Q1:A solid carton made from a 2700 cm' of paperboard, as shown in the figure. if the carton is uncovered on top, what is the extreme volume that can be made such as this carton by using the Lagrange method?

Q: The hypotenuse is √7 br. a right triangle, which is rotated around one of its perpendicular sides.…

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Q: Determine the volume if the area common with y²-3x+7y=8 and x²-4x+3=y² is revolved about the…

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Q: A cylindrical can with a height of 6 inches and radius of 1 inch is filled with a solid rectangular…

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Q: for

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Q: a) Find the volume and the lateral surface area of the solid formed by rotating this func- tion…

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Q: Q1: A solid carton made from a 2700 cm' of paperboard, as shown in the figure. If the carton is…

A: When the carton is uncovered from the top, the total surface area of the carton will be:…

Q: 4. (a) If h is the height of a pyramid and A is the area of its square base, find the volume of the…

A: Given: Let the pyramid be upside down. At y=0, x=0, y=h and x=b, the function that gives the length…

Q: Q3: A rectangular container made from 54 cm? of fiberboard, as shown in the figure. If the container…

A: Consider the provided question, We need to find the largest volume of the container if top of the…

Q: The volume generated by revolving the first-quadrant area bounded by the parabola y2 = 8x and the…

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Q: Rotate a circle of radius r around the x axis and use the method of disks to prove the formula for…

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Q: The lateral area L of any prism whose altitude measures h and whose base has perimeter P is given by…

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Q: I need to find the volume of each shape shown. I have to round to 2 decimal places and show my work

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Q: Determine the volume if the area common with y^2 - 3x + 7y = 8 and x^2 - 4x +3 = y^2 is revolved…

A: Integration of function under certain limits with respect to any of the axis gives the area under…

Q: b. A container in the shape of a right circular cylinder with no top has a surface area of 15 ft?.…

A: We have to find the height and base radius for which the volume of the cylinder will be maximized.…

Q: The volume generated when ℝ is rotated about the x-axis.

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Q: Q1: A solid carton made from a 2700 cm of paperboard, as shown in the figure. If the carton is…

A: We are given the Total surface  of Cardboard = 2700 cm2 Now, the carton is uncovered from the top…

Q: The hypotenuse is √7 br. a right triangle with one of its right sides rotated. Occurring How many…

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Q: A prismatoid has an upper base of 90cm^2 a lower base od 210cm^2 an altitude of 100cm, and a…

A: Given ,  A prismatoid has an upper base of 90 cm2 and lower base of 210 cm2 , altitude of 100 cm and…

Q: Q2: A wooden cubic made from 150 cm? of boarding, as shown in the figure. By using the Lagrange…

A: Since the area of wooden boarding is 150 cm2. Therefore, the sum of the area of all six faces of the…

Q: The area in the second quadrant of the circle x2 + y2= 2 is revolved about the line y + 1 = 0. What…

A: This problem belong to circle and line section from geometry and we solve this using the second…

Q: 5. Find the volume of spherical wedge formed by rotating through an angle of 45 a semi circle of…

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Q: 2. A right triangle with hypotenuse of 5V3 cm. is revolved about one of its legs to generate a cone.…

A: Given,          Let r, h, and V be the radius, height, and volume, respectively

Q: If the shape below is rotated around the y-axis, what is the volume of the resulting shape? Round to…

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Q: Derive the formula for the volume of a sphere by revolving about the x-axis, the region bounded by…

A: We have to derive the formula for the volume of a sphere by revolving about the x-axis, he region…

Q: A cone shaped well is drilled into a cylinder with the same base and height.  r = 6ft h = 10ft…

A: Given r = 6ft h = 10ft

Q: y = x2 – 6x + 13, y = lnx-

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Q: 2. The volume of a right circular cone is Irh where r is the radius of the base and h is the height…

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Q: 1. Find the volume generated by revolving the first quadrant area bounded by the parabola y? 8x and…

A: Proceed as shown ....

Q: When the area between the curve y= x², 0<x<2 and the y-axis is rotated about the y-axis, it forms a…

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Q: Find the largest valume of a cylinder that first into cone has base radium R and height h

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Q: A rectangular box with a square base is inscribed in a right circular cone of height 4 and base…

A: Given:A rectangular box with a square base is inscribed in a right circular cone.The base radius of…

Q: Q1: Aolid carton made from a 2700 cm' of paperboard, as shown in the figure. If the carton is…

A: Given that: Surface area of the solid carton = 2700 cm2 Find the extreme volume of the solid carton…

Q: The result of slicing through the center of the solid S is the base described by the ellipse + - =…

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Q: Find the dimensions of a right cone with surface area S=4 n that has the largest volume?

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

Q: d the volume of this rectangular pyramic sure to include the correct unit in your a

A: Here we have to find the volume of the rectangular pyramid.    We have, l=7 in w=3 in  h= 7 in

Q: y=kx? From the spandrel segment and semicircle shown from item 2, determine the volume generated by…

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Q: Find the volume generated by a parabola y2=4(51)x, its axis and its latus rectum revolves around its…

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Q: ind the volume when the area in y = 2x 2 − 8x + 12 and y = −2x + 12 is 9 sq units and revolves…

A: To find the volume of the solid that is obtained by rotating the below region about the x-axis.…

Q: +v² , but outside Find the volume of the solid in the first octant under the upside-down cone :=6-…

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Q: rated by revolving the area bounded by the parabola y² = 8x and its latus rectum about the latus…

A: Introduction: The chord that passes across the focus of a parabola and is perpendicular to the…

Q: Q1: Aolid carton made from a 2700 cm' of paperboard, as shown in the figure. If the carton is…

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Q: (23) A right triangle with a hypotenuse of 6 inches is rotated about one of its legs to generate a…

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Q: 4.) Find x so that the volume of the U-shaped rectangular structure is equal to 165 cm3. 8 cm 10 cm…

A: Please refer the attached image for complete solution. THANK YOU.

Q: Derive the equation for the volume of a sphere of radius r using the shell method.

A: Consider a circle of radius (r), which when rotated around x-axis generates a sphere.

Q: Q2: A wooden cubic made from 150 cm' of boarding, as shown in the figure. By using the Lagrange…

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Q: Q1: A solid carton made from a 2700 cm' of paperboard, as shown in the figure. If the carton is…

A: Prepare the problem as given: Volume covered: f(x,h) = hx2 Restrain: g(x,h) = x2+4hx = 2700 need to…

Q: Find volume if area enclosed is rotated about y= -2.

A: To find the volume if the area enclosed by the below curves is rotated about y = -2.

Q: Use the method of disks to rotate a circle of radius r around the x axis and prove that a sphere of…

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Q: Determine the solution in finding the dimensions of the right circular cylinder, with the greatest…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.