23. A 20-in. satellite dish for a television has parabolic cross sections. A coordinate system is chosen so that the vertex of a cross section through the center of the dish is located at (0, 0). The equation of the parabola is modeled by x² = 25.2y, where x and y are measured in inches. -10 10 a. Where should the receiver be placed to maximize signal strength? That is, where is the focus? (See Example 1) b. Determine the equation of the directrix.

Q: b) Consider now the portion of the parabola which is below the line y = 2. Which points have the…

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Q: 5. Calculate the area of a regular hexagon inscribed in a circle of radius 1 unit. a. 1.316 units b.…

A: Area of equilateral triangle = 34 a2 ; where , 'a' is the sides . Note : As per our Guidelines , we…

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given y? by the…

A: According to the given information, it is required to find the maximum and minimum value of the…

Q: 3) Assume that the parabola y=x is translated so that its vertex is (5,-4). If the parabola is…

A: According to question given that  y=x2, vertex is (5,-4)

Q: 19. Find the area of the largest rectangle with lower base on the x- axis and upper vertices on the…

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Q: The graph shows the normal lines from the point (2,0) to the graph of the parabola x = y?. How many…

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Q: 3- The parabola y= ax'+bx+e, mean that the equation y ax' is . .........

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Q: 2=2X Find the point that is close' to the pont'(,4) on the parabola y

A: Explained below

Q: 13. The parabola y = x2 + x + 1 opens: A. To the right %3D B. To the left C. Upward D. Downwarč

A: y=x2+x+1 here parabola is in the form of y=ax2+bx+c which means it can be open up or down…

Q: 16.) A woodland jumping mouse hops along a parabolic path given by y=-0.2x+ 1.2r where x is the…

A: We will find the maximum value of y, which will represent the maximum height that the mouse can jump

Q: Find the maximum and minimum values of the function f(x, y) = xy on the ellipse given. y? by the…

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Q: Given the 1-parameter family of parabolas y = trajectories of the family if the angle of…

A: We are given: y=ax2 Now, we will find the tangential slope, dyTdx=a×2x⇒dyTdx=2ax…

Q: 3. Fit a second degree parabola y = ax? + bx + c to the following data %3D 3. 4 y 1 1.8 1.3 2.5 6.3…

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Q: Find the minimum speed of a particle with trajectory c(t) =(t 3 − 4t,t 2 + 1) for t ≥ 0. Hint: It is…

A: Given a particle with trajectory : c(t)=(t3-4t , t2+1)    for t≥0 We need to find the minimum speed…

Q: c. Choose the correct description of the level curves of f(x,y) = In (3x? + 3y?). O A. Circles B.…

A: To find the level curves of the function fx,y=ln3x2+3y2.

Q: 2. Consider the equation r = 4 – y². (a) Find a parameterization of the segment of this parabola…

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Q: Find the values of y where the straight line y = x+1 intersects with the parabola y = 4x? + 3.…

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Q: 2. Write the general equation of the parabola with directrix at x FG,-1), and v (. -1). 2

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Q: Find the y-intercept and any x-intercept(s) of the parabola with equation y = -(x + 7) + 16. If the…

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Q: 1. Fit a (a) straight line (b) parabola to the given data points: X 1 3 4 6 7 8. y 1 1.5 2 3 4 5 8.…

A: (a) straight line

Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

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Q: 1. Which is the equation of a parabola that is concave down with a y-intercept of 5? 1. y -+ 5x +1…

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Q: 13. Find the point on the parabola y* = 2x that is nearest the point (1, 4). %3D

A: As per our guidelines we can solve only one question or three sub-parts. To ask more please…

Q: d the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter DNE.)…

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Q: 1. If y varies indirectly as a, and y = 3 when a = 4, what is y when a = 6? %3D y = 2 y = 1 y = 4 y…

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Q: The orthogonal trajectory of y= Ce" is a parabola of the form y = ax+b. what is the value of b so…

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Q: 8. Find the equation of the surface of revolution if the generating curve, 2x – 4y = 6 is revolved…

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Q: 4. Consider the equation of the hyperbola given by x2 + 2xy – y² = 7. Find an equation of the…

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Q: Find the equation of the normal line to the parabola y=x^2+2x−3, that is also parallel to −2x+2y=9

A: Given that normal line to parabola is parallel to -2x+2y=9. Slope of the line -2x+2y=9 is -…

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A: Given: The given reflector is 7 inches wide and 2 inches deep i.e. (x,y)=(2,3.5)

Q: drawn from the point A(2,10) on the parabola y = x^2 + bx + c Since the tangent is parallel to y =…

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Q: Given f(x, y) = x² – 4y, the parabola x - 4y = 8 = 0 is the level curve o -8 None of the given…

A: The solution is given below

Q: The equation for the line of best fit for some data comparing the height of a candle (H) with time…

A: Let the independent variable denoted as time (T) Let the dependent variable denoted as height of the…

Q: Find the length of the parabola given by c(t) = (t, t2) for 0 ≤ t ≤ 1.

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Q: 28. Find the directrix for the parabola. (y+ 3)2 + 8 2x x = 4 y = } 7/2

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Q: Find the smallest outputs of the function x^2+2y^2 on the slanted ellipse x^2+y^2+xy=3

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Q: 9.  Find the shorted distance from point A(2, 1/2) to a point on the parabola y = x2. And find the…

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Q: A train is moving at 15 m/s, while steam is shut off and brakes are applied. The speed of the train…

A: Consider the continuous function f(x) defined on an interval a,b. Then the Trapezoidal rule…

Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: First I have find the function f(x,y) and then decide the constraint.Then using Lagrange multipliers…

Q: Given f(x, y) = x² - 4y, the parabola x² - 4y - 2 = 0 is the level curve of fat 02 0-2 01 00 None of…

A: Ggg

Q: A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating…

A: Let's find how far from the vertex should the bulb be placed.

Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: O1- The straight-line AB of true length 12 cms, is inclined 25 ° to V.P., and having the following…

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Q: A parabola having its x axis parallel to the y-axis has its focus at (5,6) and vertex at (5,4).…

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Q: The line x=C where C70 intersects the cubic y= 2x3 + 3x²-9 a七 the point P and parabola y = 4x+ 4x +5…

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Q: I For the parabola -2x = 16y + 4y² + 13, for what value of y does x have a minimum? 3. If the

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Q: 1) Find the intercept(s) and vert ex of the parabola. y=x^2-1

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Q: 6- Which of the following is the shortest distance from the point (15, 0) to the curve y = V6x ? a)3…

A: Solution: The objective is to find the shortest distance from the point (15,0) to the curve y=6x

Q: 16. Evaluate (x + V9) ds where C consists of two segments: the part of the parabola y = x² from…

A: In the given question we have to evaluate the integral ∫C(x+y)ds where C is the regionconsist of two…