9.6 - Staying Cool
Here's how to plot a sphere of radius 9 over an $x$ by $y$ domain of [0,10] by [0,10]
function(9*sqrt(81-x^(2)-y^(2)), x,0, 10, y, 0, 10)
The last four numbers are the $x$-range to plot, $0\lt x\lt 10$, and then the $y$-range to plot, also 0 to 10.
If I just want to see what parts of this surface have a height greater than 4, I could plot the plane at $z=4$ with a separate geogebra command z=4 will display the plane perpendicular to $\uv z$ at a height of $z=4$.
Temperature in a 10 X 10 room
Let $T(x,y)$ be the temperature in a 10 ft by 10 ft room on a winter night. One corner of the room is at (0,0) and the opposite corner is at (10,10). For both of the numbered functions, $T(x,y)$ below, answer these three questions:
- Draw, or describe in words, or plot with GeoGebra a graph of the temperature function.
- Using your plot...describe the likely floor locations of the heating vents. Sketch the locations on a 10 by 10 square.
- Suppose you like to sleep with a temperature of 70${}^o$ or less. (Using your plot you could plot a plane at $z=70$.) Where would you put your bed? Again, sketch locations on a square.
- $$T(x,y)=78-\frac{1}{10}\left[ x^2+(y-5)^2 \right]$$
- $$T(x,y)=\frac12x-y+75$$