Consider the trough above the surface z=8y^2 and below z=8, with −1≤x≤1. Find the moments of...

Consider the trough above the surface z=8y^2 and below z=8, with −1≤x≤1. Find the moments of inertia around the x,y and z axis.ix=iy=iz=

Expert Solution

genius_generous answered 2 years ago

Consider the trough above the surface z=8y2 and below z=8, with −1≤x≤1. Find the moments of...

Consider the trough above the surface z=8y2 and below z=8, with −1≤x≤1. Find the moments of inertia around the x,y and z axis.

The surface z = 3x^(2) + (1/6)x^(3) - (1/8)x^(4) - 4y^(2) is intersected by the plane...

The surface z = 3x^(2) + (1/6)x^(3) - (1/8)x^(4) - 4y^(2) is intersected by the plane 2x - y = 1. The resulting intersection is a curve on the surface. Find a set of parametric equations for the line tangent to this curve at the point (1,1,-23/24).

Find the surface area of the part of the paraboloid x = y^2 + z^2 that...

Find the surface area of the part of the paraboloid x = y^2 + z^2 that lies inside the cylinder y^2 + z^2 = 25

Find the equation of the tangent plane to the surface x + y^2 + z^3 +...

Find the equation of the tangent plane to the surface x + y^2 + z^3 + sin(x − yz) = 7 at the point (2, 2, 1).

Given the surface x= (3 (y-1)^2)+ (2 (z+ 3)^2)+ 7. Find an equation of the tangent...

Given the surface x= (3 (y-1)^2)+ (2 (z+ 3)^2)+ 7. Find an equation of the tangent plane at the point(12,2,2) in four ways: a) By using the surface as given,x=h(y,z) b) By writing the surface as z=f(x,y)(only keep the square root whose sign corresponds to the point(12,2,2)). c) By writing the surface as y=g(x,z)(only keep the square root whose sign corresponds to the point(12,2,2)).

find the surface area of the paraboloid z = 4−x^2 −y^2 in the first octant.

Consider z = x 1 2 - 3x 1 x ...

Consider z = x 1 2 - 3x 1 x 2 + 3x 2 2 + 4x 2 x 3 + 6x 3 2 . 1)Find the extreme values, if any, of the above function. 2)Check whether they are maxima or minima.

Consider the surfaces x^2 + y^2 + z^2 = 1 and (z +√2)2 = x^2 +...

Consider the surfaces x^2 + y^2 + z^2 = 1 and (z +√2)2 = x^2 + y^2, and let (x0, y0, z0) be a point in their intersection. Show that the surfaces are tangent at this point, that is, show that the have a common tangent plane at (x0, y0, z0).

Find the volume of the solid bounded by the surface z =5 +(x-4) ^2+2y and the...

Find the volume of the solid bounded by the surface z =5 +(x-4) ^2+2y and the planes x = 3, y = 3 and coordinate planes. a. First find the volume by actual calculation. b. Estimate the volume by dividing the region into nine equal squares and evaluating the functional value at the mid-point of the respective squares and multiplying with the area and summing it. Find the error from step a. c. Then estimate the volume by dividing each...

*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z):...

*(1)(a) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=c}. (b) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): x=a}. (c) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): y=b}. *(2) Find a formula for the intersection of a cone {(x,y,z): x^2+y^2=z^2} with a plane {(x,y,z): z=kx+b} assuming both b and k are positive. (a) For what value of...

Question