For the pink region bounded by a parabola with vertex at (-1, 11 ) and the green line, solve for: a. Area b. Centroid

Q: Find the largest area possible for a rectangle inscribed between the parabola y = 9 – x² and the x-…

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Q: Determine the area bounded by the ellipse satisfying:(101x+ 10y)2+ (20x+ 2y)2= 1.

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Q: 19. Find the area of the largest rectangle with lower base on the x- axis and upper vertices on the…

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Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: XYZ is an isosceles triangle with base YZ. YZ=5cm; Height of triangle=10cm. A square is put into t

A: Solution of the problem as follows

Q: The centroid of the T-section shown is 2.5 inches above the base. What should be the value of b to…

A: Given information is as follows:The area of the shape is,The centroids are as

Q: consider the 2D ice cream topper with a delicious scoop of ice cream that is enclosed by y=6|x| and…

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Q: 1. a) Find the length of the curve: y=+[1,2]. b) Find the area of the surface obtained by rotating…

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Q: Find a Cholesky factorization of the following matrix. 553 5 7 1 24 5 31 000000 =000000 0 0 0 0 0 0

A: Cholesky decomposition: A=L×LT Formulalki=aki-∑j=1i-1lij⋅lkjliilkk=akk-∑j=1k-1lkj2A=55357131245

Q: Show that the rectangle that has maximum area for a given perimeter is a square.

A: Given the rectangle. We have to show that the rectangle that has maximum area for a given perimeter…

Q: Find the area of the region included between the parabolas y² = 4(p+1)(x + p + 1), and y² = 4(p² +…

A: As per the question we are given two parabolas defined as : P1  :  y2 = 4(p+1)(x+p+1) P2  :  y2 =…

Q: Find the area of the region bounded by the hyperbola 25x2 - 4y2 = 100 and the line x = 3.

A: We have to find the area of the region bounded by the hyperbola 25x^2-4y^2=100 and x=3 Please see…

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: y = -a(x – h)? +k (-2.1 , 2.9) (1,n)

A: The given curve is y=-ax-h2+k. Here h=-1 and k=11 given. So the curves becomes y=-ax+12+11. Also the…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

A: Given that  Plane x+7y+10z=70  To find the largest volume

Q: AP is perpendicular to PB, where A is the vertex of the parabola y^2 = 4x and P is on the parabola.…

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Q: 2. Let ~v = h3,-2,1i and w = h-1,4,2i. (a) Find cos(0) where 0 is the angle betwen ~v and w.

A: Given,   v→=3,-2,1 and w→=-1,4,2