A tank contains 90 kilograms of salt and 1000 liters of water. Pure water enters the tank at a rate…

A:

Q: 6- The dimension of a solid rectangular at given instant ( to ) are (L = 13 cm) ,(W = 9 cm ) and ( H…

A:

Q: A 5-m ladder leans against a wall. Assume the bottom slides away from the wall at a rate of 0.7 m/s.…

A: At t=0, x=1.5 m dxdt=0.7 m/s ∴xt=tdxdt+x0x2=2×0.7+1.5=>x2=2.9 m

Q: A 5,000-liter tank initially contains 1,100 liters of water with 1.2- kg of salt dissolved in it.…

A:

Q: A 5-m ladder leans against a wall. Assume the bottom slides away from the wall at a rate of 0.5 m/s.…

A:

Q: Find the amounts x1(t), x2(t), and x3(t) of salt at time t in the three brine tanks of Fig. 5.2.5…

A:

Q: 45. A cylindrical tank of radius R and length L lying horizontally as in Figure 21 is filled with…

A:

Q: 2. A honeybee population starts with 100 bees and increases at a rate of f'(t) bees per week. What…

A:

Q: 2. A particle moves in a circular orbit x² + y² = 16. As it passes through the point (2, 2/3 ), its…

A:

Q: 1) A particle moves along a line so that its velocity at time t is v(t)=t - 4t (measured in meters…

A:

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

A: a) Given A is the area of a circle of radius r A=πr2 Then, dAdt=2πrdrdt...(1)

Q: A stone is thrown into a body of still water and created ripples in the form of concentric circles.…

A:

Q: A cylindrical tank of height 13 metres is full of water at time t = 0 seconds. is turned on at the…

A:

Q: A model for the basal metabolism rate, In kcal/h, of a young man is R(t) = 95 - 0.18 cos where t is…

A: