math help anyone? PLEASE!!?

Question

alright, i have some extra credit i need help with.

1. an ant climbs to the top of a soda can following a spiral path with a slope of 45degrees. such a curve is called a helix. if the can is 6 inches tall, how far did ant walk? the answer does not depend on the width of the can! (remember that, for a right triangle, leg(squared) + leg(squared) = hypotenuse(squared).)


then there is:
what comes next: st, nd, rd, th

and this next one i have the answer to but im not sure if its right:
1 day at noon, laura runs to top of mountain. she sits and ponders life until next day at noon when she runs down mountain along same trail as she came up. was she nesessarily at some point on mountain trail at same time both days? prove answer.

thank you

Answer 1

(1).

SinΘ = Opp. / Hyp.

Hyp. = Opp. / SinΘ

Hyp. = 6 ins. / Sin 45°

Hyp. = 6 ins. / 0∙7071....

Hyp. = 8∙48528....

Hyp. ≈ 8∙49 ins.



(2).

th is next.

It's the order of the numbers:

First. (st)

Second. (nd)

Third. (rd)

Fouth. (th)

Firth. (th)



(3).

If laura run up and down the mountain at the same speed, then the half way distance will be the same time for each run.

Speed = Distance / time taken.

Answer 2

1. The can may be visualized as a rectangular piece of aluminium when unfurled, with 6 inches as its height. So, the path the ant travels is actually the hypotenuse of an isoceles triangle with the 2 equal-length sides of length 6 inches each. Thus, the answer will be x where

cos 45º = 6 / x

so x = 6√2



2. th, because firST, secoND, thiRD, forTH, fifTH.



3. Yes. Let y be some point on the trail with reference to the top of the mountain. Let t be the time elapsed since 12 noon. By plotting both graphs to describe the displacement y from the mountain from 12 noon onwards on both days, both graphs must intersect at a certain time t.

Answer 3

I will answer just the third part, and you should thank your lucky stars because you were so GRACELESS in responding to all the help I tried to give you in another question.



You described that answer as "rude," whereas it was really just straight talk. I take it that you've probably been brought up having your ego stroked all the time instead of receiving a good talking to when you deserved it.



On a graph of height versus time past noon, draw as wiggly a line as you like, of ANY shape that you choose, going from the bottom of the mountain to the top. That represents her trip UPWARDS. It also completes a rather bizarre "triangle" consisting of the y-axis, a horizontal straight line (her maximum height), and the wiggly line of arbitrary slopes at different places representing her actual position versus time.



Now, on the same graph, draw the analogous curve of her descent from the top of the mountain to the point where she's at ground level. Again, it can have ANY shape WHATSOEVER. This time you have a bizrre "triangle" consisting of the y-axis, the x-axis, and the DESCENDING wiggly line of your choice.



Now, no matter how you drew the two wiggly lines, they MUST CROSS AT LEAST ONCE. That crossing point necessarily has her at the SAME HEIGHT at the SAME TIME.



Therefore, she is NECESSARILY at the SAME POINT on the mountain trail at the SAME TIME ON BOTH DAYS. And as you can see, the argument doesn't depend in any way whatsoever on her running at any given constant speed. The argument makes NO ASSUMPTIONS whatsoever about her actual rate of progress in either direction.



And that's all the help you'll ever get from me.

Answer 4

1. The ant walked 8 inches. A can marked of and a tape measure works. By the way a soda can is only 4 7/8th inches tall.

2. The answer is no. She left at noon and ran to the top, and set untill noon the next day before running down the trail. If she leaves the top at noon she can't be at the spot she started from the day before at noon the next day. COMMON SENCE

Answer 5

1 If you roll the ant's trail of the can it forms a 45 deg triangle

with a 6 inch leg so it's trail is 8.484 in long

2.th as explained above

3.if you graph height versus time, going up has a line starting at the origin and sloping up to max hieght, and going down has a line starting at max height but on the y axis and sloping downward. These 2 lines have no choice but to intersect and will meet at a common time, but not necessarily at a common height

Answer 6

i have no freeking clue about the first one, but the second she would be at the same point at the same time only once, at the very middle (but this is only if she is going the same speed) my answer would be no because she is bound to be going slower on the way up and faster on the way down