Threatened monarch butterflies are monitored by measuring the area occupied by overwintering butterflies in Mexico. According to data collected by World Wildlife Fund Mexico, monarch butterflies occupied 0.67 hectares one recent winter, and 1.13 hectares the following winter (one year later)1. If the population is growing geometrically and grows at the same rate, how much area should the overwintering butterflies occupy one year after that

1.91 hectares

Step-by-step explanation:

Geometric growth rate formula =

Nt = Noλ^t

Step 1

We find the geometric growth rate(λ)

The formula is :

λ = (Nt/No)

Nt = 1.13 hectares

No = 0.67 hectares

t = 1

λ =( 1.13/0.67)

λ = 1.6865671642

Step 2

After another 1 year, the butterflies will cover:

No = 1.13 hectares

λ = 0.6865671642

Nt = Noλ^t

Nt = 1.13 × 1.6865671642^1

Nt = 1.9058208955

Approximately ≈ 1.91 hectares.

(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