The fruit tree yield per tree in an orchard containing 20 trees is 252 pounds per tree each year. due to crowding, the yield decreases by 3 pounds per tree for every additional tree planted. if you wish to maximize the total annual yield, what is the total number of trees that should be in the orchard?

Step-by-step explanation:

Let the number of fruit trees planted additionally be

Initially it is given that there are trees.

Number of trees after planting additional trees is

Let the yield due to each tree after planting additional trees be

Initially it is given that

Yield due to each tree after planting trees is

                                 =

To maximise yield,we take that value of for which

 =

So, and

So,32 additional trees has to be planted to maximise yield.

So,there should be 52 trees in total

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

what shape is