Ahhh!! HELP?

Question

I would really appreciate it if you can show what you did to get the answers of these 3 questions! Thank you! (please no bs-ing)
1-Imagine the Earth a perfect sphere with a long rope tightly wrapped all along the equator. The length of the rope has been increased by 10 feet and the rope was magically lifted off the Earth to form a perfect circle over the equator. Will an average cat be able to stroll under the rope without touching it? (supposed the cat is about a foot high) [i somehow ended up with .7 feet?]
2-If a bicycle rider goes over a puddle of water, both of its wheels will leave several water marks on the road. Obviously, each of the wheels will leave a periodic pattern. How are the two patterns related? Do they overlap? Does their relative position depend on the length of the puddle? The bicycle? The circumference/radius of the wheels?
3-Draw a semicircle and on its diameter a few (two or more or infinitely many) smaller semicircles that abud each other in sequence. By...

...construction, the sum of the diameters of the small semicircles equals the diameter of the large one. What about their perimeters, or, say, their total arc lengths [i totally dont understand 2 & 3] (yOUr HelP IN sOLVINg ThE sOLUTIONs WilL BE GreatlY aPPRECIATEd!!)

Answer 1

1. 2(pi)r=circumference of Earth
(where r=Earths radius)
2(pi)r + 10ft is length of rope. Now consider this. the Earth is very large compared to a basketball if you took a basketball measured it around and added 10mm to the length of string do you think a cat could get between. ten feet additional around the equator is like loosening up a notch on your belt (do you want a cat through there?)
2. bike going over a puddle will probably not get wet tires unless it is raining. A bike through a puddle will start a path at the exit pt of each tire. the size and length of the trail will depend on the size and depth of the puddle as well as radius of the wheel. Assuming you leave the puddle in a straight path the length of the bike would make less difference than the size of the puddle.
try this
get some straws and oreo cookies run them through a glass of milk and across a napkin, then get some larger choc. chip cookies and run the experiment again (see what difference change in wheel size makes)
3. If you took the time to draw a semi circle of diameter 10 and then put one inside at 9, then 8 (already you can see the sum is greater than 10) think of it like this you get a bag of Hershey's kisses and eat them all the sum of all calories consumed from inside the bag is greater than eating the bag itself.

Answer 2

1.

c = 2 pi r
c=circumference
r =radius
By calculus, or by algebra,
if c increases by 10 feet,
r increases by 10 / (2 * pi) feet = 1.6 feet

Certainly this is enough for the cat to walk under.

Answer 3

1.primeter=2pi*r
let perimeter of equator=p
p+10=perimeter of new circle
therefore new radius=(p+10)/2pi=r+5/pi=r+1.59
so i think the cat can manage if my calculations are right
2.take a bicycle ,ride it over water ,observe the pattern
3. i think it is similar to an interference generation pattern

Answer 4

q1. u cant answer the question unless the radius or diameter of the earth is given

Answer 5

1.
C = 2πR
C + 10' = 2π(R + h)
C + 10' = 2πR + 2πh
C + 10' = C + 2πh
so h = 10'/2π ≈ 1.59'

2. . . .too many questions & too many variables....

3.
Again,
C = πD
c(n) = πd(n)
∑c(n) = ∑πd(n)
∑c(n) = π∑d(n)
D = ∑d(n)
∑c(n) = πD = C

Answer 6

f1r5t 0f 4ll-------

pl0x d0nt tyPe lYk DiS Lol

Answer 7

so confused