Find the midpoint of CD. M = ( X1+X2 Yı+y2 C = (10,-1) and D = (-6,3) %3D %3D ([ ? ],[ ])

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find the tangent plane to the equation z = 6e* – 2y at the point (4,8,6) - II

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Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

Q: Find the midpoint M of CD M = (, ) X1+X2 Y1 %3D 21 C = (-2,-10) D = (-6,0) M = ([ ? ], [ ]) Enter…

A: Explanation of the answer is as follows

Q: Find the tangent/s as directed to the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x –…

A: The objective is to find the equation of tangent line to the parabola x+2y2+2x-y-3=0 which is…

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

A:

Q: Find the tangent/s as directed:to the parabola (x + 2y)^2 + 2x – y – 3 = 0, parallel to the line x –…

A: Given equation of line is  x-4y=24y=x-2 y=14x-12 So comparing with the slope equation formula,…

Q: Y is the midpoint of XZ and V is the midpoint of WZ. If VY = 32, what is WX? WX Submit

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Q: Points X and Y are respectively 12 m north and 5 m east of point Z. Calculate XY.

A: To solve this problem we use the Pythagorean theorem

Q: Find a parameterization for the line segment joining points (0,3) and (12,0) using the angle 0 in…

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Q: Use Eq. (5) to find the point P nearest to Q = (2, 1, 2) on the plane x+y+z=l.

A: Consider the provided information, Find the point P. The normal vector to the plane is 1,1,1. And…

Q: utwards from the point (0 nd S, the top half of the

A: Given, the vector field                        E(x, y, z)=x, y, z-3this vector field can be…

Q: Find the length of the curve 4t2 -1 dt, y = %3D 1<x<3 8. 15 104 3 3.

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Q: Find the distance between the point (p, 4p) and the parabola y? = 2px, where p is a fixed positive…

A: let the point on parabola be A= (x, y)  B = (p, 4p) Thus,  AB = x-p2+y-4p2 but parabola is y2=2px…

Q: Find the points on the surface x² + y² + z² = 4 farthest from the point (1,–1,1), 2 %D

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Q: Find the tangent plane to the equation z = - 32² – y² + 3y at the point ( – 5, 3, – 75)

A: z=-3x2-y2+3y  and the point (-5,3,-75)

Q: Determine the location of a point (x, y, z) that satisfies the condition y &lt; 0

A: With the given condition there are 4 scenarios 1) x&gt;0,y&lt;0,z&gt;0 2) x&lt;0,y&lt;0,z&lt;0 3)…

Q: Find the equation of the tangent plane to the surface z = 4 +y? at the point (2,-3, 10) Ox+ 4y- z =…

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Q: b) Find the point on the curve y Vr that is closest to the point (7,0).

A: Find the point to the curve y=(x)^(1/2) that is closest to the point (7,0)

Q: Give an equation for the tangent plane to x2 + y + z? = 101 at the point (-2, 9, 4). = 0.

A:

Q: Find the point (x,y) of x^2+14xy+49y^2 = 100 that is closest to the origin and lies in the first…

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Q: Find the tangent plane to the equation z = 3e²²-2y at the point (4, 8, 3)

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Q: Find an equation of the normal line to the parabola y = x2 – 8x + 4 that is parallel to the line x –…

A: Let the equation of the normal line in the slope-intercept form is, y=mx+c where m is the slower and…

Q: Evaluate yz dx +y dy +a dz, where C is the line segment from (2,0, –1) to (4, 1, 2).

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Q: Find the point on the curve y = Vx closest to the point (1,0).

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Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

A:

Q: Find the tangent plane to the equation z = 6e" -20 at the point (4, 8, 6)

A:

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

Q: Find the points on the cone z 22 x2 + y? that are closest to the point (-5,2,0)

A: Find the points on the cone z² = x² + y2 that are closest to the point (-5,2,0).

Q: Find the point on the parabola y = x^2 closest to the point (−3, 0)? and give the minimal distance?

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Q: The region S = (x, y (x- 2) + y² < 4 is rotated about the line x = 5.

A:

Q: Find the tangent plane to the equation z 5x? – 2y? – 5y at the point (3, 0, 45).

A: We need to find the tangent plane equation at (3,0,45)

Q: Find the points on the cone z 22 = x2 + y? that are closest to the point (-3,1,0)

A:

Q: Find the tangent plane to the equation z = 3x2 + 4y? – y at the point (3,5,68)

A: We have to find the tangent plane equation to the given surface at a given point.

Q: ind an equation for the tangent plane of z = –2x²y – 3x² + y at the point (1, –1, –2).

A:

Q: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: ƒ(x, y) = 4x - 8xy + 2y + 1 on the triangular plate bounded by the lines x = 0, y = 0, x + y = 1 in…

A: Given function f(x, y),f(x, y) = 4x-8xy+2y+1             ........................(1)Given conditions…

Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: What is the value of c such that the line y=2x+4 is tangent to the parabola y=cx^2.

A: Given that the line y=2x+4 is tangent to the parabola y=cx2. The derivative of y=cx2 is dydx=2cx.…

Q: (c) Given that y = x4 – 8x²

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Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: Find a formula for the distance from the point P(x, y, z) to the xz-plane

A: The distance between two points x1,y1z1 and x2,y2z2: d=x2-x12+y2-y12+z2-z12 The distance from the…

Q: The curve y = ax? + bx +c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A: Explanation of the answer is as follows

Q: Find the tangent plane to the equation z = 5a° + æy? + 2 at the point (2, – 4, - 6)

A:

Q: The domain of ƒ(x, y) = In xy is points .(x, y) in the first quadrant

A: We have to tell about given statement.

Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.