What is a directrix?

Q: Explain why the Pythagorean Theorem is a special case of the Law of Cosines.

A: Consider the following figure: Law of cosine: c=a2+b2-2abcosθ

Q: If a projectile is launched from the ground, sketch the shape of its trajectory.

A: Given data: Projectile motion.   Projectile motion is a two-dimensional free-fall motion in which an…

Q: Convert from rectangular to polar coordinates: (3,√3)

A: Given point is (3,√3). Let us consider, r cos θ=3   ;   r sin θ=3 Then we get, r2cos2 θ+sin2…

Q: if you rotate a right triangle , what feature of the triangle change?

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Q: How is it possible for two different rotations to define the same angle?

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Q: The measure of ABC is 120. What will be the measure of ABC if it is rotated about the origin (0,…

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Q: Name the line of reflection used to map each pre-image to its image

A: When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate…

Q: explain why any rotation can be described by an angle between 0° and 360°

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Q: Find parametric equations to represent the line segment from (-2, 7) to (3, -1).

A: on solving this we get

Q: If there is a 60° angle from the positive x-axis to the positive x′-axis, explain how to obtain the…

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Q: How do you find the angle between two intersecting planes?

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Q: An elliptical pool table has a ball placed at each focus. If one ball is hit toward the side of the…

A: An elliptical pool table has a ball placed at each focus. The definition of the ellipse is "The set…

Q: Plot the point (r, theta) = (6, 181) %3D Clear All Draw: Dot

A: we know that r= 6 will give a circle of radius 6 and center at originand angle θ varies from 0 to…

Q: change from polar to cartesian Corordina tes (3,)

A: We have to change the cordinate

Q: Convert from rectangular to polar coordinates: (1, 0)

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Q: An architect continues to rotate the umbrella in a counterclockwise direction until it is in its…

A: To find: The angle of rotation: Given: The architect rotates the umbrella in counterclockwise…

Q: What is the focal width and the Axis of symmetry? Given that Focus= (2,3) and Directrix=7

A: For the Parabola, given that focus is (2, 3) and directrix is x=7.

Q: An elliptical pool table has a ball placed at each focus.If one ball is hit toward the side of the…

A: Our Aim is to tell what will occur if one ball is hit towards the side of thetable provided that an…

Q: A triangle is drawn on the grid below. Which graph shows the triangle rotated 180° about the origin?

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Q: It %3D -> Retined Tcu) = Au, find The spectzem. %3D -17

A: See the detailed solution below.

Q: Plot the point whose polar coordinates are 3, 3.

A: the given polar coordinate is  here we have

Q: A security camera in a neighborhood bank is mounted on a wall 10 feet above the floor. What angle of…

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Q: What do Negative radial coordinates represent?

A: The radial coordinates in polar coordinates system is represented by r,θ when radial coordinates are…

Q: Find the new coordinates of the point (2, 4) if the coordinate axes are rotated through an angle of…

A: By rotation through an  angle θ the new cordinates x',y'of the coordinate x,y…

Q: to rectangular coordinates.

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Q: Convert from rectangular to polar coordinates:(−2, 2)

A: The rectangular coordinate system includes the points of the form x,y . The rectangular coordinate…

Q: A million years ago, an alien species built a vertical tower on a horizontal plane. When they…

A: Given points (0,0,0)  , (2,2,0)   , (0,3,2)first we find cross product of (2,2,0)    and…

Q: Find polar coordinates of the point whose rectangular coordinates are (0, -4). Express θ in radians.

A: Rectangular corrdinates = x,y = 0,-4Let, the polar coordinates be = r,θFormula for calculating r and…

Q: Describe fully a single transformation that would map triangle VAC onto triangle V"A"C". (b)

A: A single transformation which maps triangle VAC onto a triangle V"A"C" Is reflection in y- axis.

Q: a boat travels towards the northeast at 23 knots and there is an 8 knot crosswind out of the…

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Q: What is 2cis(–π/3) in rectangular coordinates

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Q: Graph the image of square RSTU after a rotation 270° counterclockwise around the origin.

A: Square RSTU lies in 3rd Quadrant. So, after rotating at an angle of 270° counterclockwise around the…

Q: A car passes through an intersection traveling East at 60 miles per hour. A camera is positioned 3…

A: Given speed of the car is 60mph towards East. ⇒dxdt=60mph; x is the distance car traveled from…

Q: Can you please help me finish solving this right triangle?

A: We use the Pythagorean theorem to find a

Q: New Challengel Find the angle coterminal to - 35°, if you travel around the xy-axis in the positive…

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Q: Any polar equation can be made rectangular.

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Q: Explain how the double-angle formulas are derived.

A: sinx+y=sinxcosy+cosxsinycosx+y=cosxcosy-sinxsinytanx+y=tanx+tany1-tanxtany

Q: Find rectangular coordinates in exact form

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Q: Plot uie points with polar coordinates (3, –n) and -6, 3 *) using the pencil. 2 4. 6.

A: The polar co-ordinates are of the form (r,θ)  To plot the polar points it is necessary to find  θ…

Q: Describe the angle and center of rotation that will carry the rectangle onto itself.

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Q: how do you find the central angle of a sector

A: Central angle:             An angle whose vertex is the center of a circle and whose sides passes…

Q: Please provide solution to the attached question on 3D Geometry.

A: From the given equations of line in Cartesian form, we can write down direction vector and a point…

Q: Maximize the angle theta between the given triangles please help

A: As per the figureAB = 6In smaller triangleBase (AP)        = (6-x) unitsPerpendicular = 3 units cotγ…

Q: What word is produced by a 180° rotation about the point? МОМ

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Q: Explain how to convert (6.3, 3.8) from rectangular coordinates to polar coordinates.

A: Find the magnitude and angle of the point from the positive x-axis.

Q: Which polar coordinate has the same point as (1,sqrt(3))?

A: Answer and explanation is given below..

Q: Describe the test for symmetry with respect to the pole.

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Q: Which 2D perspective below is the top perspective of the following image?

A: The options for the top perspective are not given, yet I will the 2d top perspective of the given…

Q: Give me the coordinates of rectangle TUVW after a rotation 180° counterclockwise around the origin.…

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