Find the center and radius of the sphere x? - 10x – 10 +y? + 14y + z² – &z = 0 O A C (5,7, -4), r = 10 O B. C(-10,14,- 8), r = 10 OC.C(-5,7,4),r = 10 O D.C(5,- 7,4), r = 10 O E. C(5,-7,4), r = 100

Q: 2) If you are given two points in space, P1 (X1,yı) and P2 (X2,yz), demonstrate why the distance…

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Q: Show that the given equation represents a sphere and find its center and radius x² + y2 + z? + ax +…

A: The given equation is x2+y2+z2+ax+by+cz+d=0. The general equation of a sphere with center h,k,n and…

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Q: Use the applet to translate quadrilateral ABCD 2 units left to create quadrilateral A'B'C'D', then…

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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: Find the point on the sphere x +y +z = 4 farthest from the point (1, – 1,1). The point is ( ID:…

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Q: Find the points on the sphere x² + y° + z?=1. that are closest to and farthest from the point (2, 1,…

A: Given, x2+y2+z2=1   ;   point (2,1,2)

Q: Find the point on the sphere x? + y² + z² = 3 farthest from the point (-6, 6, –6). Farthest point is

A: Given equation of the sphere, Given point is (-6, 6, -6). Distance of the point (-6, 6, -6) from…

Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: Apply T (x, y) = (2x/3,2y/3) to the following pentagons: (a) vertices (3,-3), (3, 3), (0, 6), (–3,…

A: Now in T(x,y)=(2x/3,2y/3)=(x/1.5 ,y/1.5) so by apply T(x,y) we are expecting that our pentagons area…

Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

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Q: Tind he latance from the pomt (-2, 4) to tu plane 37+2y4 6E5

A: Given a point (1, -2, 4) and a plane 3x + 2y + 6z = 5

Q: Find the area of the triangle with vertices P(1, 2, –5), Q(0,0,0) and R(4, 6, 1). NOTE: Enter the…

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Q: two bees leaving an area in a straight path. Bee's 1 path: r1(t) = + t and Bee's 2 path: r2(s) =…

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Q: Find an equation for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

Q: Find the point on the sphere x+y²+z²=625 that is farthest from the point (-23,14,-13). 23 625 V1200…

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Q: 3. Find the area of the rhombus. dl (2x +2) cm d2 (6x + 8) cm

A: As we know that the area for a rhombus when the p and q are the diagonal is:- A=pq2

Q: 3. A player P stands 10 metres directly in front of a soccer goal O ABC, as shown below. The corners…

A: a)Co-ordinates of GG0+7.52,0+02,0+02=G154,0,0Co-ordinates of P∵P lies on the  xy planeso…

Q: Find the point on the sphere x² + (y + 2)² + (z+ 9)² = 4 nearest to a. the xy-plane. b. the point…

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Q: Ex 6/ Find the Velume in the firstad Lacdlesiged by the Cylinder xpZ54 and the plane ye 3 22

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Q: 3. What is the distance from the line to the plane? 7-(2,3,8)+(1.1.1) 2x - 5y + 32 + 10

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Q: Which of the following point is the farthest point on the sphere z? + y² + z² = 4 from the point…

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Q: Find the distance from the point (-3, 2, -4) to the plane 5x + 5y - 4x = 3.

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Q: 10 The double integral 2x dædy, where T is the triangle with vertices (0,0), (3,0) and (6,3), equals

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