Use Cartesian coordinates to evaluate y² dV D where D is the tetrahedron in the first octant bounded by the coordinate planes and the plane 3x + 2y + z = 6. Use dV= dz dx dy. Draw the solid D. =

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Q: - complete solutions.

A: The co-ordinate related as x=rcosθy=rsinθz=zx2+y2=r2θ=tan-1yx Then,…

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Q: Consider the integral: f(t)-10e-15t = 17t- -S sen(t-u)f(u)du When applying Laplace transform in both…

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Q: Use Cartesian coordinates to evaluate [[[ 3² a dV D where D is the tetrahedron in the first octant…

A: Plane  3x+2y+z=6in first octantz : 0→6-2y-3xy=0→6-3x2x=0→2 Draw the graph

Q: 2. Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y²-3x² and…

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Q: in the firs dV= dz

A: Let us consider a triple integral of the form ∫ab∫f(x)g(x)∫h(x,y)r(x,y)F(x,y)dzdydx To solve the…

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Q: (b) Show that the continuous image of compact set is compact but the convers need not to be true.…

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Q: - x, then answer the following ( (1) Find the function's domain (2) Find the function's range. (3)…

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Q: Find the general solution of this ODE: d²y dt² +13- +36y 4t² - 6+10e-2t dy dt = The solution will be…

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Q: p the iterate sed by the hy

A: Volume enclosed by hyperboloid z=1+x22+y22 under the plane

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Q: 4.By applying the Convolution Theorem to calculate L-1 is obtained: Determine the value of (a+b): a…

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Q: 5. Solve x sin x = 1 using the following: (a) MOSS (root = 0.5) (b) Newton Raphson (root = 0.5) (c)…

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Q: • Find the upper Riemann sum U(f, P) and the lower Riemann sum L(f, P) for each of the following…

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Q: Show that (2+x, e) is linearly independent. z solve both parts within -40 mins I'll upvote your swer…

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: Given equation :      z2=4+4r2As we know that r2=x2+y2..............(polar form→cartesian form)So we…

Q: Theorems Let {xy and fyny betwo Se @ X n + Yn w X+Y в 2х ш> hx WheF

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Q: x - 1 5 = y - 2 3 Z - 2 1 2xy +z = 10

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Q: Q3: Use Euler's Method to find a numerical solution of the differential equation dy y = 3 - dx X =…

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Q: 6. s] Set up only a triple integral that will give the following: (a) the volume of R using…

A: (a) Given,R:0≤x≤1 ,  0≤y≤1-x2 and 0≤z≤4-x2-y2 we know the relation between cylindrical and cartesian…

Q: 1) USE THE INVERSE OF THE COEFFICIENT MATRIX, S.N=0 4 -1 Last digit of S.N.] A = 1 1 b = 4 1 6 0 -2

A: Here the solution is given by using the inverse matrix method. The inverse of matrix is obtained by…

Q: Q5: Use the quadratic interpolation and the following data to find f(1.4) X 1 1.2 1.3 F(x) 0.368…

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Q: At 8 a.m., you place a certain amount of bacteria on a slide. Every hour, the area covered by the…

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Q: C R using cylindrical c √1-2², 0≤ ≤ the solid B that lies +22=2 using sphe

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Q: Q3: A) Find the limits below 1) lim (x,y)—(0,0) x² + sin²y 2x2 + + y²

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Q: b) Find the area between the 2 curves f(x) = x² +4-4x and x- with the two lines = 5 &x= 2. axes and…

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Q: ns in t 2 =4

A: The co-ordinate related as x=rcosθy=rsinθz=zx2+y2=r2θ=tan-1yx The Cartesian co-ordinate and…

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Q: 14. Find the cube root of 15 correct to four significant digits by Fixed-Point and Secant methods.…

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Q: 5 By Separation of variables, Solve the following PDES- ²4 ● = 4 ²4 dx² 0 o u(e,t) = u(5,t) =6…

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Q: State the order of the given ordinary differential equation. (2x - tan(17x))y"" - x²y" + 18y' =…

A: Given the ordinary differential equation is  2x-tan17xy'''-x2y''+18y'=18sinhx+16

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Q: Evaluate the integral (t³ In ti+ 3t³ sin (t) j+k) dt.

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Q: 1) Find the absolute maximum and minimum for function f(x,y)=x²-xy+y²-6y-4, on the domain -4≤x≤2,…

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Q: Consider the integral equation: -19t f(t)-39e = 5t- - 5. s sen(t - u)f(u)du By applying the Laplace…

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Q: Solve the problem PDE: Utt=9UTT 9urz ВС: IC: u(x, t) = help (formulas) 00 u(0, t) = u(1, t) = 0…

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Q: Identify the s he Cartesian for +4r

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Q: Please answer with complete solution. The task is to answer the question below: Let A be the…

A: Here given as R→u, v=u, v, u2-v2 Now draw qudrilatral on uv plane, That is v≤u≤3 and 0≤v≤1 Also,…

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Q: Find the general Solution of the following PDES -Х • з Их + 2 Иу =0 ucx, c) = че 2 ans3- исх, у)…

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Q: Set up the triple integral that will give the following: the volume of the solid B that lies above…

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Q: Solve the following 2nd order OPEs (5 steps) 3 2 b. (x²-x) y - xy + y = 0, y(t) = 0.65, y(+₂) =0z,…

A: Let us solve the given 2nd - order ODE using Euler method in the next steps.

Q: If 64% of the people at a certain conference are doctors, 31% are women, and 29% are female doctors,…

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