What value of x maximizes the volume of an open box with a square bottom, where the surface area of the box is equal to 20?

Q: The area bounded by the curve y 4x and the lines r = 6 ,x = 10 and a axis is

A: As per guildlines we can solve one question at a time. If you want answer of all please ask them…

Q: What is the total area between f(x)=6x+6 and the x-axis over the interval [−6,3]?

A: To calculate the total area bounded between the curve f(x)=6x+6 and x-axis over the interval [-6,3].…

Q: Find the area of the “triangular” region bounded on the left by y = sqrt(x), on the right by y = 6 -…

A: It is given that,

Q: Find the value of Z such that the proportion of the area. 2. To the right of Z-score is 0.5500 3. To…

A: We have given that the proportion of the area.

Q: y= -x² + 9; 0 sxs5 x< + 9; 0 < x< 5

A:

Q: Find the area of the region enclosed by the graphs of y= square root of x+3 ,x=-3 and y= 2

A: Answer and explanation is given below

Q: What is the area of the largest rectangle that can be drawn with one side along the x-axis and the…

A: given curve is y=e-x2 find the largest area of a rectangle which has one side along the x-axis and…

Q: Find the area of the region bounded by the graph of f(x) = x² + 1, the x-axis and the vertical lines…

A: Explanation of the answer is as follows

Q: Sketch the region bounded by the graphs of the equations f(x) = x2 + 2x, g(x) = x + 2 and find the…

A: The region bounded by the graph is as below

Q: What is the area (in square units) of the region bounded by the graphs of y=r²+2, and the x axis…

A:

Q: You are designing a rectangular poster to contain 75 in squared of printing with a 6in margin at the…

A: Suppose x be the length and y be the width of the paper.As the margin width at the top and bottom is…

Q: The total area bounded by the graph of y = r- 1 and the x-axis is represented by 2.

A:

Q: What is the area enclosed between the graphs of X 4 and x = y² – 5?

A: Area between two curve

Q: Find the total area between y = 25 - x² and the x-axis for 0 < x≤ 6. Area

A: Given is the curve y=25-x2. The objective is to find the total area between this curve and x axis.…

Q: The base of a three-dimensional figure is bound by the line y = x² on the interval [0, 2]. Vertical…

A: Formula: If the area of the cross-sections of a solid at x is Ax for a≤x≤b, then the volume of the…

Q: The area of region bounded by the parab y = 2x – 4 is

A: Introduction: Integration is a method of bringing separate parts to form a whole. We find a function…

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: What is the area of the region enclosed by the graphs of f (x) = x – 2x² and g (x) = –5x?

A:

Q: What is the area (in square units) of the region bounded by the graphs of y=x2+2, and the x axis…

A:

Q: The base of a three-dimensional figure is bound by the line x = -y2-2y +3 on the interval [0, 1].…

A: Option(4) is true

Q: How many square units is the total area bounded by y=x° +1 and by the x-axis from x = -2 to x = 2?

A:

Q: What is the volume of the solid stretching over the x-interval |0, 2| whose cross-sections are…

A: Given,  The solid with cross-sections are the equilateral triangle over an interval [0,2] on the…

Q: poster is to contain 150 square inches of printed matter, surrounded by margins that are 3 inches…

A: Topic = Application of Derivative

Q: We have 48 m² of material to build a closed box whose base width is 2 times the base length. What is…

A:

Q: The diagram shows a square prism with cross-section x units by x units, and length (9- 2x) units.…

A: We know that the volume of a square prism is equal to its base area X the height. first of all we…

Q: The enclosed area between y= 2 x and y= 6/x is evaluated by

A:

Q: If A is the area bounded by y = 4 − x^2 and the x-axis, find the horizontal line y = b (not…

A:

Q: An open rectangular box is to be constructed by cutting square corners out of a 16 by 16 cm piece of…

A:

Q: Find the total area between f(x)=3x2-3 and the x-axis on the interval [-2,2]

A: Calculation:The given curve are f(x) = 3x2 – 3 and the x axis y = 0 on the interval [– 2, 2].The…

Q: What is the area of the region between y = x - 2x- 3 and the x-axis from X = - 2 to X = 0?

A:

Q: the

A: Given curve y^=x and y=√x  Line x-4=0   Find area ?

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

A:

Q: Find the area of the region bounded by y = x² - 5x + 6, the x axis, and the vertical lines x = 0 and…

A: Given that y = x2 - 5x + 6 ; y = 0 (x - axis) ; x = 0; x= 4  We have to find the area of the region…

Q: What is the area of the region between y=x^2-2x-3 and the x-axis from x-0 to x=6?

A: Given,      y= x2-2x-3and the x-axis  from  x=0 to x=6.

Q: Estimate the area under the graph of  f(x) = 4 + 4x2 from x = −1 to x = 2 using three rectangles and…

A: In this question, we find the area by using the midpoint rule for the given function f(x)=4+4x2 for…

Q: Find the number b such that the line y = b divides the region bounded by the graphs of y = 9x2 and y…

A: To find the number y=b that divides the region bounded by the graphs of y=9x² and y=16 into two…

Q: What is the area (in square units) of the region bounded by the graphs of y=x+2, and the x axis from…

A:

Q: Sketch the region bounded by the graphs of the equations f(x) = x5 + 2,      g(x) = x + 2 and find…

A: Consider the given equations, fx=x5+2 and gx=x+2 the graph of the equations on the same coordinate…

Q: A rancher has 240 ft of fencing with which to build a rectangular corral alongside an existing…

A: We know, in rectangle, pair of opposite sides are equal.In rectangular corral, let length of equal…

Q: An open box is to be constructed from a 12x12-inch piece of cardboard by cutting away squares of…

A: Let the cut away squares side is of x in. So, the dimension of the open box with height x, length…

Q: Find the area of the region above the x-axis bounded by the function y = 4x - x2 – 3

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Q: A piece of cardboard measuring 12 in by 10 in is formed into an open top box by cutting squares of…

A: Figure

Q: The area bounded by the parabola x² = 2y, and the line x - y = -4 is 18 square units. %3D

A:

Q: What is the volume of the solid stretching over the x-interval 0, 2| whose croS-sections are…

A:

Q: The area of the region bounded by the function f(x) = + 3, lines x = −2, x = 2 and the x — axis is…

A:

Q: We must maximize the area A = xy = x(32 – x) = 32x – x², where 0 < x <

A: In order to maximize the area, the area A must be positive.

Q: What is the area of the region between y =x-2x-3 and the x-axis from x=0 to x-9?

A:

Q: What is the area of the region bounded by the graphs of y= square root of 80-x squared and…

A: