Let I be the moment of inertia of the plate with density p = 1 bounded by y = ez, y = e, x = 0 about the r-axis.

Q: Q1: Find the tangent plane and normal line of the surface F(x,y,z)=x² + n + y² + z² = 10 at point…

A: Given :            F(x, y, z) = x2 + 2x + y2 + z2 - 10             Point P0(1, 1, 1)

Q: The curve C is the portion of the graph of y = 16 for 0sz5 2 (distances measured in m). The curve C…

A: The function given to us is as follows: y=116x4⇒x4=16y⇒x=2y14 Where, 0≤x≤2. For x=0,  y=0. For x=2,…

Q: Are the following functions homogeneous? If they are, determined their order. (a) f(y, t) = t^y² +…

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Q: Let h(y,z)=y(e)^−z. Calculate ∂h/∂y and ∂h/∂z.

A: Given : hy,z = ye-z

Q: Let f(x, y, z) = x cos z + y sin z and P = (−1, 1, 4). (a) (b) (c) at P. | Find the rate of change…

A: Here given function as fx, y, z=xcosz+ysinz

Q: The several variable function T(x, y, z) = 6x®y+ 4x²y°z – 5xz2 + 50 gives the temperature at a point…

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Q: Use V(P) = k / Kx, y, z2) ds Dp(x, y, z) where k = 8.99 x 10° N - m²/C°, to compute the electric…

A: Consider the provided question, VP=k∫C∂x,y,zDpx,y,zdswhere k = 8.99 x 109 N·m2c2. To compute the…

Q: 11- Find the moment of inertia about x-axis bounded by the curve y = 6- x² and the line y = x + 1

A: The given information in the question is the curve y=6-x2 and the line y = x + 1. The objective is…

Q: Calculate . F · dr where F (x, y, z) = zi + xyj - y?k On the curve C r(t) = t?i + tj + vĩ k, 0<t <1…

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Q: Example#1: determine the optimum of the unimodal function y = (x- 100)², starting at x--3 and step…

A: A unimodal function always has a global minimum or maximum in its graph. The global minimum or…

Q: (x = t³ + 7 y = t5 – 3t d²y calculate for a function given parametrically dx?

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Q: Find the equation of the tangent plane to the surface determined by z'y' + z – 25 = 0 at z = 4, y =…

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Q: Calculate distance between two Points Space 2: 2 x² + y² +2²³ - R² r = R₂0₂0 € 3

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Q5/ Find the moment of inertia about the x-axis of a thin plate of density 8 = 1 bounded by the…

A: Given: Density δ = 1Circle x2+y2 = 4

Q: Let A be a square matrix with a polar decomposition A = WP. (a) Prove that A is normal if and only…

A: Given Let A be a square matrix with a polar decomposition A = WP.(a)

Q: 0 ≤t≤ 27, then C F. dr = 0.

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Q: | 5y? dx +xy dy

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Q: Calculate the tangent plane for the function f(x, y, z) = ecos(x)+sin(y+z) at the point (7,0,0).

A: To calculate the tangent plane for the function  at the point .

Q: c find equations for the tangent Plane aut () normal line at the Point on the given Surface : X² +…

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Q: v(z): v(2) = L 1 In°(t)dt %3D

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