Find the rates at which the volume, surface area, and interior diagonal are changing at the instant when x=10, y=17, and z=11 m.

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Q: dw Find if w = xy + z,x = cost, y sint and z =t at t = 0. dt

A: In the given question, the concept of the derivative is applied. Derivative We can use a derivative…

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Q: Find the external in the isoperimetric problem of the extremum of subject to f(y² +xy'- :“)dx= 2,y…

A: Consider the functional  Iyx=∫x1x2Fx,y,y'dxwith the conditions yx1=y1 , yx2=y2and Iyx=∫x1x2Gx,y,y'dx…

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: • Suppose that the mass in a mass-spring-dashpot system with m = 25, c = 10, and k = 226 is set in…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Show that at any point (x,y) on the curve y=bex/a ,the length of the subtangent is constant and the…

A: The given curve is y=bexa.

Q: Consider the given closed rectangular box with dimensions x cm, v cm and z cm. Assume that x is…

A: Consider a rectangular box with dimensions x cm , y cm and z cm .…

Q: Suppose F(x, y) = (6x + 5y)i + (5x + 4y)j. Evaluate the line integral for each of the given paths,…

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Q: 5xy dv, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by…

A: The given integral is ∭E5xydV. The region E lies under the plane z=1+x+y and above the region in the…

Q: When the radius r of a sphere increases with time t, the change in area dA is dt Оа. 4 3 O b. dr 8n…

A: We will find the change in area with time as following.

Q: find Ix, Iy, I0, x, and y for the lamina bounded by the graphs of the equations. y = 0, y = 2, x =…

A: The value of I0,Ix,Iy.

Q: Consider a rod of length meters with density 8(x)=(2- cos x) kg/m over the interval 0<x<5.

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Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

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Q: The surface area of a sphere is expanding at the rate of 6 cm²/sec, Wher What is the change in the…

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Q: What should be A for the path independent of (2,4) 2Ay – x dy. y? XY + A (1,2) over evaluate the…

A: Consider the provide integral,

Q: Consider the curve segments: 1 - to x = 4 and 4 1 X = -to x = 16. 16 S1: у %3D = x² from x = S2: y =…

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Q: What is the value of the line integral ∫ AB y dx + x dy, if x = 3*t, y = 4*t + 4 and 0 ≤ t ≤ 1?

A: I am solving this in step 2

Q: Find an equation for the level surface of the function f(xy.z) = x+ ey+z that passes through the…

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Q: If x, y, and z are lengths of the edges of a rectangular box, the common length of the box’s…

A: Given If x, y, and z are lengths of the edges of a rectangular box

Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw…

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Q: Verify Green's Theorem by evaluating both integrals Lr dx + x* dy = / dA ду x² dy ax for the given…

A: In this question we verify Green's Theorem                 i.e, verify integral  ∫C y2 dx +x2 dy =…

Q: The line integral 2xe" dæ + a²e" dy + (1 – 2²)e¬²² dz is not independent of path.

A: The line integral ∫CF·dr is independent of path if the curl of F is zero, that is, ∇×F=0. Here, The…

Q: The value of the line integral S(2xy² dx + 2x?ydy + dz) along a path joining the origin and the…

A: To find the value of line integral  ∫c(2xy2dx+2x2ydy+dz)along the path joining origin and point…

Q: Find the value(s) of c such that the area of the region bounded by the parabolae y=x^2 - c^2 and…

A: Given: The given parabolas are y=x2-c2 and y=c2-x2. Determine the points of intersection.…

Q: 1. Evaluate fL, 2 dv where E lies below the plane z = 2+ 3x + 4y and above the region in the…

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Q: Suppose that the position of a body moving along a coordinate line at time t is a. s = a cos kt + b…

A: Part (a):Part (a):Given,Given,

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

A: Given: A is the area of a circle with radius r. To determine: dAdtin terms ofdrdt

Q: Suppose that the temperature in degrees Celsius at a point (x, y, z) of a solid E bounded by the…

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Q: let z be the from a paint minimum distance on the gra ph of y= 5€3x/2) to the Origin which is at (0,…

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Q: If f′(0)=f′(2), find the difference 2c-d for the following cubic spline S(x) with clamped boundary…

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Q: . The uejveciion of a beam is governed by the equation d'y + 81y = 0 (x) dx %3D where o(x) is given…

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Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: 20- What is the share of the formula that allows calculating the y coordinate of the center of…

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Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm³, thermal…

A: The equation is u t…

Q: d(xy) = ? tot al dofferentral ? Zryckt x dy=9 )totol pferibral?

A: Given

Q: Let y 5x? + 4x + 3. If Ar 0.1 at I = 5, use linear approximation to estimate Ay

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Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

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Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: Suppose F(x,y)=(4x+6y)i +(6x+4y)j. Evaluate the line integral for each of the given paths, which are…

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Q: 2. Suppose that the edge lengths r, y, and z of a closed rectangular box are changing at the…

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Q: 1 Integrate the function f (x, y) = over the region bounded by r-axis, line æ = 7, and the curve y =…

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Q: Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following…

A: To determine the rate at which the box’s (a) Volume, (b) Surface area and (c) diagonal length are…

Q: 4x Estimate the error in the quadratic approximation of f(x,y) = e sin y at the origin over the…

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Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

Q: 3xy dV, where E is bounded by the parabolic cylinders y = x² and x = y and the planes z = 0 and z =…

A: It is given that, y=x2 and x=y2 and the planes z=0 and z=7x+y. Define the region E as follows.…

Q: The volume of the solid generated by the curve y = e¬ª, between x = 3 and x = 7 about the |3| x –…

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Q: The volume V of a right circular cylinder of radius r and height h is V=πr2h (a) How is dV/dt…

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