i need help with algebra 1?

Question

imagine a rope wrapped around the earth at the equator (earths circumference C). then think of adding d feet to the ropes length so it can now circle earth at a distance h feet above the equator at all pionts. 1. write an equation to model this situation. 2. solve your equation for d. 3. how much rope do you need to insert if you want the rope to circle earth 500 feet above the equator? use 3.14 as an approximation for pie.

*note----- lenght of rope= C+d, C=2(pie)r

~ THANKS ~
to all who answered, and actually im in the eigth grade and thats easy compared to some of the things i have to do.

Answer 1

The original circumference of the rope would be:

C = 2πr

I'm going to use the symbol ' to mean "new", so r' is the new radius, C' is the new circumference, etc.

You add a length d to the rope, so the new circumference C' is the old circumference C plus d:

C' = C + d

And since you want the rope to be h feet above the ground, the new radius is:

r' = r + h.

The new circumference is:

C' = 2πr'

Plugging in for C' and d' from above:

C + d = 2π(r + h)
C + d = 2πr + 2πh

But since the original circumference C = 2πr, you can also write this as:

C + d = C + 2πh

So you can subtract C from both sides and get:

d = 2πh

This means that, to make the rope float h feet above the ground, you only have to add 2πh feet to the rope...that's not a lot!

So, for question 3, to make the rope float 500 feet above the ground, you only have to add:

d = 2π(500) = 3,140 feet

to the rope. That may seem like a lot, but when you consider how much rope it would take to go around the equator, it's not much at all.

-----

Unfortunately, the answer below mine, from ommfgitstvo, is wrong. It seems to make sense that you'd have to add a lot more than 3,140 feet, but you don't. Trust me and the guy above me.

Please look carefully at ommfgitstvo's math below; unfortunately he made a lot of mistakes...the first of which is multiplying d by the circumference.

Answer 2

Um...

WOW That is not Algebra1 you're taking!

I'm Algebra1 myself.

Never seen a problem like that though!



Well... first of all its C TIMES d, not adding.

1. Just asks for an equation: (2(pi*r))d=h

2. Well the height is missing, so you can't solve for d, unless you forgot to put it on here.

3. Plug it into the equation:
(2(pi*r))d = h becomes
( 2 ( 3.14 x 3,963.189 miles ) ) x d = 500 feet becomes
24,887.64 miles x d = 500 feet becomes
20,925,637.9 feet x d = 500 feet
--So at the moment, the rope is 20,925,637.9 feet around the earth with ONE rope used.--
--You need to find the circumfrence of the rope when it is 500 feet above the earth, at all points.--

( 2 ( pi x r ) ) 20,925,637.9 feet = 500 feet becomes
( 2 (3.14 x (20,925,637.9 feet + 500 feet + 500 feet) ) ) 20,925,637.9 feet = 500 feet becomes
(131,415,006 feet) 20,925,637.9 feet = 500 feet becomes
2.74994283 × 10^15 feet of rope to circle the earth at its equator to reach a height of 500 ft.

2.74994283 × 10^15 feet of rope.

THE BIGGEST MATH PROBLEM A NINTH GRADER HAS EVER DONE HAS BEEN ACCOMPLISHED TONIGHT!!!

~T.VO of Minnesota.



EDIT: The two people who posted ahead of me, they said you would need like 3140 or 31400 feet of rope to add to the length of rope already at hand. How is that going to reach 500 ft above ground?
3140 ft is BARELY a mile of rope
31400 ft is 5.9469697 miles, or almost six miles of rope. But circling the Earth to reach 500 ft above the equator is NOT ENOUGH!

So... those people DEFINITELY do not have the bes answers.

Answer 3

Length of original rope = C = 2*pi*r
Length of new rope = C+d
so, d = Length of new rope - C

Length of new rope = 2*pi*(r+h)
so, d= 2*pi*(r+h) - C = 2*pi*(r+h) - 2*pi*r = 2*pi*r+2*pi*h-2*pi*r
=2*pi*h

so d = 2*pi*h
if h = 500 ft then
d = 2*3.14*500ft = 3,140 ft

Edit: Ommfgitivo (?) math is wrong - the question asks how much rope to ADD to the original length not for the actual length - so my answer and the other gentleman who got the same answer are correct

Also, Phantome's answer is wrong too because he adds 500 ft to 3959 miles in his formula - he would have to convert 500 ft to miles (0.1 miles) first...

Answer 4

The average radius of the Earth is 3,959 miles
1) The circumference of the earth would be:
Pi . 2. r or Pi . diameter:

2) The answer is:
7,926 x 3.141592 = 24887.64 miles

3) The radius is now (r+500). The circumference is now:
Pi. 2. (r + 500)=
Pi .2. (3959 +500) =
Pi .2. (4459)=
Pi. (8918)= 28002.52 miles