Question

My question is attached,

thanks!

Answer 1

A circle (of radius 5) with a quarter pi missing.

Answer 2

The bow of the boat can travel in a circle shape until it hits the 5 foot edge of the dock or the 4 foot edge of the dock. This shape is 3/4 of a circle. You will need to calculate the area of 3/4 of a circle first.

\[A = \pi r^2\]
3/4 of the area of a circle is \[\frac{3}{4}\pi r^2\]
Now, something interesting happens when the boat floats toward the 4 foot side of the dock. There is 1 foot of rope to go after the bow of the boat is parallel with the 4 foot edge of the dock; this creates another fraction of a circle. This time 1/4 of a circle shape. So the total area is:

\[A _{TOTAL = } A _{1} +A_{2}\]
\[A _{1} = \frac{3}{4} \pi r _{5}^2\] where the radius is 5 feet, and
\[A _{2} = \frac{1}{4} \pi r _{1}^2\] where the radius is 1 foot

Answer 3

Alright! Do you think you could work it out to the end?

Answer 4

That is up to you ;) I put all the theory there, all you have to do is understand the theory and put in the numbers.

Answer 5

Amistre!!??!!

Answer 6

amistre, high-five! :D

Answer 7

R=5; angle = 3pi/2

Area = 5^2 3pi
------
2 * 2

r=1; angle = pi/2


area = 1^2 pi
------
2 * 2

add the areas then

Answer 8

The last two?

Answer 9

75 1
pi(--- + ---) = 76pi/4 = abt.59.66 ft^2; which one is it rounded to?
4 4

Answer 10

aha!!

Answer 11

So it would be rounded to 60 ft?

Answer 12

if I did it right, then id round it to 60 :)

Answer 13

right?

Answer 14

Thanks! I owe you one!

Answer 15

:) youre welcome

Answer 16

if you ever have spare time, there were two previous posts of mine that I was helped on, but the person wasn't too sure what he was doing...