PLEASE HELP:
A zookeeper is buying fencing to enclose a pen at the zoo. The pen is an isosceles right triangle. There is already a fence along the hypotenuse, which borders a path. The area of the pen will be 4500 square feet. The zookeeper can buy the fencing in whole feet only. How many feet of fencing should he buy?
If you could please explain how you got the answer

He should buy 189.47 feets. ( i think this is right.)

Step-by-step explanation:

Since there's a hypotenuse this triangle is rectangular and since it's an isosceles triangle we know that both cathetus are equal. We were given the area of this triangle, wich is 4500 square feet, the equation to compute this area is A = b*h/2, since the cathetus are equal b = h and we can solve for either of this variables. So we have:

A = b*b/2

4500 = b*b/2

b*b= 9000

b = sqrt(9000) = 94.87 feet

Since the hypotenuse of this triangle already has a fence we only need to buy the fencing for the cathetus, wich should be two times b, since there are two cathetus. So the amount of fence is 2*b = 2*94.87 = 189.74 feets.

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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}

40% off the regular price is the correct answer.

step-by-step explanation: