find a polar equation for the curve represented by the given cartesian equation 5x^2 +y^2 = 8x (r is not equal to 0)

Q: and you take it from the rectangular system into the polar system. What will the new limits of…

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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: Find parametric equations for the line passing through the points (10,3,1) and (8,6,-2) using the…

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Q: parametric

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

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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: Explain why the vertical-line test used to identify functions in rectangular coordinates does not…

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Q: (3) Find a parametric equation for the line segment joining (1, 0, 1) and (0, –2, 1).

A: The direction vector of the segment is: (0,-2,1) - (1,0,1) = (-1, -2, 0) Initial point is (1,0,1).…

Q: . Two trains A and B moving on a horizontal track with velocities Va = (40 + i30 km/h and V = (25 -…

A: Given, VA=40+30ikm/hVB=25-50ikm/h So, the relative velocity from A to B is,…

Q: 9. Identify the surface whose equation in spherical coordinates is given by

A: We have to solve given to problem:

Q: What is y2 = 3x in polar form? r = 3 sin 0 sin 0 O Option 4 r = 3 csc 0 cote Option 2 r = 3 sin 0 -…

A: Given y2=3xTo find polar form:

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

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Q: Convert the point (3,3 7) from polar coordinates to Cartesian coordinates. Give exact values. y =…

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Q: Convert the rectangular equation to a polar equation that expresses r in terms of 0. y = 19x (Type…

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

Q: Find the slope of the tangent line to the polar curve r = sin(70) at 0=. Enter as an integer or…

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

A: Given,

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

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Q: Find the area of the surface formed by revolving the polar equation over the given interval about…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: Find parametric equations for a circle of radius 2, centered at (3, 5).

A: Solution:Given    radius of the circle=r=2centre of the circle(h,k)=(3,5)To find the parametric…

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

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Q: Find two polar coordinate representations for the rectangular coordinate point (-√2, √6), one with…

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Q: What are the rectangular coordinates of the point with polar coordinates (r, 0) = (-10, (x, y) Enter…

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Q: In an open space, Thomas throws a ball at an angle of 70° to the horizontal with an initial velocity…

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

A: The given equation of circle at (a,0) is The general parametric equation of circle is where x,y…

Q: find parametric equations for the lines with the given description.  Perpendicular to the yz-plane,…

A: To find parametric equation perpendicular to yz plane passes through (0,0,2)

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

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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…

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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…

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Q: find parametric equations for the given curve. Circle of radius 4 with center (3, 9)

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Q: Find the slope of the tangent line to the polar curve r = cos(e) at e =. Enter as an integer or…

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Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: make a table values t x=t+sint y=cost -π x=-π +sin-π=-π +0=-π =-3.14 y=cos-π=-1 -π2…

Q: determine the slope of the tangent line to the polar curve r = 3 + 8 sin 0 at 0 =

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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: 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: Given, the surfaces:               x+y2+2z=4,   x=1  Point: (1, 1, 1) Let         z = 1-2t

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

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Q: Find the corresponding Cartesian equation of the parametric equation       x=3cosθx=3cosθ.…

A: Given:           x=3 cos θ,   y=4 sin θ            0≤θ≤2π From: x= 3 cos θ            cos θ=x3 From:…

Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?

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Q: What are Polar curves and what is their significance

A: We need to define polar curves.

Q: The polar equation of the curve is expressed as r = 2sine + 2cose. area bounded by the curve.

A: To find the area.

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: 3) (i) Eliminate the parameter to find a Cartesian equation of the curve. (ii) Sketch the parametric…

A: Our objective is to eliminate the parameters to find the cartesian equation of the curve and sketch…

Q: Determine the parametric equations of the path of a particle that travels the circle:

A: Given,        (x-4)2+(y-3)2=49 Time interval is 0≤t≤2π

Q: Find the slope of the tangent line to the polar curve r sin(30) at 0 = %3D

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Q: State an example of: Parametric equation Polar equation Definite integral

A: Consider the given information. Since, you have post the multiple question. I am answering the first…

Q: What is the polar equation of the horizontal line y = 5?

A: Given the cartesian equation of horizontal line: y=5

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.