The width of a rectangle field is 3h yards and its length is 3 yards longer than the width. the field has a fence around its perimeter with a gate 4 yards wide as shown below. right in expression for the perimeter of the rectangular fields in terms of h excluding the width of the gate

Part a)

Part b) The expression that represent the cost of fencing the field is

Part c)

Step-by-step explanation:

The complete question in the attached figure

Part a) we know that

The perimeter of the rectangular field (excluding the width of the gate) is equal to

we have

substitute the given values

Part b) we know that

To find out the cost of fencing the field (excluding the gate) , multiply the perimeter by the cost of $28 per yard

so

Part c) we have

h=5

substitute the value of h in the expression of the cost

add an image

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}