Question 410949
I don't have all the time and energy to tackle every problem but I'll get you started on them.


1. We have two ordered pairs (p,x): (20, 42), and (10, 52). However, in an economic system, the demand typically causes changes in price, so (x,p) might have to be the format of the ordered pair, instead of (p,x) (the difference is which variable is (in)dependent). From your question it seems like we want (x,p) even though the beginning of the question words it similar to (p,x).


Anyway, we have (20, 42) and (10, 52) on our line, so both must be solutions to an equation x = mp + b --> 42 = 20m + b and 52 = 10m + b. You can solve the system to find m and b. The rest of the problem should follow (note that the cost equation would simply be written C = 300 + 6x).



2. Use your demand equation and your cost equation, set them equal and solve for x.


3. $58,200,000,000 is {{{5.82*10^10}}} in scientific notation, and $90,800,000,000 is {{{9.08*10^10}}}. You can figure out the rest using elementary techniques.


4. The distance from the edge of the teepee to the center would be half of the diameter of the teepee, or 6 feet. If the PVC pipe is along the outer edge, then by the Pythagorean theorem, {{{c^2 = 6^2 + 8^2}}} and we get c = 10 (feet).