91Ó°ÊÓ

The path of a diver is given by \(y=-\frac{4}{9} x^{2}+\frac{24}{9} x+12\) where \(y\) is the height (in feet) and \(x\) is the horizontal distance from the end of the diving board (in feet). What is the maximum height of the diver?

The cost \(C\) (in millions of dollars) of removing \(p \%\) of the industrial and municipal pollutants discharged into a river is given by \(C=\frac{255 p}{100-p}, \quad 0 \leq p<100\) (a) Use a graphing utility to graph the cost function. (b) Find the costs of removing \(10 \%, 40 \%,\) and \(75 \%\) of the pollutants. (c) According to this model, would it be possible to remove \(100 \%\) of the pollutants? Explain.

The game commission introduces 100 deer into newly acquired state game lands. The population \(N\) of the herd is modeled by \(N=\frac{20(5+3 t)}{1+0.04 t}, \quad t \geq 0\) where \(t\) is the time in years (see figure). (a) Find the populations when \(t=5, t=10,\) and \(t=25 .\) (b) What is the limiting size of the herd as time increases?

(a) find the interval(s) for \(b\) such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients. \(3 x^{2}+b x+10=0\)

Determine whether the statement is true or false. Justify your answer. A polynomial can have infinitely many vertical asymptotes.

The graph of a rational function can never cross one of its asymptotes.

The graph of a quadratic function with a negative leading coefficient will have a maximum value at its vertex.

The graph of a quadratic function with a positive leading coefficient will have a minimum value at its vertex.

Find the values of \(b\) such that the function has the given maximum or minimum value. \(f(x)=-x^{2}+b x-16 ;\) Maximum value: 48

Use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero. Adjust the table to approximate the zeros of the function. Use the zero or root feature of the graphing utility to verify your results. \(h(x)=x^{4}-10 x^{2}+3\)