Set up the triple integral for the volume of the sphere of radius 8 in Cartesian coordinates. 864-x2 V64-x2-y² dz dy dx V64 -x² S N64 - x2 V64 – x² - y² dz dy dx N64-x². dz dy dx dz dy dx

Q: 1. Find the intersections between the curve y=√√3-x and line y+1-x=0 (a) Sketch the region R bounded…

A:

Q: z2 = 9 and outside the cylinder x? + y? = 1.

A: coordinates, x=r cos θy=r sin θz=2 x2+y2=r2cos2θ+sin2θ=r2x2+y2+z2=9r2+z2=9⇒z=±9-r2 x2+y2=r2⇒r=2

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: Find the area of the region enclosed by the parabolas y = x² and y = 2x – x².

A: Draw the graph of two parabolas and shade the region between the two parabolas.

Q: Two curves having an equation of x = 2 vy and y = 2 vx intersect each other. Compute the centroid of…

A: Given,           x=2y    and     y=2x