A hotel wants to put a fence around a circular spa. The radius of the spa is 5/(√2-1)feet. If the fence is built along the immediate edge of the spa, what is the perimeter of the fence? (Recall that the perimeter of a circle is 2πr, where r is the radius of the circle.)
A.5π/√2 feet
B.5π feet
C. (10√2+10)∙ π feet
D.30π feet
The first answer that I did, it was a, and I got it wrong. I did the dividing radicals part again, and now I think the correct answer is C. Can someone check it, I would appreciate it.
If someone can help me as soon as possible with a walk through, it would help a lot!
2πr = 2π(5/(√2-1)
= 2π(5/(√2-1)*(√2+1)/(√2+1)
= 2π(5/(√2+1))/(2-1)
= 10π(√2+1)
(C) is correct
Thank you Steve! You helped a lot, I was working on it for a while, but after a little bit I had my sister help me. She didn't know, so i turned to this site. It helps a lot, and you guys help a lot. Thank you again!
To simplify the radical below, which of the following expressions would be multiplied by the radical?
A swimmer must swim along the length of a rectangular pool, from one edge to the other, as shown below. He knows the distance from one corner of the pool to the other, as well as the width of the pool. How far must he swim along the length? The picture below is not drawn to scale
i need the answers
To find the perimeter of the fence, you need to calculate the circumference of the circular spa.
The given radius of the spa is 5/(√2-1) feet, which is an irrational number. To simplify it, we can rationalize the denominator.
To rationalize the denominator of a fraction, we multiply the numerator and denominator by the conjugate of the denominator (√2+1). This eliminates the radical in the denominator.
So, the simplified radius is:
(5/(√2-1)) * (√2+1)/(√2+1)
= (5√2 + 5)/(2 - 1)
= (5√2 + 5)/1
= 5√2 + 5 feet
Now, we can calculate the circumference of the spa by using the formula 2πr, where r is the radius.
Circumference = 2π * (5√2 + 5)
= 2π(5√2) + 2π(5)
= 10π√2 + 10π
Therefore, the correct answer is C. (10√2+10) * π feet.