1) Find a set of parametric equation to represent the graph of y= 1-x^2 using each parameter a) t =x b) t =1-x

Q: Find parametric equations and a parameter interval for the motion of a particle in the xy-plane that…

A:

Q: Consider the curve defined by the parametric equations X = cos t, y = 3sec t on the interval…

A: To eliminate t and find cartesian equation.

Q: What is the parametric equation of line through the point (1,2, -1) and perpendicular to the plane…

A:

Q: Sketch the plane curve represented by the given parametric equations x = 4 cos t + 2, y = 4cos t -…

A: We first make a table for the function t 0 π/2 π 3π/2 2π x 6 2 -2 2 6 y 3 -1 -5 -1 3

Q: parametric

A:

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A:

Q: Find parametric equations and a parameter interval for the motion of a particle that starts at the…

A:

Q: Find the exact value of the number a so that the length of the curve defined parametrically by

A: We have been given the parametric curves and have to find the value of a constant a.

Q: he rectangular equation from the parametric equations by eliminating the paramet

A: 11. Obtain the rectangular equation from the parametric equations by eliminating the parameter t X=t…

Q: By eliminating parameter t, sketch the parametric curve for the given parametric equations. Then,…

A:

Q: Determine the parametric equations of the curve of of the ellipsoid 4x² + y2 + 4z2 = 4 and the…

A: Solution: Given equation:ellipsoid: 4x2+y2+4z2=4; and half−cone: y2=x2+2z2 To find: parametric…

Q: Find the area of the surface obtained by rotating the curve of the parametric equations, x =…

A:

Q: What is the rectangular equivalence to the parametric equations? z (8) = 4 cos 0 + 2, y (8) = 2 sin…

A:

Q: Find a set of parametric equations for the line passing through the point (8, 0, 9) that is parallel…

A:

Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…

A: Given that z=x2+y2 and 3x−5y+7z=24 and point is 3,4,5. Let fx,y,z=x2+y2−z and gx,y,z=3x−5y+7z−24 We…

Q: A particle moves in space along a path whose parametric equations are given by x1 = b sin(wt), x2 =…

A:

Q: . Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² =…

A:

Q: Give parametric equations that describe a full circle of radius R, centered at the origin with…

A: The general parametric equations for circle which has center at (0,0) and radius R orientated in…

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² + ¹/² = 4…

A: We need to obtain a set of parametric equations for the curve of intersections of the cylinders:…

Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

A:

Q: Let parametric equation of a line L: (x,y) = (1,1) + a (-2,1), therefore it is besides through to…

A: Given that, L: (x,y) = (1,1) + a (-2,1)point (1,1)

Q: Find a set of parametric equations for the line passing through the point (7, o, 9) that is parallel…

A: Parametric equation of line in 3D

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

A:

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² +: 4 the…

A: We will use trigonometric identity  sin2t+cos2t=1 and parametric form of standard ellipse to find…

Q: Find the parametric and symmetric equation for the satisfying the given condition. 1. Through the…

A:

Q: 4. Sketch the parametric equations by eliminating the parameter. Be sure to include arrows to…

A: From given equations, we find sin theta and cos theta Then we plug them in the Pythagorean identity…

Q: Give parametric equations that describe a circle of radius R, centered at the origin with clockwise…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find parametric equations of the line containing the .point (2, 3,-1) and normal to the plane x+…

A:

Q: Find parametric equations for the path of a particle that moves along the curve y=x from (1, 1) to…

A: Given Parabola is y = x²

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

A:

Q: Find an equation of the circle with center at (-4,1) that is tangent to the y-axis in the form of…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: Find the length of the curve defined by the parametric equations

A: Given parametric equations are x=(5/6) t and y=5 ln((t/6)2-1) from t=7 to 9 W need to find length of…

Q: . Find the slope of the line tangent to the parametric curve x = 2cost and y = 2- cos²t for 0<t<n at…

A:

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

A:

Q: Find parametric equations for the line through (-4,1,1) parallel to the x-axis. Let z = 1. y-z=…

A:

Q: Let line 1: x = = = and point P(1,0,1). 2 ● Find the set of parametric equations of the line…

A:

Q: Explain how a pair of parametric equations generates a curve in the xy-plane.

A: Our Aim is to explain the fact that how a pair of parametric equationsgenerates a curve in the…

Q: Find a set of parametric equations for the line passing through the point (7, 0, 2) that is parallel…

A: We are asked to find the equation of the line.

Q: 6. Find the distance between the point (- 3, 2, 1) and the line with parametric equations x = 3 –…

A: Consider a point on the line (3-2t, 1-t, -3t) which is the foot of the perpendicular to the point…

Q: find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: The tangent line in the solution should be perpendicular to the normal vectors of the surfaces. The…

Q: Find the parametric equation for line l that is parallel to line m with equation: x = 1 + 4t; y = -…

A: Two lines are said to be parallel if their direction ratios are proportional. We will use this fact…

Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve). x…

A:

Q: parametric equations representing the given curve.  Line passing through (0, 2) and (3, 1)

A:

Q: Find a parametric equation for the line through the point (- 1, - 5, - 2) and perpendicular to the…

A: The parametric equation of the  line through the  points P0x0,y0,z0 and Plane a, b, c is x=x0+at…

Q: Find parametric equations and a parameter interval for the motionof a particle that starts at (a, 0)…

A:

Q: Find parametric equations for the line formed by the intersection of planes x+y-z=3 and 3x-y+3z=5.

A: First we find a point on the intersection of these planes with the plane z=0. And next find the…

Q: Find parametric equation of a helix radius 5 from a point (5, 0 ,0) to a point (0, 5, 1)

A: Given that the radius of the helix is R=5. We know that the parametric equation of helix is given…

Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: &lt;3, 1, 1&gt; +…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.