Rearrange the equation so u is the independent variable.

4u+8w=-3u+2w4u+8w=−3u+2w

Step-by-step explanation:

4u + 8v = -3u + 2v

Solving 4u + 8v = -3u + 2v

Solving for variable 'u'.

Move all terms containing u to the left, all other terms to the right.

Add '3u' to each side of the equation. 4u + 3u + 8v = -3u + 3u + 2v

Combine like terms: 4u + 3u = 7u 7u + 8v = -3u + 3u + 2v

Combine like terms: -3u + 3u = 0 7u + 8v = 0 + 2v 7u + 8v = 2v

Add '-8v' to each side of the equation. 7u + 8v + -8v = 2v + -8v

Combine like terms: 8v + -8v = 0 7u + 0 = 2v + -8v 7u = 2v + -8v

Combine like terms: 2v + -8v = -6v 7u = -6v

Divide each side by '7'. u = -0.8571428571v

Simplifying u = -0.8571428571v

19.side- angle- side

20. angle- side- angle

step-by-step explanation:

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}