a 1000-liter (L) tank contains 500 L of w. ater with a salt concentration of 10 g/L. Water with a saltconcentration of 50 g/L flows into the tank at a rate of Rin= 80 L/minutes (min). The fluid mixes instantaneously and ispumped out at a specified rate Rout. Let y(t) denote the quantity of salt in the tank at time. Assume that Rout = 40 L/min.(a) Set up and solve the differential equation for y(t).(b) What is the salt concentration when the tank overflows?

Q: The surface area of a sphere, initially zero, increases uniformly at the rate of 4 xq.in. per sec…

A:

Q: Given that x and y are functions of time, find the indicated rate of change. dy when x 1, y=2, and…

A:

Q: The edge of a cube was found to be 20 cm with a possible error in measurement of 0.2 cm. Use…

A: As we know that; The expression for the volume of the cube is: V=a3    ....(1) Where a is the edge…

Q: Find the total differential. z = e-X tan(y)

A: Given, fx=z=e-xtany To find fx=z

Q: The radius and height of a right circular cone are measured with errors of at most 1% and 4%,…

A:

Q: dx 3. J TxVx-1

A: the given integral is: ∫dxxx-1 we have to evaluate the given integral.

Q: Use the differential dV to estimate the change in volume of a sphere when the radius changes from 9…

A: ddxxn=n xn-1

Q: Find the total differential, given: (b) \theta = arctan (y/x)

A: Let us consider the function z=f(x,y)  The partials derivative are obtained as…

Q: Find the total charge on the curve y = x43 for 8 < x< 27 (in centimeters) assuming a charge density…

A:

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A:

Q: Determine the average rate of change of the function y = sinx from X = 0 to x = 2 O1 2

A: The average rate of change of the function f(x) can be calculated using the formula Average rate of…

Q: The edge of a cube was found to be 107 cm with a possible error in measurement of 0.03 cm. Use…

A:

Q: A cylinder object has radius 2 cm and height 3 cm. Use differentials to approximate the error…

A:

Q: The length and width of a rectangle are measured with errors of at most 3% and 5%, respectively. Use…

A: Let the length and width of a rectangle are L and W respectively. Now, The length and width of a…

Q: The forces of the human gastrocnemius tendon during traction and during recoil can be approximated…

A:

Q: O Use differentials to approximate the increase in the area of a soap bubble when its volume…

A: Given query is to find approximate are increased.

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.l cm. Use…

A: Let the edge of the cube be x= 30cm And given error in measurement of edge dx= 0.1cm a) Volume of…

Q: 1 find the total differential dz. axeta TU

A: Find dz

Q: Recall that the volume of a right circular cylinder of radius r and height h is V = r’h. Suppose…

A:

Q: What is the average rate of change of the function g(t) over the interval from t = a to t = b? How…

A: The average rate of change of the function g(t) over the interval from t = a to t = b is given by:…

Q: Use differentials to estimate the relative error in the lateral surface area of a right circular…

A: Relative error

Q: A spherical ball is measured to have a radius of 6 cm with a possible measurement error of ±0.1rmcm.…

A:

Q: Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. a. Use…

A: The measurement of the side length is accurate to within 0.1 cm. Therefore,  -0.1≤dx≤0.1  The volume…

Q: Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. Use…

A:

Q: The diameter of a spherical ball bearing was measured to be 7.8 mm with a possible error of 0.07 mm.…

A:

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A:

Q: 8. Use differentials to approximate the change in the volume of a cylinder if the height is…

A: Let's find.

Q: 2 Evaluate the inteyral. dx dy dz taken. throughout the volumeofsphere 23=

A: We have to solve given integral:

Q: The dimensions of a closed rectangular box are measured as 97 cm, 60 cm, and 30 cm, respectively,…

A: Let the dimensions of the box be l, w and h (for length, width and height).Surface area of the box…

Q: Find the total differential. z = 10x8y6 dz =

A: GIVEN: z = 10x8y6

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: Solution.

Q: A certain close box having a square base has a volume of 100 in^3. Compute the rate of change of its…

A: Given is a box

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of.1 cm. Use…

A: Consider the edge length of the cube is a , so the volume of the cube is: V=a3 The surface area of…

Q: The volume of a right circular cylinder of radius X and height y is given by V= TXy, Suppose that…

A: Given Information : The volume of a right circular cylinder of radius x and height y is given by V =…

Q: The dimensions of a closed rectangular box are measured as 88 cm, 53 cm, and 32 cm, respectively,…

A: Given: The dimensions of closed rectangular box is : =88cm×53cm×32cm

Q: THE AREA BETWEEN THE CURVES 4 y = x²³² AND y ²³ = 4X IS REVOLED 2 ABOUT THE LINE X= -1. SOLVE FOR…

A:

Q: For the volume or a cylinder V = RR*H Find the total differential dV

A:

Q: The dimensions of a closed rectangular box are measured as 74 cm, 51 cm, and 50 cm, respectively,…

A: For a function y=fx, ∂y,∂x,dy and dx represents partial derivative of y and x and then differential…

Q: Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the…

A: Given: length,h=20 cmd=6 cmdr=0.001dV=?

Q: (b) Use differentials to estimate the maximum error in the calculated volume. What is the relative…

A:

Q: Suppose the side length of a cube is measured to be 5cm with an accuracy of 0.1cm. a) use…

A:

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of .1 cm. Use…

A: Topic = Derivative

Q: Find the total differential. z = 10x6y7 dz =

A: Differentiation of xⁿ = nxn-1

Q: The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use…

A: (a).            Volume of cube :                       V  =  x3                      dV  =  3 x2…

Q: The thickness of the shell is a = 0.5 centimeter. Use differentials to approximate the volume of the…

A: Given:        a=0.5 cm       r=100cm     Volume of shell V=43πr3     differentiating on both sides…

Q: A sphere is measured and the radius is 5 inches with a possible error of at most 0.02 inches.…

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

Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

Q: Let y = tan(5x + 3). Find the differential dy when a = 3 and dæ = 0.4 Round to 4 decimal places if…

A: For calculating dy, first we have to differentiate y w.r.t x, then find dy from that expression. The…

Q: Assume that a rectangle with sides x and y is changing with time. Let y = 2x and x(t)=t^2 What is…

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

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.