The distance between the point P(x₁, y₁, 2₁) to the plone with equation Ax+By+ (z+D=0 is equal to | Ax₂ + By₁ + C₂₁ +DI √√A²+ B² + (² Why? 11

Q: (a) √|2|=3 (2²+1)2dz. (b) S₁2=22(2²1) dz. z³(z−1)

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Q: Find the cartesian coordinates of the point  (4,3π/2) (√2, π/4) (-9,-π/6)

A: To find the Cartesian coordinates of the following points.

Q: 2) xe-X dx 0. A) -Se-7-1 B) -8e-7+1 C) -6e-7+1 D) -8e-7

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Q: 2. Evaluate z²+1 Z (a) J₁2-2 (2-13dz. (b) √₁2-2|=1 (2²-4)²· √3dz.

A: The given problem is to evaluate the given complex integrals over the given counter of region. We…

Q: Find the point on the line 3x + 7y+ 6 = 0 which is closest to the point (-4,-3). )

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Q: 8. Evaluate (a) J₁2-2 22+2+d; (b) J₁2-22²-22-3dz

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Q: b) I = (x-8)² +2=y+3

A: Given that:To find: The value of x.Formula used:

Q: Suppose you are climbing a hill whose shape is given by the equation z = 2000 - 0.005x²-0.01y2,…

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Q: In each part, determine whether the equation is linear in x₁, x2, and x3. (b) x₁ + 3x₂ + x₁ x3 = 2…

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Q: y" + 3xy' + y = 2x %3D

A: Given differential equation is y''+3xy'+y=2x

Q: 2) y=x' – 9x² + 24x – 18; [2, 4] -

A: let y=f(x) f(x)= x3-9x2+24x-18, [2,4] using rational roots tests: x could be :±1,±2,±3,±6,±9,±18 If…

Q: Мaximize z = 3x1 + 5x2 subject to: 4x] + х, < 25 2х, + 3x, < 15 with х, 2 0, х, 2 0.

A: To Maximise  z= 3x1+5x2subjected to : 4x1+x2 ≤25                         2x1+3x2≤15 with…

Q: 19) Find the distance between these two points. (-8, 5) and (15, -9) Use the formula: d = square…

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