In February, Yvonne’s hair was 47.0cm long. She continued to measure her hair each month to track its growth. In March, it was 50.1 cm; in April, 53.2 cm; in May, 56.3 cm; and in June, 59.4 cm. Use an arithmetic series to find the common difference and determine the rate of hair growth.

The rate of Yvone's hair growth is 3.1 cm per month.

Step-by-step explanation:

WIth the data from Yvonne's hair we can create a sequence that goes as follows:

A = {47, 50.1, 53.2, 56.3, 59.4,...}

This is an arithmetic sequence, the numbers are related to each other by a common difference, in other words to find the next number we just need to add a constant "r". To find this constant we can subtract any adjacent numbers on this sequence, this is shown below:

r = 50.1 - 47 = 3.1

r = 53.2 - 50.1 = 3.1

r = 56.3 - 53.2 = 3.1

and so on.

The rate of Yvone's hair growth is 3.1 cm per month.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form