A rectangle has its two lower corners on the x-axis and its two upper corners on the curve y = 64 – x². For all such rectangles, what are the dimensions of the one with largest area? NOTE: Enter the ezact answers. width of rectangle = height of rectangle

Q: Find the value of x for which y = x5 – 5x3 – 20x – 2 will have a maximum point.

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Q: Find the longer dimension of the rectangle enclosed in a semicircle y=V144- x2 with the largest…

A: Suppose the dimension of the rectangle is x & y. Now, the height of the rectangle should be…

Q: 5x+5 2. f(x) %3D x²+4x+4

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Q: (3) If a projectile is launched into the air at 29.4 feet per second from aheight of 60 feet, its…

A: 3. given that                                                         u=29.4 feet per secondh=60…

Q: 4. Use the Intermediate Value Theorem to show that the equation 2x3 + x – 2 = 0 has a root in the…

A: The given equation is 2x3+x-2=0 has a root in the interval -1,1

Q: The average cost per hour in dollars of producing x riding lawn mowers is given by the following.…

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Q: Complete the following questions and submit them to the dropbox. 1. Find the minimum value of the…

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Q: Q2. Use Lagrange Multiplier to find the point on the circle: x² + y² = 45 that are closest farthest…

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Q: Find the intercepts and the vertical asymptote of   f(x)=x2−4x−5/x−6 Enter the intercepts as…

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Q: Find the points of discontinuity for 3(x+2)2 x3 + 4x2 + x – 6 a) h(x) = 6х— х2 b) f(x) = 9 – x2

A: we will find domain in second question and then find discontinuos  point.

Q: Given the equation  5x2 = 6x + 18 determine: The minimum value of y

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Q: A rectangle is bounded by the x-axis and the semicircle y = √(25 − x2). What length and width should…

A: Given, A rectangle is bounded by the x-axis and the semicircle y=25-x2. The figure,

Q: Find the dimensions of the rectangle of maximum area having two vertices on the x-axis and 2…

A: Let the rectangle has its two vertices on x-axis and remaining two vertices on the parabola y=4-x2.…

Q: Find the dimensions of a rectangle with an area of 100 square feet that has the minimum perimeter.…

A: Given P=2x+2y ....... (1)           A=xy           Area A=100 square feet that is 100=xy, then…

Q: Find the vertex, zeros, the X-intercept(s), and the y-intercept of the quadratic function f(x) =…

A: Consider the following function: fx=2x+92+3 Compare above equation with y=ax-h2+k: h=-9, k=3 Hence,…

Q: IV. The path of a ball is given by y = - 16x? + 48x + 5, where y is the height of the ball and x is…

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Q: Find the area of the largest rectangle with one corner at the origin, the opposite corner in the…

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Q: Find, in factored form, the equation of the quartic function y that has been graphed. Let the…

A: We have to find the quartic equation represented by the given graph.

Q: 3) Find the minimum and maximum values y = 2x5 +5x² on the interval [-2,2]

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Q: The path of a diver is modeled byf(x) = (−4/9)x2 + (24/9) x + 12where f(x) is the height (in feet)…

A: Givenf(x) = -49x2+249x+12here, a = -49 , b = 249this is downward opening parabola.

Q: Find the curvilinear asymptote. x4 - x² – 5 (x) x² - 3 y =

A: We will find the curvilinear asymptote of the given function.Below find the solution in the image.

Q: If y = x2 - 4x and x = square root of (2t2+1), find y' when t = square root of (2)

A: Explanation of the solution is given below...

Q: Determine the graph of g = x^2 + sqrt of (x + 1) and solve for its extrema, concavity, and points of…

A: Please see the below picture for detailed solution.

Q: he quarterly profit (in thousands of dollars) of Cunningham Realty is given by P(x) = -x2 x² + 9x +…

A: Given data:   The given expression for the quarterly profit function is P(x)=-x2/3 +9x +28. The…

Q: A rectangle is bounded by the x-axis and the semicircle  y = square root of (49-x^2)  (see figure).…

A: Let the length along the x axis is = 2x So the height= 49-x2 So the area is: A=2x49-x2

Q: Draw the given optimization problem and solve. Find the area of the largest rectangle (in units)…

A: Since, We have to find area of the largest rectangle that fits into the triangle which sides form by…

Q: Use desmos to find the vertex for f (x) = x² – 6x + 13. -

A: Given :- f(x)=x2-6x+13 To find:- use desmos to find vertex

Q: True or false: The y-coordinate of the vertex of f(x) = 4x² – 16r + 300 is f(2). . %3D

A: Given quadratic expression is: fx=4x2-16x+300 Let y = f(x) We have to find the vertex of f(x).

Q: Express y=-2x2+6x+12 in completing the square form. Hence, find the maximum/minimum values of each…

A: We will find out the required values.

Q: If a projectile is fired straight upward from the ground with an initial speed of 96 feet per​…

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Q: The back of Jill's property is a creek. Jill would like to enclose a rectangular area, using the…

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Q: Q4B: Find min,max points for y = 2x- x2 %3D

A: The given function is y=2x-x2. Compute the critical point as follows. y'=0ddx2x-x2=02-2x=02x=2x=1…

Q: A window has perimeter 10 m and is in the shape of a rectangle with the top edge replaced by a…

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Q: Which quadratic function has it's vertex at (-2,7) and opens down? a. y = -3(z + 2)² +7 b. y = -12(z…

A: To find the quadratic equation

Q: The white square in the drawing below is located in the centre of the grey rectangle and has a…

A: Given: The white square in the drawing is located in the centre of the grey rectangle and has a…

Q: A church window consisting of a rectangle topped by a semicircle is to have perimeter p . Find the…

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Q: Find the x coordinate of the vertex: f(x)= 3x-4x+1 %3D

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Q: If the zeros of the function f(x) = x² + 16x + 60 are x = -6 and x = -10, wl are the coordinates of…

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Q: а. What is the maximum value of f(x) = -2x² – 4x + 3? The figure shows a segment joining the…

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Q: Find the absolute maximum and absolute minim r) 3x- 12x + 5, [1.71

A: The function represents a quadratic function. Its leading coefficient is 3 which is greater than…

Q: Find the longer dimension of the rectangle enclosed in a semicircle y=V144- x2 with the largest…

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Q: Consider the equation below. f(x) = 2x3 + 3x2 − 252x   Find the local minimum and maximum values of…

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Q: 4 f(x) = 2x + 7m (т — х)2

A: For m=9, to to find the extrema of: fx=2x+7m-4m-x2

Q: Consider the following quadratic function. f(x) = 2x2 + 36x + 169 Find the vertex. (x, y)=

A: Consider a quadratic equation

Q: A rectangular box for a new product is designed in such a way that the Three dimensions always have…

A: Given: A rectangular box for a new product is designed in such a way that the Three dimensions…

Q: Determine the point/s of discontinuity, if there is any, and the type of discontinuity at that…

A: h(x)=x-2x2+2x-8The function will be discontinuous at point where denominator is zeroconsider…

Q: use graphs to find approximate solutions 2x = 5

A: Given that, 2x=5

Q: The slope of the graph of the function y = 2x at (32,8) is %3D Tuno n mplifGed fraction

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Q: The number of photo copies distributed is given by C = 50t² - 200t + 10000, where t is in years.…

A: Here, C=50t2-200t+10,000

Q: Find the local extrema of the cubic functionf(x)=x3−3x2−9x+2.

A: Differentiating with respect to x, we get Again differentiating with respect to x, we get