(b) A cake is shaped like a hemisphere of radius 4 with base on the xy-plane. A wedge of cake is removed by making two cuts from the center of the cake outward, perpendicular to the xy-plane and separated by an angle of o. IT (b1) Use a double integral to find the volume of the slice for = (b2) Now suppose that the cake is shaped like a cylinder with the same radius and you take a slice in the same way with the same angle. How high the cake should be so that you get the same amount of cake as in part (b1)?

Q: Determine a real root of f (x) = x* – 2x - 4x? +4x+4 using the Newton-Raphson method. Use an initial…

A: Given fx=x4-2x3-4x2+4x+4, εa=0.1%, xo=1.5.

Q: Find the volume of the solid that sits above the rectangle [−1, 1]×[0, 1] in the xy-plane and below…

A: Given: Rectangle [−1, 1]×[0, 1] in the xy-plane Surface z = x^(2/3)+y^(1/3)

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

A:

Q: Determine the volume of the solid formed when a circle that passes through the points (l , 3), (3 ,…

A: As per the question we are given a circle passing through the three points : (1, 3) ; (3, 1) ; (1,…

Q: A thin metal plate of uniform density covers the area between the curves y = 2+ 6x – x² and y = 2 –…

A:

Q: a pluke is composed of hwo semi - cireles, y= = vi- x? and a y> Ju-x?. find the center of mass of…

A: Given the semicircles are  y=1-x2y=4-x2 For the first semicircle, y=1-x2y2=1-x2x2+y2=1 So the radius…

Q: Find the volume of the region under the surface z = 9x5 and above the triangle in the xy-plane with…

A:

Q: [Boyce-di Prima, p 125] Show that y₁=x√ssin(x-s), x²y + xy + (x³²-1)y=√x (x>0) dx ds is a solution…

A: Let gx,s=ssinx-ss32. By the Leibnitz rule,…

Q: A body T with the parameters  (1/2)(sqrt(x^2)+(y^2))≤z≤sqrt(16-(x^2)-(y^2) Use the sphere…

A: The given problem is to find the volume of the body formed by the cone and spherical region, we have…

Q: Calculate the volume of the solid formed by rotating the region between the circle (x - 2)^2 + y^2 =…

A:

Q: Find the area of the plane region that lies below the line y = 2x and between the parabolas y= 2x^2…

A: Given Curves are:…

Q: Find the surface area of the closed circular cylinder of greatest volume that can be inscribed in a…

A: solution:

Q: Find the area of the portion of the unit sphere inside the cylinder x2 + y? = 1/2 and z > 0. Select…

A: The equation of the sphere is x2+y2+z2=r2. Here, r is the radius of the sphere. The equation of the…

Q: Find the area of ​​region R bounded by y = 2x, y = 5x and y = 5 in the first quadrant  NOTE: The R…

A:

Q: The total amount of a cylinder inserted into a hemisphere of radius 1 unit Finds the maximum value…

A:

Q: enclosed

A:

Q: Find the area of the surface generated when the curve: =y=+on [1,2] is rotated about the x-axis. 2 0…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…