How do you apply polynomials to solve problems?

DO NOW – A window of fixed perimeter 8 m consist of a

rectangle surmounted by a semicircle. What is the radius that will admit most sunlight?

HOMEWORK – STUDY for the exam on Tuesday.

Dan invests $10, 000 in an account that pays 8.5% interest per year,

compounded quarterly. Write an equation to express the amount of money Dan will have after y years.

What is the amount of money that he will have after 3 years?

• 10,000(1+(.085/4))4y 10,000(1.02125)4y

• Y=3 $12,870.20

In the following problem, when I graph the equation, will I look for the roots,

the local maximum, or the local minimum on the graph?

For which numbers t will the value of 16t2-4t4 be as large as possible?

Find t

• maximum• t= 2

A rectangle is inscribed in a circle of radius 6 inches. Express the area of

the rectangle as a function of its width x.

• A= 2144x x

Find the minimum distance from the point (4,2) to y= 8x to the nearest

hundredth.

• d=

• dminimum=3.72

2 2(4 ) (2 8 )x x

Product of two positive numbers is 16. Find the two numbers such that the

sum is minimum.

• xy=16• y=16/x• Sum=x+16/x• x=16 y=0

Find the sum of the roots of x3+3x2+2x+2=0

Find the product of the roots of x4+x2+2x+8=0

• sum=-3• product=8

In a certain type of soil, if 20 apple trees are planted, each will yield 100 apples. But if more trees are planted for each addition tree planted, the

yield will be reduced by 2 apples. How many trees should be planted so that

the total yield is maximum?

• (20+x)(100-2x)=2000+60x-2x2

• xmax=15• Trees = 20+15=35