Gthe sixth row of pascal's triangle is: 1 6 15 20 15 6 1 (a) what is the 7th row of pascal's triangle? (b) use your answer to the previous problem to write the expanded form of (x + y)7.

ANSWER

a)The 7th row is:

1 7 21 35 35 35 21 7 1

b)

EXPLANATION

The sixth row of Pascal's Triangle is:

1 6 15 20 15 6 1.

We generate the 7th row by repeating the eXtreme 1s and adding the entries directly above to generate the entries within as show in the attachment.

The 7th row is:

1 7 21 35 35 35 21 7 1

b) We can use this to expand

We know that the degree of x is going to decrease from left to right and the degree of y is going to increase from left to right.

This simplifies to,

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12