91Ó°ÊÓ

You have 50 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

You have 80 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum area?

A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Six hundred feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area?

Why must every polynomial equation with real coefficients of degree 3 have at least one real root?

Use the position function $$s(t)=-16 t^{2}+v_{0} t+s_{0}$$ \(\left(v_{0}=\text { initial velocity }, s_{0}=\text { initial position, } t=\text { time }\right)\) to answer Exercises. You throw a ball straight up from a rooftop 160 feet high with an initial velocity of 48 feet per second. During which time period will the ball's height exceed that of the rooftop?

If you have difficulty obtaining the functions to be maximized. Read Example 2 in Section \(1.10 .\) The annual yield per cherry tree is fairly constant at 50 pounds per tree when the number of trees per acre is 30 or fewer. For each additional tree over \(30,\) the annual yield per tree for all trees on the acre decreases by 1 pound due to overcrowding. How many cherry trees should be planted per acre to maximize the annual yield for the acre? What is the maximum number of pounds of cherries per acre?

Explain how to decide whether a parabola opens upward or downward.

Find the inverse of \(f(x)=\frac{x-10}{x+10}\) (Section \(1.8,\) Example 4 )

Perform the indicated operations and write the result in standard form. $$\frac{1+i}{1+2 i}+\frac{1-i}{1-2 i}$$

A parabola that opens upward has its vertex at (1,2) Describe as much as you can about the parabola based on this information. Include in your discussion the number of \(x\) -intercepts (if any) for the parabola.