a 1000-liter (L) tank contains 500 Lof water with asalt concentration of 10 g/L. Water with a salt concentration of 50 g/Lflows into the tank at a rate of Rin = 80 L/minutes (min). The fluidmixes instantaneously and is pumped out at a specified rate Rout. Lety(t) denote the quantity of salt in the tank at time t. 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…

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Q: Find z = f(x, y) and use the total differential to approximate the quantity. (2.04)2(1 + 8.8)3 −…

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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: Assume that after few w months, butterf lies papulace in looa is Calculated as: F(w)=12W+Cos (lbw)…

A: Minimum and maximum of a function can be calculated by testing the function against all the values…

Q: Find z = f (x, y) and use the total differential to approximate the quantity.

A: Given: The expression

Q: A worker on a roof 30 m above the ground needs to lift a 50 kg bucket of cement from the ground to a…

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Q: Find dy at taal dt and ya Vltx? and X = t.

A: Explanation of the solution is given below...

Q: Use double integral to find the average temperature of T(x. y) = 10-8r -2y

A: Temperature function is given as - Tx, y = 10-8x2-2y2Average temperature = ∬10-8x2-2y2dxdyGiven…

Q: Find the equation of the tangent plane to g ( x , y ) = e x cos ⁡ ( y )  at ( 0 , π ). Does g have a…

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

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Q: Find y(2) and yG) For fundion yft) that saticFies initial-valve dy +2 dy +y dt =2+ (t-3) 6 Ult-3) ;…

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Q: The dimensions of a closed rectangular box are measured as 93 cm, 66 cm, and 50 cm, respectively,…

A: Given,           The dimensions of a closed rectangular box are measured as 93 cm, 66 cm…

Q: The maximum rate of change of the finction f(x, y, z) =x In(yz) at (1;2;5 is equal to: O None of…

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Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: Find the total differential of the function. 4y f(x, y) 5x - y df =|

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

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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 maximum rate of change of the function f(x,y,z) = x In(yz) at (1;2;) is equal to: V17/2 None of…

A:

Q: Compute the work required to stretch a spring from 4 to 15 cm past equilibrium, assuming that the…

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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…

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

A: Relative error

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: A cylindrical tank has a radius of 8ft and a height of 10ft. Both dimensions are measured with a…

A: Given : Cylindrical tank has radius of 8 ft and a height of 10 ft,both dimensions are measured with…

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

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: 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: Compute the work required to stretch a spring from 7 to 13 cm past equilibrium, assuming that the…

A: Given query is to find the the work required.

Q: The thickness of the shell is a = 0.7 centimeter. Use differentials to approximate the volume of the…

A: Volume of sphere V= 43π×r3 From given figure radius is 100 cm .

Q: The radius of a circular disk is measured as 24 cm with a maximum error of 0.2 cm. By the…

A: The radius of a circular disk is measured as 24cm with a maximum error of 0.2 cm.

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

A: To find out the relative error in the lateral surface area of the cylinder.

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: Find the total differential z = e−x tan y

A: we have to find the total differential of z = e−x tan y           dz=∂f∂xdx+∂f∂ydy        (1) where…

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: the outside diameter of a thin spherical shell is 12 ft. If the shell is 0.3 inch thick, use…

A: Volume of a sphere with radius r is V=43πr3

Q: Patient has 1,000 mL LR infusing at 80 mL/hr. A. Determine the infusion time in hours and minutes.…

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Q: find the general selution of the differential equetion by the fimear methodi sxy'-2y=x

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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…

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Q: Compute the work required to stretch a spring from equilibrium to 8 cm past equilibrium, assuming…

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Q: S S.(x + y)dxdy by reversing the order of integration.

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

A:

Q: Find the work done in stretching a spring of natural length 8 cm, from 10 cm to 13 cm. Assume a…

A: Given information:- Find the work done in stretching a spring of natural length 8 cm, from 10 cm to…

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

A:

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…

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.