91Ó°ÊÓ

Find a polynomial function of lowest degree with integer coefficients that has the given zeros. $$2+3 i, 2-3 i,-5,2$$

Find a polynomial function of lowest degree with integer coefficients that has the given zeros. $$6+5 i, 6-5 i, 2,3,5$$

Use synthetic division and the Factor Theorem to determine whether the given binomial is a factor of \(P(x)\). $$P(x)=x^{4}-25 x^{2}+144, x+3$$

The rational function $$M(t)=\frac{0.5 t+400}{0.04 t^{2}+1}$$ models the number of milligrams of medication in the bloodstream of a patient \(t\) hours after 400 milligrams of the medication have been injected into the patient's bloodstream. a. Find \(M(5)\) and \(M(10) .\) Round to the nearest milligram. b. What will \(M\) approach as \(t \rightarrow \infty ?\)

CANNONBALL STACKS Cannonballs can be stacked to form a pyramid with a square base. The total number of cannonballs \(T\) in one of these square pyramids is $$T=\frac{1}{6}\left(2 n^{3}+3 n^{2}+n\right)$$ where \(n\) is the number of rows (levels). If 140 cannonballs are used to form a square pyramid, how many rows are in the pyramid?

Give an example of a rational function that intersects its slant asymptote at two points.

List all natural numbers that are factors of 12.

WEIGHT AND HEIGHT OF GIRAFFES A veterinarian at a wild animal park has determined that the average weight \(w,\) in pounds, of an adult male giraffe is closely approximated by the function $$w=8.3 h^{3}-307.5 h^{2}+3914 h-15,230$$ where \(h\) is the giraffe's height in feet, and \(15 \leq h \leq 18\) Use the above function to estimate the height of a giraffe that weighs 3150 pounds. Round to the nearest tenth of a foot.