Question

Select the equations which graphs in space represent a cylinder. a) y = ln (z) b) y = cos(x) c) z = sin(y) d) xy = 8 e) x² + y² = z = 2 f) z = xy

Answer 1

The equations that represent a cylinder in space are x² + y² = z = 2 and z = xy.

Step-by-step explanation:

To represent a cylinder in space, the equation must have two variables and describe a relationship that forms a cylindrical shape. Looking at the given options:

a) y = ln(z) - This equation involves the natural logarithm of z and does not have two variables. It does not represent a cylinder.

b) y = cos(x) - This equation involves the cosine function and only has one variable. It does not represent a cylinder.

c) z = sin(y) - This equation involves the sine function and only has one variable. It does not represent a cylinder.

d) xy = 8 - This equation has two variables and represents a rectangular hyperbola, not a cylinder.

e) x² + y² = z = 2 - This equation involves two variables and represents a cylinder with a radius of 2.

f) z = xy - This equation has two variables and represents a cylinder.

Therefore, the equations that represent a cylinder in space are x² + y² = z = 2 and z = xy.