Question 9. 20 Jerry kicks a soccer ball which follows a parabolic trajectory given by: y = -x² +x wherey is the height of the ball at x metres away from Jerry. What is the maximum height of the ball? (291

Q: 14. Find the maximum and minimum values of the function f(x,y) y? = xy on the ellipse given by the…

A: Given f(x,y)=xy subject to    g(x,y)=x2+y24-1=0 We have to find the maximum and minimum values of…

Q: ine the orthogonal trajectories of the family of ellipses 16x² + 121y² = C. Sketch some of the…

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Q: 5. Find the maximum and minimum values f(x, y) = xy can take on the ellipse 4x²+y? = 16.

A: The given function f(x,y)=xy to the ellipse 4x2+y2=16

Q: 1 -2? + 4x +3 16 y = where a is the horizontal distance in feet from the point at which (a) How high…

A: The height y (in feet) of the ball thrown by the child is  y=-116x2+4x+3 ..................(1)

Q: Find the equations of both the tangent lines to the ellipse x^2 +3y^2 = 9 that passes through the…

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Q: Refer to the figure above. In the upward-sloping portion of the curve that connects points A, B, and…

A: Answer:- Independent

Q: Find the maximum and minimum values of the function f (x,y) = 2x² – y² on the ellipse p² + 2 (y –…

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Q: Derive the equation of the parabola with a focus at (-7, 5) and a directrix of y = -11. O (x)= (X +…

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Q: Find equations of both the tangent lines to the ellipse  x2 + 4y2 =36 that pass through the point…

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Q: Consider the following. x = et − 4,    y = e2t   Eliminate the parameter to find a Cartesian…

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Q: NOTE: Solve this as soon as possible, I need this urgently. If tangent lines to the ellipse 9x² +…

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Q: Figure 4.6 shows the curves y = Vx,x = 9, y = 0, and a rectangle with its sides parallel to the axes…

A: Given

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: Ex(4) A particle moves from point (-2,5) to y-axis in such a way that Ay = 3Ax. Find its new…

A: Solution is given below:

Q: Find the point(s) on the hyperbola x^2 - y^2 = 2 closest to the point (0, 1).

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Q: Evaluate fF dR given that F(x, y) = 2yî + (xy – 2x)j and C is the curve in the third quadrant from…

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Q: Find the point on the hyperbola xy = 8 that is closest to the point (3,0)

A: Given: xy=8 so, y=8x now any point of given hyperbola can be written as x,8x so, let's that point on…

Q: State the equation of the parabola which has a focus of (9, 3) and a directrix of y = -3. (Let a be…

A: To find the equation of the parabola having focus and a directrix, let we choose (x, y) be any point…

Q: The graph of the curve described by the paramnetric equations x = 3t – 4, y = 6t + 2 is a straight…

A: Consider the curve  x=3t-4,y=6t+2

Q: Question 24 Fit a least-squares parabola having the form y = a + bx + cx- to the given data. 1.2 1.8…

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Q: Find the y-intercept of the tangent to the ellipse x + 3y = 1 at the point %3D 1/2

A: We differentiate both sides with respect to x and then solve for dy/dx

Q: Sketch the graph of y = m(r) in Figure 2. %3D 음-3, rS-1 m(x) = 4 %3D 1<r<5

A: Given,          mx=13x-3x≤-141&lt;x&lt;5

Q: 1. Find the minimum and maximum values of f(x,y) : = x²y on the ellipse 4x? + 9y? = 36. %3D

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Q: for the given audratic equation determine, i- which way the parabolla opens ii- the cordinate of…

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

A: We have the given function is f(x,y)=xy    ..... (1)   The equation of ellipse  x2+y24=1 Let…

Q: Зу — 4у 3D —х — 2 The curve above can be parameterized as which of the following pairs of equations?

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Q: An equation for the level surface passing through the point (2,0, - 1) is z =

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Q: Find the equation of the line tangent to the hyperbola x2 −y2 =16 at (5,3).   Give your answer in…

A: The line is tangent to the given hyperbola at (5,3).Tangent line is a straight line.Therefore, the…

Q: Consider the following.x = et - 6y = e2t(a) Eliminate the parameter to find a Cartesian equation of…

A: From the equation for x, write t in terms of x.

Q: 1. Let P(r1, y1) be a point on the parabola r? be the angle between the parabola and the line…

A: angle with a curve at a point means angle with tangent line at that point of curve .

Q: Given the parabola y=2x2. A secant is drawn through the 2 points of the parabola, which have the…

A: Basic strategy for this question is that we will find the slope in two ways and then equate them to…

Q: Find an equation for the parabola that has its vertex at the origin and satisfies the given…

A: Solution Given V=(0,0)F=(a,0)=(5,0)To find the equation of the parabolaFormula:y2=4ax

Q: Question 17 Find the point on the parabola y= - x¯ whose tangent line is parallel with y= 3x-5 +4 3…

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Q: 14. Find the maximum and minimum values of the function f(x,y) = xy on the ellipse given %3D by the…

A: Let f(x,y)=xy subject to     g(x,y)=x2+y24-1=0 We want to find extreme values of f(x,y)=xy on the…

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: - Find a parabola with equation y = ax? + bx +c that has slope 4 at x = 1, slope –8 at x = -1, and…

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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: 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: Question 6 In the xy-plane, what is the y-intercept of the graph of the equation y = V4 -T?

A: Let's find.

Q: Find the extreme value of the function f(x, y) = xyon the ellipse x2 + 2y2 = 1.

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Q: At what point does the normal to y = 2x2 – (3 + 2x) at (1, –3) intersect the parabola a second time?…

A: Given: y=2x2-3+2x Point: 1,-3 Objective is to find the point where the normal to y=2x2-3+2x at…

Q: The point on the curve x? + 2y = 0 that is nearest to the point (0,-;) occurs where y'is A) 0 B)…

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Q: 3. Find equations of both the tangent lines to the ellipse x²+4y?=36 that pass through the point…

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Q: Discuss the properties of the curve (w/ solution) and sketch fully: y = x?e-*

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Q: Let f(x, y) = x? + 4y. Find the extreme values of f on the ellipse x? + 2y? = 1.

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Q: 1. Find the point on the parabola y = 3 – x² that is closest to the point (6, 0).

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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: Solve the following problems. Show the complete solution. What is the equation of the line to the…

A: For tangent line first  find the slope of the line at that point ..then find the equation of line

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…