Determine whether the statement " If x > 0, then the point (x, y) on the rectangular coordinate system can be represented by (r, ) on the polar coordinate system, where r = √(x2 + y2) and = arctan( y/x)" ,is true or false. If it is false, explain why or give an example that shows it is false.

Q: What is the rectangular equivalence to the parametric equations? z (0) = 4 cos 0+2, y (0)=2 sin 0-5,…

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Q: Sketch the curve in the complex plane given by | Z-3| = | 7 + 3i } %3D i, z'+ 2?= 2. %3D

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Q: A torus of radius 2 (and cross-sectional radius 1) can be represented parametrically by the function…

A: The surface area (A) of torus is given by the formula mentioned below with given values as.

Q: Find the parametric equations of a vertical line through point (0,9). Assume v = 0 corresponds to…

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Q: 1) Find the parametric equations of the line that is tangent to circle x² + y2 = 25 %3D at point (3,…

A: Given: Equation of circle: x2+y2=25 and tangent at point 3, -4

Q: The parametric equation of the line resulted from intersection of x-y 0, and z = 2 is %3D

A: Use the given planes.

Q: Find parametric equations of the line through (-1,0,1) that is parallel to 2i – 6 j+ k. -

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Q: osen y

A: Is it sen y =x

Q: Find a parametric form for the line through the point (8, –6, –3) and perpendicular to the plane 2x…

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Q: (Picture of question is attached)

A: Calculate the values using the given polar equation and complete the table.

Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

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Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

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

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Q: Show that the parabolas $r=c /(1+\cos \theta)$ and $r=d /(1-\cos \theta)$ intersect at right angles.

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

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Q: 4. Determine the parametric equation of the line that passes through (2, -1, 3) and is perpendicular…

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Q: 5. Given the parameter 7, constants a and c, show that the parametric equations: X(+) = (cosh () –…

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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: The parametric equation of the segment [AB] with A(1,0,5) and B(3,1,2) is: O x=1+2t y%3Dt z-5-3t -o<…

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Q: Find the 1st  and 2nd Derivate of y with respect to x from parametric equations. Complete solution…

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Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is per- pendicular to…

A: Let's find.

Q: x = 12 + 3 y = 2t [-2, 2]

A: Substitute t value

Q: Find a parametric equation for the line through the point (6,5, - 3) and perpendicular to the plane…

A: Given plane is, 7x+4y+4z=15 Since, the line is perpendicular to the plane then the normal vector…

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: 5. Find the distance from the point (3, 0, 10) to the plane 2x+3y+ z = 2. 6. Write the parametric…

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

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Q: Find the parametric equations for the line through the point (5, 2, 9) and perpendicular to the…

A: The parametric equation of a line passing through the point and has a direction cosines &lt;a , b…

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

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + 4y +…

A: Equation of line normal to graph of functions f(x) is :  r&lt;t&gt; = &lt;x0,y0,z0&gt; +…

Q: Find a parametric equation for the line through the point (2,3, – 1) and perpendicular to the plane…

A: Given that The point on the line (2,3,-1) and perpendicular to the plane 8x+3y+3z=5 A vector…

Q: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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Q: Find parametric equations of the line through (–3, 0, 3) that is parallel to 5i – 8j+ k. x(t) y(t)…

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Q: Find the lengths of the curves given by the polar coordinate equations in Exercises 51-54. 51. r =…

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

Q: Find parametric equations for the line through Po = (14, –1, 1) perpendicular to the plane 3x + 8y –…

A: A vector perpendicular to the plane ax+by+cz+d=0 is given by &lt;a,b,c&gt; so a vector perpendicular…

Q: Find the parametric equations for the line through the point (0, 1, 2) that is perpendicular to the…

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Q: Find parametric equations for the line through (3, – 7,6) parallel to the x-axis. Let z = 6. X= , y…

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Q: Find parametric equations for the line pass- ng through the point P(1, –1, 3) and perpen- licular to…

A: Given that: Line is passing through P(1,-1,3) and perpendicular to the plane:       4x+3y-2z=6.

Q: Find the parametric equations for the line through the point (1, 7, 2) that is parallel to the plane…

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Q: Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a…

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Q: Find the parametric equations for the line through the point (5, 2,9) and perpendicular to the plan…

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 4x+2y…

A: Let F(x,y,z) define a surface that is differentiable at a point (x0,y0,z0), then the normal line to…

Q: What is the rectangular equivalence to the parametric equations? z (0) = 4 cos 0+2, y (0)=2 sin 0-5,…

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Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y2 = 8 ,…

A: We have given the surfaces; And the point (2,2,8)

Q: y+3x-6z=8

A: answer is in next step

Q: Prove that using the only the form of the given equation (no graphing) that it is a paraboloid.…

A: We need to prove that the the equation: x2+z2-y4=1 is a paraboloid.

Q: (3) Find parametric equations for the line of intersection of the planes. x + y - z = 2 and y + z =…

A: Given equation of the planes are  x+y-z=2     y+z=0 we rewrite them as x+y-z-2=0, and    0x+y+z=0…

Q: Provide parametric equations for the line passing through the coordinates (1, −3, 2) and…

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Q: Find the parametric equations of the line that is perpendicular to the plane 2x +y +3z = 4 and goes…

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Q: The angle and the parametric equations for the intersect line between planes x + y = 1, and 2x + y–…

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