Which of the following are considered cylinders? hint : try to do this as if it were on the exam. use the traces (or cross-sections) method to draw a picture to you classify. (click all that apply to get credit.)

a. 5y^{2}+2z^{2}=2

b. y=-\left(2x^{2}+2\right)

c. 5x^{2}+2y^{2}+4z^{2} = 5

d. 4x^{2}-4y^{2}+4z^{2} = 2

e. -\left(\cos\! \left(-4y\right)\right)=1-z

f. 2x^{2}+4y^{2}-4z = -1

g. none of the above.

Step-by-step explanation:

A cylinder is a surface that consists of all lines (called rulings) that are parallel to a given line and pass through a given curve in some plane.

a)

this is cylinder , this is ellipse in y-z plane ,but along x-axis ,we shall get the same curve in every possible plane parallel to the yz-plane.

b)

We have to be careful not to draw interpret it as an equation in 2-space even though there is no z - that just means it does not depend upon z. If we sketch this graph in the xy-plane (so z = 0, we obtain the parabola ) . Since there is no z-value in the equation, we shall get the same curve in every possible plane parallel to the x-y-plane. In particular, the graph of this surface will be all vertical lines passing through the curvey = -2x^ 2 - 2 . in the xy-plane. By definition, this makes the graph a cylinder.

C)

this is ellipsoid

d)4x^(2)-4y^(2)+4z^(2) = 2

hyperboloid

{x,y,z can be exchanged to each other}

e)1-z = - cos (-4y)

this is some curve in y-z plane ,so it is cylinder.

f)    

2x^{2}+4y^{2}-4z = -1

elliptical paraboloid

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490

i'm sorry i don't know

step-by-step explanation: