nstructions: Reflect the given the coordinate points across the y-axis. K(0, -1) L(2,3) М65, -1) K' L'( M'(

Q: X =. Vy, x = -y,y = 2 about the x-axis

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Q: 7. Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass…

A: Given a function of the curve, y=ax4+bx3+cx2+dx+e To find the coefficient a,b,c, and d such that the…

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

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Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z2 22, P = (2,…

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Q: e Green's Theorem to evaluate [(-y²)dx + (x²)dy if the curve C is a triangle with rtices at (0,0),…

A: Top:- application of integration

Q: There is an ant on a circular heated plate. The plate temperature is given by f(x, y) = y² – x² + 12…

A: Consider the function fx,y=y2-x2+12, with equality constraint x2+y2=121 (since the radius is given…

Q: 4.) y = VT, y = 3, x = 0 around the y axis %3D

A: Given, y = x1/2, y = 3, x = 0, we have to find the volume by rotating about the y-axis.

Q: 2. XY has an endpoint X at (2,– 4). If the midpoint of XY is (– 3,– 1), what are the coordinates of…

A: The midpoint of two points and is given by: where are coordinates of the midpoint.

Q: Find the equation of the tangent plane to x^2/16 +y^2/9 −z^2/36 = 1 at the point (4, 3, 6). Simplify…

A: Use tangent plane formula

Q: Find the parametrization of the line through (5, 9) with slope 12 for given x(t) = 5t. (Use symbolic…

A:

Q: 9) reflection across the y-axIS

A: Png the reflection of the given graph across y-axis

Q: x = e2t – 1, y = et

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Q: Equation of the tangent drawn from the point S(2,4) on the 8x = y^2 parabola ? 2y=2x+2 y=2x+2…

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the length (in units) of the curve y =    16 − x2between x = 0 and x = 2.

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Q: Q: Use Lagrange's Formula to Prove that : 1) Y = Y3 – 0.3 * [ Y5 – Y_3] + 0.2 * [Y_3 – Y_5] . -

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Q: The temperature at the point (x, y) on a metal plate is T = x² + y2 Find the direction of greatest…

A: The temperature at point (x, y) is given by: T=xx2+y2 To find the direction of greatest increase in…

Q: e length of the curve y = V 4 – x2, 0 <x< 2. ing the shape of the curve.

A: Use the arc length formula to find the length of the curve.  y=(4-x2)1/2 , 0&lt;=x&lt;=2

Q: e tangent line to the ellipse 25 = 1 at the point (x, y). 9. %3D s where the slope is not defined?…

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Q: y = e", y = 0, x = 0, and x = 2; about the x-axis %3D

A: This question can be solved using the definite integral formula of the volume of solid generated…

Q: 10. Find the acute angle of intersection of the curves x + xy = 1 and y3 (x + 1)2.

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: -dx using 4 trapezoids. What is the error bound for the approximation this problem

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Q: A uniform cable is suspended between two poles of equal height. Assume that the equation of the…

A: (a)

Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

A:

Q: 3. Curve A given by x(t) = 4cos(t) and y = 4sin(t), Curve B given by x(t) = 4cos(2t) and y = For…

A: Use trigonometric identities

Q: y 2 Find the length of the curve x y? from y = 1 to y = 9. -

A:

Q: Evaluate |-y dx+x dy , where C consist of the curves along the horizontal line from (-4,4) to (-2,4)…

A: The given integral is: ∫C -ydx+xdy Where C consists the curve along the horizontal line from -4,4 to…

Q: Find the equation for the tangent plane and the normal line at the point Po(3,2,3) on the surface 2x…

A:

Q: Find the center of the circle(s) tangent to 5x – 2y – 1 = 0 at (1, 2) with a radius of 3. Express…

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Q: 13. y = x², y = 0, x= 1; about the y-axis

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Q: s) Find an equation of the tangent plane to the surface z = 2+2x² +5 at the point P(-,1,3). our…

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Q: A/Find the distance between the line 2x + 3y = 5 and the point(-1,0). ( B/Find by integrating along…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Consider the curve defined by the equation x(^2)+2xy+y^(3)=4. Part a: Find the local linearization…

A: Given informationDefine curved equation

Q: vember 12, 20Z1 m # 3 Find an equation of the tangent plane to the face at the given point. f (x,y)…

A: Solve the given problem.

Q: Find the equation for the tangent plane and the normal line at the point Po(2,3,1) on the surface 3x…

A:

Q: Q: Find the point on the curve 4x' +a'y = 4a', 4< a < & that is farthest from the point (0,-2).

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Q: 2. Rotating around a vertical axis: y = 4x -x2, y = 3 and rotated about x = 1.

A: We have to find point of intersection and draw the region bounded , Then rotate the region about x=1…

Q: 3. Lapluce of lunction fct)_is givan by -Fes)-S Pct) d. 6-F4) - C) et dt C. -00 SA

A:

Q: Siupe of the langent iine al any point (X, Y) on the curve 3x2 -2x +7 and the point (1, the curve.…

A: Topic:- application of integration

Q: A uniform cable is suspended between two poles of equal height. Assume that the equation of the…

A:

Q: 1 y == (x² + 4)°%2 ,0 sxS 2 (x2 + 4)°/2 ,0<x< 2 6. deur die berekening van die volgende bej…

A: The given function y is - y = 16x2+432     ........(1)Formula for calcualting the lenght of a curve…

Q: Find an equation of the tangent plane to the surface at the given point. 4x2 + 2y? + 4z? = 22, P =…

A:

Q: Integrate h(x, y) = (x+y)i+-x)j over the closed curve that begins at (-1, 0). goes along the x-axis…

A: Let me tell you , In this problem we are going to use Green's theorem. Note: Green's theorem is only…

Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

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Q: The length of the curve defined by x =÷(y² + 2)E, y E [0,3] %3D

A: Arc length=∫ab1+dxdy2dy

Q: Find the parametrization of the line through (2, 8) with slope 11 for given x(t) = 41. (Use symbolic…

A: SOLUTION-

Q: oves from origin at the curved Path -³x) m

A: Concept used: Velocity is the derivative of position with respect to time. Acceleration is…

Q: 3. When origin shifted to the point (2,3), the transformed equation of the curve is x2 + 3xy – 2y2 +…

A: Shifted origin is 2,3. Transformed equation is x2+3xy-2y2+17x-17y-11=0. Replace x with x-2 and y…

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.