The convex surface area of a cylinder is at maximum. Determine its dimension in order to be inscribed in a given sphere.

Q: Suppose that 208 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given:  208 ft of fencing is used to enclose a coral From given figure diameter of the semicircle is…

Q: The minimum surface area for a given volume of a square-based rectangular prism occurs when the…

A: Let us assume the length of a edge of the base=xAnd height =y And volume=VSo, V=x2yor, y=Vx2

Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D %3D x² +x – 6' has…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,…

Q: The base of a three-dimensional figure is bound by the circle x2 + y2 = 4. Vertical cross sections…

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Q: Use Picard's theorem, find the largest interval for which the IVP y y(0) = 1, %3D x² +x – 6' has a…

A: Given that, y''=yx2+x-6,y(0)=1 Let F(x,y,y')=yx2+x-6 Then, ∂f∂y=1x2+x-6 Since,∂f∂y=0,…

Q: Determine whether the following statements is true or false, and explain why. In the trapezoidal…

A: The given expression is In the trapezoidal rule, the number of subintervals must be even.

Q: Find the dimensions of the rectangle, with the largest possible area, enclosed in the semicircle, y…

A: we use second derivative test to find out maximum area of rectangle

Q: Find a formula C(x,y,z) that gives the cost materials for the closed rectangular box, with…

A:

Q: For what minimum integer value of a, will the line ax+(a+1) y =18 www (a> 0) have two intersection…

A: If the line cuts the circle at two points then given line is secant line of the circle .The…

Q: The bending moment, M, varies with distance, x, from one end of a beam according to: 1 M = - zwx? +…

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Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle = 13. 5. x² + y

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Q: According to U.S. postal regulations, the girth plus the length of a parcel sent by mail may not…

A: Given the volume function Domain are the set of x values for which the function is well defined.…

Q: Cylinder Q has a base radius of 10 cm and a height of 5 cm. Cylinder R has a radius that is half of…

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Q: Consider the cone-shaped paper cup. The paper cup is 12 cm tall and the circular opening has a…

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Q: 37. Suppose that 1200 sq. cm of material is available to make a box with a square base and an open…

A: Let the side of the bottom be ax and the height of the box  h.  The volume of the box will be…

Q: Suppose that 202 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given that 202 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

Q: In calculus, it can be shown that the largest possible volume for the inscribed right circular…

A: Inscribe a cylinder in a sphere. We draw the cross section of the solid as follows   Let  be the…

Q: Find the points on the cone z = x +y? that are closest to the point (3,-2,0)

A: Solve the following

Q: Find the value of c>0c>0 such that the area of the region enclosed by the parabolas y=x^2−c^2 and…

A:

Q: If a gun is fired with and a =30o and V0 = 500m/s, whenwill the bullet hit the ground? How far from…

A:

Q: Apply the midpoint and trapezoid rules to the following intergal. Make a table showing the…

A: Consider the provided question,

Q: Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of…

A: Given, The dimension of the rectangle of the largest area can be inscribed in a semicircle of radius…

Q: The shortest distance between the parabolas y² = x – 1 and x' = y-l is V2, then the value of…

A:

Q: The total surface area of a cone with radius x and slant height 3x is equal to the area of a circle…

A: Solution:-The total surface Area of cone=πrl+πr2    radius=x    slant height=3x⇒πr3x+πr2…

Q: The given rectangle has a perimeter of 120 cm. Find the values of x and y that result in a maximum…

A: Consider the rectangle

Q: The cross-sectional area of a wide-flange I-beam has the dimensions shown. Obtain a close…

A:

Q: A farmer wants to fence in two rectangular corrals, equal in area, using an inner fence as shown in…

A: Given;

Q: A closed rectangular container with a square base is to have a volume of 1152 in³. The material for…

A: Let the length of the base=xAnd height=ySo, the volume=x2y=1152Or, y=1152x2

Q: Building Play Area

A:

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins.  What…

A: Given volume of the can is (128)πcm3 Let height=h radius=x

Q: Suppose that 259 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given, Perimeter of corral = 259 ft Then, x+2y+2πx22=259y=259-x-πx22            ... (1)

Q: Suppose that 465 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: We are given that 465 ft of fencing is used to enclose a corral in the shape of a rectangle with a…

Q: Suppose that 477 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given that: Length of total fencing =477ft                             NOTE: As per our answering…

Q: The volume of a right circular cone whose base has a radius r and that has a height of h is given by…

A: Given that: Volume of cone, V=π3r2h, h=10cm and r=30 cm and errors in height and radius = ±0.1cm

Q: A closed rectangular container with a square base is to have a volume of 2592 in. The material for…

A: Given: A closed rectangular container with a square base is to have a volume of 2592 in3. The…

Q: if the hypotenuse of a right triangle is 25, show that the area is a maximum of it is isosceles

A:

Q: In solving for the area bounded by y = x, y = 2x and x + y = 6 using a horizontal element, the total…

A: Follow the procedure given below.

Q: Suppose that 404 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Area of the shape=Area of the semicircle+Area of rectangle .Area of semicircle=πx22x12…

Q: A closed rectangular container with a square base is to have a volume of 3456 in3. The material for…

A: The solution of the problem is given in the next steps.

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A:

Q: Find the dimensions of a rectangle with area 1728 m whose perimeter is as small as possible. (I both

A: Length of rectangle = 24√3 m  Width = 24√3 m

Q: According to U.S. postal regulations, the girth plus the length of a parcel sent by mail may not…

A: Given the parcel sketch as:

Q: The quadrilaterals ABCD and PORS are similar. Find the length x of QR.

A:

Q: The sum of the dimensions of a box with a sqaure base is 48 m. Find the maximum volume of the box.

A: Volume

Q: A waste management company is designing a rectangular construction dumpster that will be twice as…

A: Explanation of the answer is as follows

Q: Find the dimensions of the rectangle, with the largest possible area, enclosed in the semicircle, y…

A:

Q: With α> 0, the circle of (x-2α) square + y square = 4α is rotated around the line x = -1. A torus is…

A: We find the volume of the solids using Washer method. Given equation of circle is…

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

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Q: The dimensions of a closed rectangular box are measured as 21 cm, 17 cm and 11 cm, respectively with…

A: