Cylinders in ℝ3 Consider the following cylinders in ℝ3. a. Identify the coordinate axis to which the cylinder is parallel. b. Sketch the cylinder. x - 2z2 = 0

Q: What is (8, 207°) in Cartesian coordinates? PCr,e) = P(xy). %3D Select one: t of a. (-3.63, -7.13)…

A: Given coordinates are in polar form thus use the formula for polar to Cartesian coordinates…

Q: Find d?y/da? without eliminating the parameter. A) t2 + 8t, y = t2 2t, t + -8 2 B) 10 1 (t + 8)3 t -…

A: This question is related to differentiation, We will solve it using given information.

Q: Evaluate CurlF ndS F(x,y,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x? + y? with…

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Q: (5 pons) Find the point (x, y) of x² + 14xy + 49y = 100 that is closest to the origin and lies in…

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Q: (a) Find the approximations T4 and M4 for 7el/x dx. (Rou T4 = %3D %3D

A: We have to find approximations T4 and M4 for the integral ∫127e1xdx Here T4 stands for trapezoidal…

Q: 35. f(x, y) = x² + 2y² – x; R is the disk x? + y? < 4.

A: fx,y=x2+2y2-x which is bounded by R, R:x2+y2≤4, where R is a disk Partially differentiating fx,y…

Q: Check for homogeneity and obtain the general solution. (Let 4C=C) (x² + y?)dx + xy dy = 0

A: The given equation is; (x2+y2)dx + xy dy =0

Q: 6) The insulation resistance of the cable with length F in ohm and a radial thickness (r2 -r1) is…

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Q: (xq + X2 Y1 +Y2° 2' 2 The formula for a segement on the coordinate plane is M =

A: The midpoint formula for a line segment joining the two points (x1,y1) and (x2,y2) is given by…

Q: Hw÷ find the Voctor Peralle I to the line intersedbetween the two flane 3X-6y-2Z=5 and 2x+4-27=5

A: The equation of the given planes is, 3x-6y-2z=52x+y-2z=5 If n1 and n2 are the normal to the planes,…

Q: 54. Find numbers a, b and c such that x = 1 + at y = 2+ bt is perpendicular to 2x + y - 3z = 1 z 3+…

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Q: P is the circumcenter of AXYZ. Use the given information to find PY. P. PX = 4x + 3 PZ = 6x - 11 Y

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Q: tind the diFfe rential equation rolution is whore y C1cos 7x t C2 sin 7x

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Q: Which of the following does GE contain? Check all that apply. E (3y + 4)° (5y–10)° D G F O A…

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Q: Apply Gauss-Seidal method to sulve the fotlowing Lineur equativns 5 X-2 X z =18 -2XI + lo X2…

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Q: H.W.3: For which values of z is w =1/(z – i), defined? For these values obtain u and v and evaluate…

A: Explanation of the answer is as follows

Q: Q1.Find the general solution of following PDE equation (a) (5z+ R)uz + (7x+ R)u, R (b) (z + R)u, +…

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Q: (c) Evaluate ff, 2z + 1dS where S is a portion of the cylinder x² + z² = 16 that lies between y = 0…

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Q: An object is moving with v(t) = 4' and the position X(1) = 4. What is the position of the object at…

A: This question is related to distance and speed , we will use integeration to solve this problem

Q: 1. f(x, y) = 192x³ + y² – 4xy2 on the triangle with vertices (0,0), (4,2) and – 2,2). %3D

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: dz (D² + 16)³(D² + 4D – 5)²(D² + 2D – 3)*z = 0, Dz = dr

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Q: make outbound JÄ x -4/3B = -12Ä ·B jän;B sà nai } = "i the corner achieve True false

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Q: Writing In (x+jy + a/(x+jy-a)]-u+ je, show that (a) x+y-2ax coth u + a = 0

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Q: Solve this equation: ди + a = at %3D u(0,t) = 0 %3D ди (L, t) = 0 az u(z,0) = 2 %3D

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Q: 2. Which of the following is the domain of y sec(x)? %3D A. [-1,1] B. R- (n+ 1) C. IR D. [-1,0}

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Q: Q: If the point (x, y) is equi distant from the points (a+ b,b-a) and (a-b,b+a). Prove that bx = ay.

A: Use given conditions to prove bx=ay

Q: (a) Evaluate APA: – 6) R where R is the solid hemisphere r² + y² + :² – 2r + 4y = 4, : 0.

A: We want to evaluate  ∫∫∫R9-z2dV where R is the solid hemisphere x2+y2+z2-2x+4y=4, z≥0 We can write…

Q: 2. Evaluate 22 - iz dz, where the contour C goes from z = 1 to z 2 to z = 2+ 3i.

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Q: M(t)=(1-t) then E(X) of X about the origin (2 (12 24

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Q4. Evaluate and ди at given point (u,v), z = 4e*Iny, x = Inu cosv, y = usinv at point(u,v) = (2,…

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Q: Which of the equation(s) are dimensionally compatible? E i. = v2 + 2aAx m iii.F = mv + v² A. all of…

A: Option ' C ' is correct .

Q: p ry*dx + x*dy, where C is the rectangle with vertices (0,0), (1,0), (1,5), and (0,5) Evaluate

A: We will convert this line integral to surface integral using greens theorem

Q: (ii) Assume that d = in E-coordinates and 7 in B-coordinates. y' Find a' and y' expressed in x and…

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Q: Check for homogeneity and obtain the general solution. (Let y=vx and 2C=C) dy x-y dx x+y

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Q: C. uoing Separahion af variables, find_the general 'solu ton of the given' D.E. dr = bCcoLedr +rsnt…

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Q: Apply Gauss Seidal me thod to Sulve the fotlowing Lineor equations 5 X-2 Xz -2X1 + loXz-2X3=-60 =18…

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Q: Find the length of cardioid r = a cos2 ½ θ. Show complete solution. a. a b. 2a  c.3a d.4a

A: Given:         r=acosθ22 Length of cardioid =2∫0πr2+drdθ2dθ             drdθ=ddθacosθ22…

Q: Q4: Let z = 2x2 – y? . Find all points at which |Vz| = 4. Then find V|Vz| at the point (1,4).

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Q: AL = 7x –6 x = AB = %3D BC = 1013 2. Point S is between R and T on RT. Use the given information to…

A: Use algebra for solve

Q: alve the following problem by y' = 1 ++ xy yca? = 1 , k = 0.1 a two-step methad.

A: Please refer to the image below

Q: Given r"(t) = , r'(0) = and r(0) = < 3, Find the j-component of r(6). %3D %3D %3D

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Q: Solve following Couchy probiem . the 2x e^uxy -Uxx +Ux =ye uloy) -0, Ux(0,y) =승 y %3D

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Q: I. For z = 3 – j5 and z2 = -2 +, find the rectangular form of the following: d. m[²2] Im e. ? Re f.…

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Q: Use the Chain Rule to find ∂z/∂s and ∂z/∂t. z = er cos(θ),    r = st,       θ = The Square Root of…

A: We have given

Q: (Write the answer in your own handwriting, scan and then upload the file) Q1. Prove that V = (y - z²…

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Q: B) Find real numbers x, y, z for the identity below 2xi + 2yj – 2i + 3j + 2k = 3i – j+ zk %3D

A: Given: 2xi+2yj-2i+3j+2k= 3i-j+zk To find x, y, and z

Q: 60. w %3D 5x? + 2ху — Зу?z, Р(1, 0, 1), v 3D i +j-k

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Q: AA Given: APLU = ATOE PL = x2 TE = 8 |3D TO = 2x + 15 OE = 13 + x U E T. %3D Find: a.) All values of…

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Q: Eliminate the parameter t: x = (v0cosa)t, y = (v0sina)t-16t2

A: *to find:- equation in the form of x &amp; y only, by eliminating the parameter t.

Q: Evaluate (2 + y² + z²) dV , where W is the cube given by W = {(x, y, z) E R° | 0< # < 1,0 < y< 1,0<…

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