A parabola property Let f(x) = x². f(x) – f(y) x - y %3D f(*"), forall x + y. a. Show that 2 b. Is this property true for f(x) = ax?, where a is a nonzero real %3D number? c. Give a geometrical interpretation of this property. d. Is this property true for f(x) = ax??

Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

Q: 3. Find the average height of a point on the semicircle y =4- x over the interval -2 < x S 2.

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Q: Find the absolute extrema of the function f(x, y) = x + y + 3.ry on the closed region bounded by the…

A: Absolute Maximum and Absolute Minimum

Q: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

Q: The cubic function y = ax3 + bx² + cx + d pass through (0, -6), (1, -2) and tangent to the line 3x –…

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Q: 02. What is the maximum or minimum of the function y = -x? + 2x + 4? A. maximum at y=5 B. minimum at…

A: Given that: y=-x2+2x+4

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Q: Consider the following. Rx) = - 18x? 4 Ix4 - 18x2 %3D Find all relative extrema. (If an answer does…

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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: 2. The figure below shows a point P on the parabola y = x2 and the point Q where the perpendicular…

A: Consider the given figure. Let's redraw the the figure and mention the points.

Q: Which of the answer choices best describes the domain of f(x, y) 49 + x2 – y? All points below and…

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Q: valuate f (z) dz.where C is the parabola y =x2 from z =-1+i ti 7 = 1+i and S (z ) = 6.x

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Q: Find formulas for the distances between (0, 0) and (a, a2 ), a &gt; 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b Occurs at the point…

A: The given parabola is : f(x)=x2+ax+b We need to find the values of a and b so that the minimum for…

Q: and the line perpendicular to Find the area of a triangle bounded by the y axis, the tine f(z) - 9 -…

A: We have to find the area of the region bounded by the y-axis, the line f(x)=9-67x, and the line…

Q: What is the maximum vertical distance between the line  y = x + 12  and the parabola  y = x2 for…

A: See the attachment

Q: Q4. (a) Divide “a” into three parts such that their product is maximum.  (b) Find the asymptotes of…

A: (a) We have to divide a number a into three parts such that their product is maximum. (b) Find the…

Q: Wrat is the equation in standard form of ahyperbola whose asymptotes are y=- うオー and y= -x- and a…

A: Given: y=32x-92         asymptote 1 to hyperbola                                         1y=-32x -32…

Q: 7. For whit value of b will the line y =- y 3x +4x -1? 2x+ b be tangent to the parabola

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Q: Minimum distance between the parabolas y² – 4x –8y + 40 = 0 and x² –8x –4y + 40 = 0 is (A) 0 (B) 3…

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Q: An airplane is flying at altitude H when itbegins its descent to an airport runway that is at…

A: Given- y=ax3+bx2+cx+d To find- dydx at x=-L. Formula used- The power rule of derivative. ddxxn=nxn-1

Q: A small aircraft starts its descent from an altitude of h = 6/5 miles, 4 miles west of the runway.…

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Q: Show that the equation of the tangent ine to 'the graph of the parabola at the point Pt'=(t,t²) 1s…

A: Consider the given function whose equation of tangent is required to calculate.

Q: y= 3* is an increasing function C. O d. y=x2-2x+1 represents a parabola

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Q: a) Determine the point at which the slope of the tangent to each parabola is zero. i) y= 6x2-3x + 4…

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Q: Q3 Determine the area of a surface when the curve y==x² 3 1 x², 1<x<3, is revolved about 2 the…

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Q: 1 3. The curved surface of a funnel is generated by revolving the graph of f(x) = x³ + on 12x the…

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Q: What is the maximum vertical distance between the line y = x + 42 and the parabola y = x for -6 s xs…

A: Consider the equation y=x+42 and y=x2; -6≤x≤7. Substitute y=x+42 in y=x2.…

Q: Find the point on the parabola x = t, y = t²,-∞ < t < ∞o, closest to the point (2, 1/2). (Hint:…

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Q: 2. Noemi had a 3 × 5 ft² piece of plyboard. She needs to have it cut it into a parabolic shape that…

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Q: a. Show that if the position x of a moving point is given by a quadratic function of t, x = At2 + Bt…

A: a) The position x of a moving point is given by,

Q: Find the points on the cone 2 = r² + y? that are closest to the point (4, 2, 0). (Hint: You can…

A: Here we use the distance formula  D=(x2-x1)2+(y2-y1)2+(z2-z1)2 where D is the distance between the…

Q: II1. True or False (no reasons necessary) If Vf(a, b) = 0, then f (x, y) definitely has a local…

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Q: To design the interior surface of a huge stainless-steel tank, you revolve the curve y = x3, 0 ≤ x ≤…

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Q: 3 A tangent to the parabola y = 3x? – 7x + 5 is perpendicular to . Determine the equation of the the…

A: A tangent to a curve is a line that just touches the line and in some sense is "parallel" to the…

Q: Q2/ Find the first moment about y-axis of the region in the first quadrant bounded by the x-axis,…

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Q: The region in the first quadrant bounded above by the parabola y = x ^ 2 below by the x -axis, and…

A: Follow the steps.

Q: స్థాగ The length of the curve y = Ex3/2 between x = 0 and x = 1 is %3D 2/3

A: Length of the curve=∫ab1+f'(x)2dxy=f(x)=23x32f'(x)=23×32x12=xf'(x)=xLenth of the curve between x=0…

Q: Find a parabola with equction Y=ax +bx+c that has a Slope I at x -1, slope 9 at x=-1, and passes…

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Q: 3(rnevious) Evaluate the flax of P=(3ry +3x)7-Z5 across Hhe the parabola y= 1-(x-o*, =1 A the closed…

A: Consider the given information: Let F→=3xy+3xi→-32y2j→ And the region is given by, y=1-x-12, x=1 and…

Q: Let F(x, y) = (x + 1)j, and let C be the portion of the parabola y = x² that starts at (0,0) and…

A: The integral ∫CF⇀.dr⇀ is positive. From the graph the angle between direction of F⇀ and dr⇀  is…

Q: For which parabola is the function f(x,y) Illustrate your answer. sin(xy) y-x² not defined?

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Q: 13. Calculate the area of the smaller region (to the left of the parabola) bounded by (x + 5)²=2y,…

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Q: What is the maximum vertical distance between the line y -x = 2 and the parabola y = x? in the…

A: We have to find the maximum vertical distance between the line y-x=2 and the parabola y=x2 in the…

Q: y= {(x) -2 -1 0 1 2 3/4 5 6 7 --2 %23 The graph of the quadratic function ƒ is shown in the xy-plane…

A: We have to check

Q: A bowl is in the shape of the graph of z = x2 + y2 from z = 0 to z = 10 in. You plan to calibrate…

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Q: 3 Find the area bounded by the curve y=-x3- 16 A) 8 square units (B) 10 square units C 4 square…

A: The region is bounded by the curves y=116x3-34x2+3x and the line y=x

Q: Consider the graph of (x^2) - (y^2/10) - (z^2/10) =1 1.What does the cross-section in the -plane…

A: The given equation represents a hyperboloid of two sheets.

Q: Find the absolute maxima and minima of the function on the given domain. 6) f(x, y) = 6x + 5y on the…

A: f(x,y) = 6x+5yfx(x,y) = 6     fy(x,y) = 5  (Hence No critical points of the function itself)Lets…