Minimize Q=6x^2+2y^2​, where x+y=8

Q: A box with a square base and open top must have a volume of 62,500 cm. Find the dimensions of the…

A: Topic- Application of Derivative

Q: What value of x maximizes the volume of an open box with a square bottom, where the surface area of…

A: The Volume of an open box with a square bottom x length and h height is given by V = x2h…

Q: Find the three areas of the region bounded by y=2x^2+10, y=4x+16 and the lines x=-2 and x=5.

A: Given: y=2x2+10y=4x+16x=−2x=5

Q: Find the area of the region bounded by the curve  y=2x2-3x+2  x axis and vertical lines x=0 and x =…

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Q: There is a line through the origin that divides the region bounded by the parabola y = 5z – 2z and…

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Q: Find the minimum cost of a rectangular box of volume 140 cm³ whose top and bottom cost 2 cents per…

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Q: Find the area between the curves (x^2)-(y^2)=9 and the line y=2x-6

A: Recall: Area between two curves:          A=∫abf(x)-g(x) dx           OrA= ∫abUpper function-(Lower…

Q: Find the area of the region bounded by y=x^2-6x+5, y=0 and the lines x=2 and x=5

A: We have to find the area of the region bounded by y=x2−6x+5, y=0 and the lines x=2 and x=5. The…

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x and the…

A: Answer

Q: There is a line through the origin that divides the region bounded by the parabola y = 8z – 32 and…

A: According to question given :There is a line through the origin that divides the region bounded By…

Q: A box (with no top) is to be constructed from a piece of cardboard with sides of length A and B by…

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Q: A storage box with a square base must have a volume of 70 cubic centimeters. The top and bottom cost…

A: Given volume =70cm3 The storage box has square base. let x be the side of the square and y be the…

Q: he area bounded by y^2=4x and the line 4x-3y-4=0.

A: In this question, the concept of Integration is applied to determine the area bounded by two curves.…

Q: Find the area between the curves. 3x х%3 -2, х%34, у%33е3X, у%3D2е 3X +1

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Q: Consider a rectangle which is on the region bounded by the lines y=x+4 y=-x+4  and X-axis. If its…

A: Consider a rectangle which is on the region bounded by the lines y=x+4 y=-x+4  and X-axis   Let…

Q: A rectangular field of fixed area is to be enclosed and divided into three lots by parallel to one…

A: Given: A rectangular field of the fixed area is to be enclosed and divided into three lots parallel…

Q: What is the area of the region between y3Dx^2-2x-3 and the x-axis from x-D0 to x-6?

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Q: Find the three areas of the region bounded by y= 2x2+10, y=4x+16 and the lines x=-2 and x=5.

A: Given : y = 2x2 + 10, y = 4x + 16 and the lines x = -2 and x = 5.   To find the three areas.

Q: Find the area of the region bounded by y = 2x2 + 10, y = 4x + 16, x = -3 and x = 4.

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Q: Integrate completely

A: Solution-

Q: A plastic right cylinder with closed ends is to hold 1000 cubic centimeters of oil. If there is no…

A: Let K be the ratio of height (h) to the radius (r) Hence, h / r = k Hence, h = kr

Q: Find the area of the region bounded by y=square root of 2x, y=3x-4, and y=0

A: Recall: Area between the curves:      If f(x) and g(x) are two continuous functions and f(x) ≥g(x)…

Q: Find the distance between the point (-1,2) and the line with x-int 1/3 and y-int 3/4.

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Q: y = 4 – x2 y = 4 – 4x - -5-

A: Definition used -             The area between two curves f(x) and g(x) -…

Q: A box with a square base and open top must have a volume of 512 cubic inches. Find the dimensions of…

A: The solution is given below:

Q: A poster needs to have 75 square inches of printed material with margins of 5 inches at the top and…

A: Given: Area of rectangular page = 75 square inches Also, we have margins of 5 inches at the top and…

Q: There is a line through the origin that divides the region bounded by the parabola y 7z 5x and the x…

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Q: What is the area of the region bounded by the parabola y^2 = 2x and the line x-y-4 = 0? *

A: See the details solution in below

Q: Sketch the region bounded by the graphs of the functions. y = x2 - 4x + 4, y = x2 - 12x + 36, y = 0

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Q: There is a line through the origin that divides the region bounded by the parabola y 2x 5x? and the…

A: Shown below

Q: There is a line through the origin that divides the region bounded by y = x − x^2 and the x-axis…

A: Area between curves

Q: find the area between the two curvesx=2-y^2x=y^4

A: Given thatx = 2-y2         ...(1)x = y4            ...(2)

Q: How many square units is the area of the region bounded by the two curves y = x^2 - 4x and y = x^3 -…

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Q: An oil refinery is located 1 km north of a straight river that is 2 km wide. A pipeline is to be…

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Q: Find the three areas of the region bounded by y= 2x2+10, y=4x+1 and the lines x=-2 and x=5.

A: Given: y=2x2+10y=4x+1x=-2x=5……1   To find: Area of the region enclosed with the above curve and…

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−4x2y=8x-4x2…

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Q: Determine the area of the region bounded by y = 2x2 + 10, y = 4x + 16, x = -2 and x = 5.

A: Following is the graph First obtain the points of intersection…

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

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Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

A: Consider a box with square base and open Top and have a volume of 4000 cubic centimeters. Let the…

Q: d Find dt 4x – 2 dx + 20 4t x2 2 – 16t 16t2 + 20 4t – 2 t2 + 20 2 – 4t t2 + 20 8 64t 16t2 + 20 64t –…

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Q: A box with square base and open top has a volume of 1000 m³. Find the dimensions of the box which…

A: This question can be solved using the concept of maxima and minima.

Q: Integrate by parts S xsin2xdx.

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Q: use intergration by parts intergral x(x-6)5dx

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Q: The area of the region bounded by the curve y= e2x, the x-axis, the y-axis, and the line x = 2 is…

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Q: The region is bounded by the curve y = 4x – x², y = 4 and the y-axis.

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Q: A box with a square base and open top must have a volume of 13,500 cm3. Find the dimensions of the…

A: To find the dimensions

Q: A storage box with a square base must have a volume of 90 cubic centimeters. The top and bottom cost…

A: Given that Length of the sides of the square base = x Height = y Volume of the box = 90 cubic cm.

Q: A line with negative slop X-axis and y-axis and passes through the point (2, 2). What is the sum of…

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