Fill in the missing partial to help find 27 × 34

27 × 34 = 918

Solution:

27 × 34 using partial product.

27 = 27 + 7

34 = 30 + 4

Multiply 27 by 34

          = 27 × 34

          = (20 + 7) × (30 + 4)

Multiply each of the first term with each of the second term

          = 20 × (30 + 4) + 7 × (30 + 4)

          = (20 × 30) + (20 × 4) + (7 × 30) + (7 × 4)

          = 600 + 80 + 210 + 28

          = 918

27 × 34 = 918

The reference image is attached below.

your answer is b ^w^ hope i

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}