91Ó°ÊÓ

Find an equation for a circle satisfying the given conditions. [ 1.1] Center: \((0,-3) ;\) diameter of length \(\frac{7}{2}\)

Solve. $$2 y-3 \geq 1-y+5$$

The population \(P,\) in thousands, of a resort community is given by $$ P(t)=\frac{500 t}{2 t^{2}+9} $$ where \(t\) is the time, in months, since the city council raised the property taxes. (Graph can't copy) a) Find the population at \(t=0,1,3,\) and 8 months. b) Find the horizontal asymptote of the graph and complete the following: $$P(t) \rightarrow \text{ _____ } as \quad t \rightarrow \infty$$ c) Explain the meaning of the answer to part (b) in terms of the application.

a) Find the vertex. b) Determine whether there is a maximum or a minimum value and find that value. c) Find the range. [ 3.3] $$h(x)=-2 x^{2}+3 x-8$$

What does Descartes' rule of signs tell you about the number of positive real zeros and the number of negative real zeros of the function? $$F(p)=3 p^{18}+2 p^{4}-5 p^{2}+p+3$$

a) Find the vertex. b) Determine whether there is a maximum or a minimum value and find that value. c) Find the range. [ 3.3] $$g(x)=x^{2}-10 x+2$$

What does Descartes' rule of signs tell you about the number of positive real zeros and the number of negative real zeros of the function? $$H(t)=5 t^{12}-7 t^{4}+3 t^{2}+t+1$$

The Hold-It Container Co. is designing an open-top rectangular box, with a square base, that will hold 108 cubic centimeters. (Image can't copy) a) Express the surface area \(S\) as a function of the length \(x\) of a side of the base. b) Use a graphing calculator to graph the function on the interval \((0, \infty)\) c) Estimate the minimum surface area and the value of \(x\) that will yield it.

Solve. $$|x+6| \geq 7$$

What does Descartes' rule of signs tell you about the number of positive real zeros and the number of negative real zeros of the function? $$C(x)=7 x^{6}+3 x^{4}-x-10$$