A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 1 – x². WF are the dimensions of such a rectanale with

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 4 – x². What…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

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Q: For Exercise, find an equation of the form  y = ax2 + bx + c that defines the parabola through the…

A: Consider the given equation of parabola:

Q: Prove that for any point (a, b) ≠ (0, 0) on the parabola y = x2 , the normal line intersects the…

A: The given equation of parabola is y=x2  For the point (a,b)≠ (0, 0), the slope of normal is and at…

Q: For the hyperbolic PDE u, +bu, =0 a) Find the finite difference equation, using forward for u, and…

A: Given: The given hyperbolic PDE  ux + buy = 0 a) To find the finite difference equation, by using…

Q: C) lie in the parabola 16y = 160 – x². Find the maximum area of the triangle if side rtices B and C…

A: Sol

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 12 –…

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Q: 3) Fit a parabola to the data. X 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y 3.1950 3.2299 3.2532 3.2611…

A: Given : x y 0 3.195 0.1 3.2299 0.2 3.2532 0.3 3.2611 0.4 3.2516 0.5 3.2282 0.6…

Q: Compute the length of the latus rectum of the parabola y2 + 8x – 6y + 25 = 0.

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Q: has its vertex at the origin and has directrix at z = 38

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Q: 2. Circle the parabolas that are stretches of the graph y = x². а) у3 1.25х? c) y = – x? b) y = 0.25…

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Q: Show that the center of the osculating circle for the parabola y = x2 at the point (a, a2) is…

A: We need to show that the centre of the osculating circle for the parabola y = x2 at the point (a,…

Q: rectangle is Mnscribed with its base on the x-is and its uper corners on the parabola y Ae the…

A: We have to find the width and height of rectangle .

Q: In the xy-plane, if the parabola with equation y = ax² + bx + c, where a, b, and c are constants,…

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Q: /hich of the following is an endpoint of the latus rectum of the parabola = = 4(x – 1)2?

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: Draw the parabola y=7-x^2.

Q: What is the equation of the parabola containing the points (0, 5), (–1,9), and (2, 3)? O y = r-z+5 O…

A: The standard form of a parabola is y=ax2+bx+c. The required parabola passes through the 3 points are…

Q: 3) Fit a parabola to the data. X 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y 3.1950 3.2299 3.2532 3.2611…

A: The equation of a parabola is y=a+bx+cx2. The method of least square can be used to obtain the best…

Q: Fit a second degree parabola to the following data : 1.0 1.5 2.0 2.5 3.0 3.5 4.0 y 1.1 1.3 1.6 2.0…

A: The equation is y=a+bx+cx2 ∑y=na+b∑x+c∑x2 ∑xy=a∑x+b∑x2+c∑x3 ∑x2y=a∑x2+b∑x3+c∑x4   make a table as…

Q: A point moves on the parabola 10y = 5x² + 3 in such a way that when x = 6, the abscissa is…

A: Given: A point moves on the parabola 10y=5x2+3, when x=6 the abscissa is increasing at the rate of 2…

Q: 19. Find the total area between the parabola y = x² - 4x, the x-axis, and the ordinates x = -2 and x…

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Q: Find the asymptodes of Hx)= x²- 5x+6 the funchion given below X-2

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Q: 19. Find the total area between the parabola y = x2 - 4x, the x-axis, and the ordinates x = -2 and x…

A: We can use integration to calculate the area

Q: Find the dimensions of the reclanyie uf iurg lying on the parabola. y = 6- x2 width units height…

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Q: A rectangle is inscribed in the parabola y=8– x - such that one side lies on the x-axis and two…

A: Answer

Q: A rectangle has its two lower corners on the x-axis and its two upper corners on the parabola y = 7…

A: here the width of the rectangle is  w=2x and the right is l=7-x2

Q: Let F(r, y) = (x + 1)7, and let C be the portion of the parabola y = x² that starts at (0,0) and…

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Q: Sketch the parabola y = x² + 2x +1. Use arrows to indicate the maximum and minimum values of y over…

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Q: The area bounded by the parabola y2 = 4ax, its axis, and its latus rectum revolves  about the x-

A: The given equation of parabola is y2=4ax. The objective is to calculate the area bounded by the…

Q: Given the point P =,(a,b) in the first quadrant, find the downward-opening parabola that passes…

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Q: A rectangle is inscribed with its base on the z-axis and its upper corners on the parabola y = 5-z.…

A: Let the width(side resting on x-axis) be 2x , since rectangle is symmetrical around y-axis so height…

Q: The vertex of the parabola f(z) = z²+ 14z + 10 is %3D

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Q: Find the two values of c such that the area of the region enclosed by the parabolas y = x² – c² and…

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Q: 8. Find the function that will generate the points on a parabola that opens down, has a base of 4…

A: A parabola has base 4 and height 6

Q: Find the vertex, focus and endpoints of the latus rectum of the parabola  4y^2 - x + 2 y = 0

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Q: What is the largest possible area of a rectangle inscribed in the region bounded by the parabola y =…

A: According to the figure, we have

Q: =r such that the point (2, 1) is on the segment AB and the midpoint of Determine the coordinates of…

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Q: If a chord of the parabola y? = 4ax is a normal at one of its ends, show that its mid-point lies on…

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Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. 2(x -…

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Q: The points P(ap2 , 2ap) and Q(aq2 , 2aq) lie on the parabola y2= 4ax. Prove that if PQ is a focal…

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Q: 2. Find the dimensions of the rectangle of largest area that has its base of the x-axis and its…

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Q: If a parabola defined by f(x)=2−x^2 is inscribed under an equilateral triangle ABC, so that the…

A: Given data:     The given equation of parabola is: f(x)=2-x2.     The below figure represents the…

Q: 3) Fit a parabola to the data. X 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 y 3.1950 3.2299 3.2532 3.2611 |…

A: The equation of parabola : y=a+bx+cx2 . And, normal equations are : ∑y=an+b∑x+c∑x2 ∑xy=a∑x+b∑x2+c∑x3…

Q: Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)…

A: The quadratic function is given by fx = 2x-32+1 To evaluate : The vertex of the parabola defined by…

Q: Show that the envelope of the family of circles whose diameters are the double ordinates of the…

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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: below Find the asymptoles of the funchion given Hx)= x²- 5x+6 (x-2) Cx+3)

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Q: Find the asymptoles of the funchon given below Hx)= x²- 5x+6 (x-2) Cx+3)

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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: If P(a, a²) is any point on the parabola y = x², except for the origin, let Q be the point where the…

A: To Determine: If P(a,a2)is any point on the parabola y=x2,except for the origin,let Q be the point…

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.