Suppose you have 100 ft of string to rope off a rectangular section for a bake sale at a school Fair. The function A=x^2+50x gives the area of the section in square feet, where x is the width in feet. What width gives you the maximum area you can rope off? What is the maximum area? What is the range of the function?

Therefore the width is 25 feet for getting maximum area.

The maximum area of the rectangle is 625 square feet.

Therefore the range is 0≤A≤625.

Step-by-step explanation:

Given function is

A = - x²+50x

We know that ,

If y = ax²+bx+c

For the maximum

Here a = -1 , b= 50 and c=0

Therefore the width

Therefore the width is 25 feet for getting maximum area.

The maximum area =[ -(25)²+50.25] square feet

                                 = 625 square feet

The area can not be negative and maximum area is 625 square feet.

Therefore the range is 0≤A≤625.

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

answer: the answer is 30 miles per hour.

ft/s -> mphmph = ft/s 1.466667mph = 44 divided by 1.466667mph = 30.00000

- r3ktforgood ☕