A rectangle has its two lower corners on the x-axis and its two upper corners on the curve y = 49 – x². For all such rectangles, what are the dimensions of the one with largest area? NOTE: Enter the exact answers. width of rectangle %| height of rectangle

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

A: We have to find - the number of riding lawn mowers to produce in order to minimize average cost,…

Q: A car-leasing firm must decide how much to charge for maintenance on the cars it leases. After…

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Q: . The Minimum point of y = x3 3x+6

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Q: Find the equation of the quadratic function f whose graph is shown below. (5, 4) s(x) = | 10 12 14…

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Q: 5x+5 2. f(x) %3D x²+4x+4

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Q: Show that the equation x3 - 15 x + c = 0 has at most oneroot in the interval [-2, 2] .

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Q: The area of a parallelogram bounded by the y-axis, the line x=6, the line f(x) =6+2x, and the line…

A: The line parallel to y = 2x +6 will be of the form y = 2x + k…

Q: Find the x-intercepts (if any) for the graph of the quadratic function. 2) f(x) = x2 + 16x + 47 Give…

A: The X-intercept is a point where the y-coordinate is 0. You can find the x-intercept of a function…

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

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Q: 6. Determine the vertex and the axis of symmetry for f(x) = 3x2 – 5x + 12

A: We have given a quadratic function.  We have to find the vertex and line of symmetry

Q: Use a graphing utility to solve x3 - 3x2 - 4x + 8 = 0.Round answers to two decimal places.

A: x3 - 3x2 - 4x + 8 = 0.

Q: Find the Critical points of the ff equation and Determine the Maximum and Minimum. - 2. y= 4x -432x…

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

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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: The graph of the quadratic function f(x) = cx2 + d has a vertex at (0,8) and passes through the…

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

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Q: The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0? %D

A: Given,          The graph of y=fx is shown below :

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: A company's profit when it sells x thousand items is predicted to be P(x) = – 2x2 + 880x – 15000. a)…

A: function P(x)=-2x2+880x-15000 is given, Where in begining No items will be Sold.

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: 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: A rectangle has its two lower corners on the x-axis and its two upper corners on the curve y = 64 –…

A: Given that: y=64-x2

Q: Among all pairs of numbers (x,y)such that 4x+2y=22 , find the pair for which the sum of squares,…

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Q: What values of a and b, with a < b, minimize the value of (x* – 2r?) dr?

A: The given integral is ∫abx4-2x2 dx. Draw the graph of the function y=x4-2x2 as shown below. .

Q: Find the area of the largest rectangle that can be inscribed in the region bounded by the graph of…

A: Given: y = 4-x2+xArea of the rectangle = xyA = x(4-x2+x)= 4x-x22+x

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

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Q: Which is an equation with a degree of 4, zeros located at (4, 0) and (3, 0) and a y-intercept…

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Q: What is the vertex for this equation? f (x) = – (x + 3)² + 1 %3D

A: The given equation f(x)=-(x+3)2+1

Q: Find the maximum and minimum points in the curve, and identify intervals where the function is…

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Q: The average cost per hour is dollars of producing x riding mowers is given be the following: C(x) =…

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Q: A rectangular page is to contain 50 square inches of print. The margins at the top and bottom of the…

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Q: Tearabola has one x-intercept of x=-2 and an axis of symmetry of x=4. Which of the following…

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Q: 24. Find the point of inflection of the curve x3 – 6x2 + 2x + 14.

A: Using formula of point of inflection of the curve.

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: What is the vertex for this equation? f (x) = (x+3)² + 1

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Q: box

A: We will find out the height.

Q: Discuss the maximum and minimum of x?+y'+6x+12.

A: Given: x2+y2+6x+12

Q: Find the smallest root of the equation f(x) = 2x – 6x + 11x – 7 = 0

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Q: The daily profit from the sale of a product is given by P = 32x − 0.2x2 − 200 dollars, where x is…

A: Given that: P(x)=32x-0.2x2-200

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: Among all pairs of numbers (x,y) such that 6x+2y=36 , find the pair for which the sum of squares,…

A: Given,            Among all pairs of numbers (x,y)  such that 6x+2y=36 and to find the minimum value…

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

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Q: In the xy plane, the graph of the function f(x) = x2 + 5x + 4 has two x-intercepts. What is the…

A: x- intercepts are the points where the function touches the x-axis. So if the function touches the…

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: c(x)= .4x2+17x-291+2200/x grapg and find minimum

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Q: Determine whether the graph of q(x)=−6x3−7x2+8x+2 is concave up or down at the point with an…

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