I don't really understand what these two questions are asking. Nor do I know how to start it.
1) Describe in words the region of $\mathbb {R}^3$ represented by: $x^2 + z^2 \le 9$.
2) Write an inequality to describe: The solid upper hemisphere of the sphere of radius 2 centered at the origin.
Can some please explain what I am supposed to do here? Thanks in advance.
For question no. $1$, notice that if we plot $x^2+z^2 \le 9$ in $\mathbb R^2$, we get a filled circle of radius $3$. Add another axis, and what happens? For example, a plate is a circle, but what 3d shape is made when plates are stacked?
For question no. $2$, recall that an (empty, i.e. not solid) sphere of radius $r$ has the equation $x^2+y^2+z^2=r^2$. Noting that the radius is $3$, we have $x^2+y^2+z^2=9$. How do we now make this sphere filled? Look at what was done in question $1$ to make a filled circle.