Suppose point A(6,1) was rotated clockwise 90 degrees around the origin.  What is the x coordinate of A'?

Q: Find the equation of the circle passing through the points A(2,1), B(0,5), C(-1,2) using LU…

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Q: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: Find the length of one arc of the curve whose parametric equation are x=2θ-2sinθ and y=2-2cosθ.

A: We have to find length of arc whose parametric equations are : x=2θ-2sinθ and y=2-2cosθ Suppose 0 ≤…

Q: Graph the curve r = 1 - cos θ in the Cartesian xy-plane

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Q: 5) Find the orthogonal trajectory of the family of curve given by y = In(r+b) %3D

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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: Find the parametric equation for a line that is tangent (intersection) of the two fields below: −2x…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

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Q: Two children weighing 18 and 20 kilograms are sitting on opposite sides of a seesaw, both 2 meters…

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Q: Find three different parametrizations of the graph of y = x3.

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Q: 6. Find the image equation of the line -2x + y + 3 = 0 under the rotation about C = (1, 1) at an…

A: The resulting image is perpendicular to the given line.

Q: 7) What will be the coordinates of K' after a +90 degree rotation about the origin? Use parentheses.…

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Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2, 5/6). Sketch the…

A: To find the trajectories of the hyperbola write dydx by dxdy  and solve the system.

Q: Find the equation of the tangent line of the parametric equations x = 2 – 3 cos 0, y = 3+2 sin 6 at…

A: Given that: x=2-3cosθ and y=3+2sinθ

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

A: Given,

Q: Find the linear speed v for a point on the edge of a gyroscope of radius 83 cm, rotating 680 times…

A: To find the linear speed.

Q: Find the slope of the tangent line to polar curve r=9sinθ at the point (9/√2,π/4)

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Q: 4. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch the…

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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: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: Suppose that a projectile is fired into a headwind that pushes  it back so as to reduce its…

A: Given a projectile is fired into a headwind that pushes  it back so as to reduce its horizontal…

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 3x + 4y +…

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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: 4. Find the equation of the tangent plane at the point (-2, 1, -3) to the ellipsoid 22 + y? + = 3 4

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Q: Two children weighing 16 and 24 kilograms are sitting on opposite sides of a seesaw, both 2 meters…

A: Given,           Two children weighing 16 and 24 kilograms are sitting on opposite sides of a…

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

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Q: slime mold grows in a spiral pattern with polar radius . If the mold grows by continuing the spiral…

A: We have to find the Cartesian location of the endpoint at given angular velocity.

Q: A shape with rotational symmetry can be rotated around a point so that all of its characteristics…

A: Given : A shape with rotational symmetry can be rotated around a point so that all it's…

Q: find The unit Vectors tanent and normal to The ellipse x+2y= 6 at The Point (2,1).

A: Given, ellipse x^2+2y^2=6   point=(2,1)

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: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

A: We have to find parametric equation for a line that is tangent (intersection) of the two fields…

Q: Produce three isoclines with appropriate direction markers, and sketch one solution curve passing…

A: given differential equation is…

Q: u =1-1,y=6-2+름 x = 1-, y = 6-

A: We have given parametric equations x=1-1t, y=6-7t+2t2. First, evaluate the first derivative dydx. To…

Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

Q: 9. What will be the coordinates of point Nafter a 270 counterclockwise rotation about the origin?

A: When rotating a point 270° counterclockwise about the origin our point N(x,y) becomes N'(y,-x). This…

Q: polar Co-ovdina 4x²= y²-44+8

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

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Q: Find parametric equations for the path of a particle that moves along the circle x 2  + (y - 1)2…

A: A particle that moves along the circle .

Q: What solid of rotation is created here if the axis of rotation is the x-axis? -2

A: to find:- type of solid generated after rotation about the x-axis.

Q: 3. Parametrize the circle of radius 5 having centre (8, –3) and hence find a tangent vector and the…

A: We have to find parametric equation, tangent vector and tangent line for the given circle.

Q: find parametric equations for the given curve. Segment joining (1, 1) and (2, 3)

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Q: Find parametric equations of the line through (-3,1,1) that is parallel to 2i – 5j+k. -

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Q: Which of the following is the cylindrical coordinates of (-1, -/3,2)?

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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: 1) Find the parametric equations of the line that is tangent to circle x² + y² = 25 at point (3, -4)

A: Given, Equation of circle: x2 +y2=25 at a point (3,-4). now, parametric equation of the line is…

Q: Find the orthogonal trajectory of y=c cos x.

A: