A rectangle has a perimeter of 600 cm. The width of the rectangle is 40 cm less than the length. What is the length of the rectangle, in cm?

170cm

Step-by-step explanation:

Given data

perimeter of 600 cm

let the Length be x

L=x

W= x-40

P=2L+2W

600=2(x)+2(x-40)

600=2x+2x-80

600= 4x-80

600+80= 4x

680= 4x

divide both sides by 4

x= 680/4

x=170

Hence the length is 170cm

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}

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europa2433

step-by-step explanation: