a) Find the maximal volume of the rectangular box whose three faces belong to the coordinate planes and with one vertex at the plane with the equation x +y + z = 3. Find the position of the vertex. Hint: use

Q: The intersection of the sphere (x-3)^2 + (x+2)^2 + (z-1)^2 = 49 with each of the coordinate planes…

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Q: Use the method of Lagrange Multipliers to find the area of the largest rectangle with edges parallel…

A: The rectangle inscribed the ellipse x218+y232=1. Let sides of rectangle be 2x and  2y.  Draw the…

Q: Find the perimeter of the polygon with the vertices Q(−3, 2), R(1, 2),  S(1,−2),Q(−3, 2), R(1, 2),…

A: Perimeter of polygon = Sum of length of all sidesLet A(x1, y1) and B(x2, y2) . Then,   Length of…

Q: Use slopes to show that the quadrilateral with vertices at (1, 3), (-5/2, 2), (-7/2, 4), and (2, 1)…

A: Given that Vertices of quadrilateral are A1, 3, B-72, 4, C-52, 2 and D2, 1   It is known that the…

Q: Find the dimensions of a rectangle with an area of 16 square feet that has the minimum perimeter.…

A: Step 1:​Area of rectangle =16 square feet Perimeter of a rectangle is given by P=2l+2w,where l is…

Q: 18. A) Complete the square for y = 2x² − 12x – 14 B) Determine the coordinates of the vertex. Is it…

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Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: Use an algebraic proof to show that the points A(-3, 1), B(0, 4), C(0, 2), and D(-3, -1) form a…

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Q: Find the dimensions of a rectangle with an area of 196 square feet that has the minimum perimeter.…

A: It is given that area of the rectangle is 196 square feet. Let l and w be the length and width of…

Q: A satellite dish is the shape of a paraboloid. The dish is 30 inches wide, and 10 inches deep. How…

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Q: What value represents the approximate length of x, the distance from the center of the octagon to…

A: Answer is mentioned below