3 Divergence the oven SS F. da S = = y*² 2 + (xy^² - 32¹) ŷ ? ^ use evaluate + + (x² + y²) 52) 3 and "S" is the surface of the sphere of rading (4) zzo, y ≤ Jsstv. ربع كرة to dz sphelial

Q: Rit +1 ,2it ait -| = î7 e +iz (1-iz)eit 1+iz %3D iz

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Q: * +(x) = 3x6-4 (x-k)² +17, the value of the parameter k for f(x) to be a function pair IS?

A: For f(x) to be a function pair  it needs to be one-to-one, which means that each input value must…

Q: Liad para mean'c ecquation foo line 6f intersecton of planes 21-4+Z=4 3x +y + Z =l

A: Solution: The objective is to find the parametric equation for a line of intersection of planes…

Q: Each point of the parallelogram is translated up 3 units and left 2 units and then connected to form…

A: After shifting parallelogram 3 units up and 2 units left the new parallelogram will be

Q: 24 What are the center and radius of the circle 2 +y² + 4x = 5 ? whose equation is 1) (2,0) and 1 2)…

A: Using general equation of circle

Q: Line segment AB is a diameter of the x² +y² + z² - 2z + 8y = 9. Find point B if A = (0, у, 0).

A: To find the point B if Coordinates  of A are given for the sphere.

Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: Find the points on the cone 2² = x² + y² that are closest to the point (3,-3,0)

A: Cone Equation: z2=x2+y2 Given point: 3,-3,0 To find: the points on the cone nearest to the given…

Q: Which of the following would be the positive x-coordinate where the line y=x+3 intersects the circle…

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Q: 5. Find the exact value of distance from the point (1, -3, -1) to the plane 2x-y+3z = -5

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Q: Use the diagram to answer each. Circle O with tangent ED and BD= 60° E B ZDAB= LADC= ZDEA=

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Q: Iz+2-ik1 represents the interior of the circle of center (-2,1) and radius 1 (without the boundary).…

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Q: Shear a square whose opposite vertices are at (1,1) and (2,2) by i) 2 units along the x-axis and…

A: Step:-1 Given that a square whose opposite vertices are at (1, 1) and (2, 2) then square is Step:-2…

Q: 5 Find the distance between the points (3,-2) and (6,4) a) V85 units 9.219 go to station 7 b) v79…

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Q: Calculate Non-zero Christoffel symbol for the metric ds² = −dt² + A² (t)dx² + B² (t)dy² + C² (t)dz²

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Q: Determine parainetric cquations for the line L representing the interscction of the planes x – y +…

A: Given equation of plane are:-           x - y + 2z = 0 and             3x + y - z = 1

Q: GENERAL FORM x²+10x+y²+6y+33=0

A: From the given problem:   x2+10x+y2+6y+33=0   As we know that the standard form of the circle is:…

Q: 5. Write the standard form of the equation of the circle with the center at (-2,9) and passing…

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Q: (Challenging): Curve y =x*(x+3) is calleo Tschirnhausers cubic. Graph this at desmos.com/cal.cuator.…

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Q: Q4. equation of circle x² + y² - 6x-2y +6 = 0 2 )2 (x-3)² + (y-13² = 4 circle with center line y =…

A: Note: As per your request, the solution is in digital format is given below.   Q4.  Equation of…

Q: 2. Find the area of a parallelogram defined by PQ and QR when P = (4, 0, 1), Q = (5, -3, 0), and R =…

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Q: Discribe the topology through diagrams of surface and curves

A: Describe topology through diagrams of surface and curves.

Q: (b) Every continuous map S? →T² is homotopic to the constant map.

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Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

Q: 1) Find The coordindtes of the ciritical point Of the 2. Corve Y= メー R.) Find the courdinates Of the…

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Q: (x+10)2 +(y-pie)2 = M A) give the center point location. B) what is the radius of the circle

A: We know that the general equation for a circle is (x-h)2+(y-k)2=r2, where ( h, k ) is the center and…

Q: > Evaluate [ ²(x² + y²) dx + (x + y)²dy C › C is the triangle with vertices (1,1), (2,2) and (1,3)

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Q: 1. The following equation shows your retained information depending as a function of the hours of…

A: we have been given the function for retaining information as a function of t -'hours of study'…