Mr. johnson currently has a square garden. it is in his garden and into a range of 5 feet shorter than three times shorter than times it width. he decides that the perimeter should be 70 feet. determine the dimensions, in feet, of his new garden

The Dimension of new garden is

Step-by-step explanation:

Given:

Perimeter of new garden = 70 feet.

Let the length of the new garden be 'l'.

Also Let the width of the new garden be 'w'.

We need to find the dimension of new garden.

Now Given:

Length is 5 feet shorter than three times it width.

framing the equation we get;

Now we know that;

Perimeter of rectangle is equal to twice the sum of length and width.

framing in equation form we get;

Now Diving both side by 2 using Division property of equality we get;

Now Substituting equation 1 in above equation we get;

Adding both side by 5 Using Addition Property of equality we get'

Now Diving both side by 4 using Division property of equality we get;

Now Substituting the value of 'w' in equation 1 we get;

Hence The Dimension of new garden is

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}