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

Q: Q2/ Find the area of a region bounded by the curve f(x) = 8x' and x-axis and the two lines x=1, x=3.…

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Q: You are designing a rectangular poster to contain 27 in? of printing with a 3-in margin at the top…

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Q: A box with no top is to be built by taking a 12"-by-16" sheet of cardboard and cutting x-in. squares…

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Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two positive number is 750. The sum of one and 10 times of another is minimum.

Q: A rectangular corral of 486 square meters is to be fenced off and then divided by a fence into two…

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Q: limit the of solution The مرفق

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Q: Find area of region f(x)=x2-10x+9 g(x)= -x2+8x+9

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Q: 2 Find the average value of the function f(x) = 6x² on the interval 3 < x < 5

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Q: A company that produces cell phones has a cost function of C = cost in dollars and x is the number…

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Q: By the use of local linear approximation of g at x=2, estimate g(-1.998) if g(-2)=-1 and g’(-2)=10

A: local linear approximation formula for g(x)g(x)=g(a)+g'(a)(x-a)

Q: A manufacturer has determined that the total cost C of operating a factory is C = 2.5x2 + 75x +…

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Q: (b) Find the value of r that minimizes V(r).

A: 8(b) The expression for Morse potential is given by Vr=e-r-Ae-ar, r&gt;0, where A and a are positive…

Q: A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a…

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Q: Find area of region f(x)=x2+4x+4 g(x)=4x+13

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Q: 6. Find the maximum area of a rectangle in the first quadrant where one side of the rectangle lies…

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Q: Find the point on the graph of y = 1x that is closest to the point (2, 0). [Hint: 2(x - 2)2 + y2 has…

A: Given: y=x Let the point closest to (2,0) be P(x,y). Distance between point P(x,y) and (2,0) is:…

Q: The upper right-hand corner of a piece of paper, 15 in. by 4 in., as in the figure, is folded over…

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Q: Find the area of the region bounded by the graph of f(x) = 4 – x², the x-axis, and the vertical…

A: function f(x)=4-x2 To find area of region bounded by f(x), x-axis and the line x=1 and x=2.

Q: Find two positive numbers x and y that maximize Q = x2y if x + y = 2.

A: Given function - Q = x2y               ...........(1)And,x+y = 2y = 2-x…

Q: 1. Find non-negative numbers x and y such that x + y = 150 and ²y is maximized. 2. You are to…

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Q: A small island is 5 miles from the nearest point P on the straight shoreline of a large lake. If a…

A: Let 'x' be the distance from point to the landing position. Given situation in graph is represent as

Q: 9. The difference of two numbers is 30. What two numbers will minimize the prod- uct?

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Q: Find two positive integers such that their sum is 10, and minimize the sum of squares.

A: Given  two positive integers such that their sum is 10, To minimize the sum of squares

Q: You are designing a rectangular poster to contain 75 in? of printing with a 3-in margin at the top…

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Q: The upper right-hand corner of a piece of paper, 12 in. by8 in., as in the figure, is folded over to…

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Q: A piece of wire of length 67 is cut, and the resulting two pieces are formed to make a circle and a…

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Q: The area bounded by the curve y = 14.x and the lines x = 4 and x = 6 above the x- axis is 364 square…

A: Area=∫ab(upper curve-lower curve)dx∫xndx=xn+1n+1+C

Q: 3. Prove that of all rectangles with a given area, the one with smallest perimeter is a square. (Let…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 8. Find the area bounded by y = (11 – x)7, the lines 3x=2, x=10, and the x-axis.

A: We have to find volume of solid generated by revolution.

Q: 2 Find the area of a triangle bounded by the y axis, the line f(x) = 8 – -x, and the line…

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Q: if we have the following polynomial regression function Yi=5-24X+2(X^2)+ei. then the value of Xi…

A: An estimated polynomial model of y on x of order 2 can be written as

Q: Two positive numbers x and y add up to 100. What values of x and y will minimize 1² + 3y?

A: Given that x&gt;0 ,y&gt;0 and x+y=100 To find the values of x and y such that x2+3y will minimize.…

Q: Minimize F = 24x2 + 24y2 with xy2 = 16.

A: Minimize F = 24x2 + 24y2 with xy2 = 16.

Q: the number and its reciprocal.

A: Given: The smallest sum of a number n and its reciprocal 1n is 2 which occurs when n=1. Any other…

Q: Estimate the area between the x-axis and the graph of f(x) = 9 – x² over the interval [– 1, 2] by…

A: Given the graph of the function :

Q: The area bounded by the curve y = 3/x and the lines x = 3 and x = 8 above the x axis - is _square…

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Q: b. A square root function with a stretch factor of 4, with the vertex at (-5, 0).

A: To write the function from the given details

Q: 5. Find the area of a parallelogram bounded by the y-axis, the line x = 3, the line f (x) = 1 + 2x,…

A: Given:A parallelogram bounded by the y-axis, the line x = 3, the line f (x) = 1 + 2x, and the line…

Q: Find the area of the shaded region. f(x) = x* - 8x + 21x, g(x) = 6x + 36 (3,54) (-1,30 by -10

A: GIvenf(x)=x4-8x3+21x2g(x)=6x+36To find the area of shaded region from given figure.

Q: Find the number of units x that minimizes the average cost per unit C. C = 0.03x3 + 30x + 20,580 X =

A: The given question can be solved as shown in step2.

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

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Q: find the area of a parallelogram bounded by the y-axis, the line x=5, the line f(x)= 4+2x, and the…

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Q: What necessary conditions are replaced by "minimize"? obeyed by a solution to (1) if "maximize" were

A: To write the  necessary condition for min ∫t0t1F(t,x(t),x'(t))dt with x(t0)=x0

Q: A piece of wire of length 63 is cut, and the resulting tow pieces are formed to make a circle and a…

A: The total length of the wire is 63.Let x be the length of the wire cut for the circle.Then, 63-x is…

Q: The upper right-hand corner of a piece of paper, 12 in. by 8 in., as in the figure, is folded over…

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Q: A river flows between the lines x = 3 and x = 4. Where should a bridgebe constructed to minimize the…

A: A river flows between the line x=3 and x=4. Bridge constructed to the path from O(0,0) to P(5,4).

Q: Suppose x and y are positive integers such that the sum of x^2 and y is 10x. Find the values of x…

A: Given x^2+y=10x.From there find y.

Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

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Q: #10

A: Given  We find the derivative of this function with respect to x, we get,

Q: What values of a and b minimize the value of - 2x?) dx? (x*

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