using maclaurin series for tan(x) and equation for length of cable to prove that x=
tan(?)=?+(1/3)?^3
wrapping a cable around the earth once then adding one metre to the cable (radius is R=6378km)
Find two expressions for the length of the cable. Use these together with your Maclaurin polynomial for tan(?) to show that (.003/2R)^(1/3)

I really don't understand the question. Can you rephrase it?

Sanguine12343214: Your question is very unclear. Are you taking about the following problem? "You are standing on the equator and you have a string around the equator that is the length of the equator + 1 meter. What is the maximum height you can lift the string off the ground?"

Even if that were the case, I still don't see what does it have to do with the Maclaurin series of the tangent.

the exact wording of the question is find two expressions for the length of the cable use together with your maclaurin polynomial for tan(x) to show that x=(.003/2R)^(1/3) i was given a diagram that is supposed to help me but i am unsure on how to post it on this and the height of the string of the ground was a different part of the question

https://imgur.com/a/9yltwqi this is the diagram

I think I have a wild guess now, seeing the picture, but I'm far from sure. I don't mean to be rude, but it's extremely poorly worded (and flat out impossible without picture  you don't even say what x is supposed to be). Anyway, if my guess is right, then it's way too much work for 3$. I'm not sure about how to approach the problem and I don't even have a precise statement. Also beware that your expansion for tan(x) is approximate.

If I have to ballpark it, finding a solution and writing it properly would take me about 40 min, for which I usually ask 20$ (~15$ after website's cut and PayPay fees), varying a little depending on the level of detail you want. Maybe someone else would try it for less, let me know if you are interested.

ive increased the bounty

I'll give it a shot. I hope I got the question right.

Are you ok with a handwritten solution? I usually type them down, but think it's better in this case so I can include a proper picture.

yeah completly fine with that aslong as i can read it

Don't worry, I have good handwriting. I'll polish it and upload it soon.
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