Calculate see integral image where see second image is the part of the plane x + y + z = 1 in the first octant with downward orientation. answer is -1/6

Q: What three dimensional object is generated by rotating the two-dimensional figure about the x-axis?…

A: Find out the three dimensional object generated by rotating the two dimensional figure about x-axis…

Q: Without using a graphing utility, sketch the surface with equation x2 + y2 − z2 = 0.

A: Surface with the equation

Q: ABC is rotated around the line x=0 to produce a solid. What describes the shape of the solid?

A: While rotating the triangle around x=0 it becomes a cone

Q: 6. Find the area of the surface generated when y = v4x + 6 is revolved about the x- axis on the…

A: 80π

Q: Verify greens theorem form 1 for F=x^3i+yj and c is the circle x^2+y^2=1, oriented anti clockwise

A: Find ∫CFdr, the line integral of F, where C is the circle x2+y2=1, oriented anti clock wise…

Q: Find the slope of the tangent in the positive x-direction to the surface z = 3x - 6xy at the point…

A: We have to find the partial derivative with respect to x

Q: Convert to standard from and give the center and radius: x^2+ Y^2 - 2x +6y - 1=0

A: x-h2 +y-k2 =r2 (h , k) is centre and r is radius .

Q: Find three different parametrizations of the graph of y = x3.

A:

Q: find a parametrization for the curve. the upper half of the parabola  x-9=y^2

A: The given curve is x-9 = y2  ...(a) Putting y = t in (a) then x = 9+ y2…

Q: Identify the type of surface (in space) given by the equation, and sketch the surface. a. x^2+y^2=25

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 1. y = 2t2 – 7t3, x = 9t – t5

A: dy/dx and d2y/dx2  are find in next step dy/dx = (dy/dt) /(dx/dt)

Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

A:

Q: Pentagon MNPQR is shown on the coordinate grid. Pentagon MNPQR is dilated with the origin as the…

A: As dilation is done thus the size pentagon M'N'P'Q'R' compared to the size of the pentagon MNPQR…

Q: Find the area of the cap cut from the paraboloid y^2+z^2=2x by the plane x=2

A: To Find: Area of the cap cut from the paraboloid y2+z2=2x by the plane x=2.

Q: enclosed betw parabola y = x2

A:

Q: The curve y = sqrt(x2 + 1), 0<=x<=sqrt(2), which is part of the upper branch of the hyperbola…

A: Find dy/dx from the given curve using power rule and chain rule.

Q: Determine the y-coordinate of the centroid of the shaded area shown. 13" Parabolic. 5" I 5" -x

A: We know that centroid coordinate y (y-)=∫05xf(x)dx∫05f(x)dx let equation of parabola is f(x)=…

Q: nd the area of the surface generated by revolving the curve x= Osys2, about the y-axis. 3

A:

Q: What quadric surface is the following an equation for and how do you know? -9x^2-3x+y^2+z^2= 1/4

A: The given quadratic equation is .We know that the quadratic surface of the form  form a cone.

Q: y=8-4x² - 9z²

A:

Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

A: I am attaching image so that you understand each and every step.

Q: particle started at A(1,0) circled the origin once  an d returned toA(1,0) .what were the change in…

A: Given: A particle started at A(1,0) circled the origin once  and  returns to A(1,0)