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Question: Confirm whether the leaning tower of pisa is leaning, and if the lean is changing (between any two random days). Only tools given: Ability to measure vertical angles and fixed length rod (say 2m). Supposed to use basic geometry and trig. Made my head hurt for real trying to figure that out.
hi headstillhurts
Welcome to the forum.
When AD is a diameter, the angle ABD will always be 90 (or pi/2) so that should get you started.
Bob
Thanks Bob. It took me some time to figure out what the question was even asking. But together with your answer, the whole thing finally clicked.
PS Had problems logging in with my normal account for some reason. So just used a temp account to put that question up earlier.
Q. If a ball is thrown vertically upwards with velocity 28 m/sec, its height (in metres) after t seconds is given by y=28t−4.9t^2. Find the velocity at t = 2.
I do know how to solve this problem... as an initial velocity problem, using integration.
However, this question was covered near the beginning of the semester so long before we got to integration so there's obviously some way to figure out the answer without integration.
AOB is isosceles so S = pi - 2T (I'm using radians)
Thank you!!!
Couldn't quite figure out that relationship before you mentioned isosceles triangle. So many relationships to remember. D:
Good old rowing vs walking optimization problem.
In this case, we have a circular lake with radius 2. Walk 6kmph, row 2kmph. Go to the opposite side of the lake.
Say I walk from point A along the circumference to point B, then row across to destination C.
Since the three point on the semicircle will make a right angle, I can compute BC in terms of 'theta' (angle CAB).
But how do I compute the distance AC (perimeter of the wedge) in terms of 'theta'? In other words, how do I compute the angle AOB in terms of 'theta', since I need the angle AOB to compute the perimeter of the wedge.
Welcome to the forum, headhurts.
Thanks for all the links.
On a somewhat related note: is Spivak the best calculus book? My uni, just like most others, insist on using Stewart.
Quick intro: I was getting my math kicked by calculus. Everything past in a tangent after the first few weeks. Tried many websites, youtube tutorials, library books. Still confused. Was right on the verge of going for a private tutor. Decided to try the mighty intrawebs one last time. Ended up on math is fun.
Suddenly calculus makes sense. Almost easy even. Everyone understands differently and the way it's explained on this website just... worked for me! I can narrow it down to few things:
a. Good explanation of basic concepts - very thorough. One of many examples: I had no idea derivatives and f' and d/dx are all the same darn thing. I kept getting confused when the lecturer kept interchanging the terms in class.
b. Good examples to apply theory into practice.
c. GREAT selection of practice problems at the end of lessons. Really helps to hammer in the knowledge.
So really: A BIG THANK YOU to the people who put in such a great effort.
Secondly, now that the basics are out of the way, I need to move on to other course topics like implicit differentiation, related rates, newton's method etc. And I am really hoping that someone can point me in the direction of any other good website like mathisfun where I can PROPERLY learn those topics. Not just learn to solve individual problems using rules (which the youtube videos are great for) but actually understand why and what am I doing. I seem to learn a lot better that way since I have a math memory so if I don't understand it, I forget it by next week.
Cheers
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