Use the green triangle how? I don't know the short side or the hypothenus of it. I can't know how to aim the angle to the zero point 'inside' the mountain...
No, it's not that easy unfortunatel. I don't know the distance to the zero point. In fact, I don't know any distances at all. Only the height of the two mountains. And the point was to use angles along with the mountain heights to solve the problem...
The point of the problem is this:
Let's say you outside taking a hike somewhere. You can see the summit of to mountains (which you know the height of), and you're wondering how high above sea-level you are right now. The only tools you have is some kind of instrument making you able to measure...
I'm leaning towards there not being a solution.
However, if you perform two measurements, with the distance between measuring points known, the angles could tell you the distance to either mountain. Then it would be possible!
I can measure the angle between top A and B, but that's about it. I don't know any other length in that triangle. So I would say no. But I'm not sure...
Homework Statement
I want to know if the problem needs another variable, or if it is possible to solve as it is.
Homework Equations
See figure in image included:
You are a point x, some height h above zero-level. The two mountains have known height 500m and 400m. But you don't know how far...
Aha! So i get a simple second degree equation: 64x^{2}-50x+4=0
Thanks :)
But I'm thinking now that these numbers were 'convenient'...are there other ways to solve this if the numbers don't play along this nicely?
Homework Statement
Problem: find t in the following equationHomework Equations
64000e^{-1600t}+4000e^{-400t}=50000e^{-1000t}
The Attempt at a Solution
I know the answer: t=6.17\cdot\;10^{-4}s. But I'm struggling with how to get there. This is my attempt:
Factorizing down to...
I apologize if this problem is more of a math- than a physics problem. At least it is applicable in real life :)
You are standing on some mountain and in your view are two other mountains, A and B. Also you can see the ocean as a referance zero point. The height of both mountains A and B are...
Nevermind. I did it now.
It was a simple mistake on my part.
The integral should look like:
\int_0^1{\frac{2u}{1+u}du}
after substitution
and then it should be calculated with integration by parts from there.
I'm having trouble calculating an integral:
\int_0^1{\frac{1}{1+\sqrt{x}}dx}
I decided to do a substitution:
u=\sqrt{x}
du=\frac{1}{2\sqrt{x}}dx=\frac{1}{2u}dx
thus making the integral look like this:
\int_0^1{\frac{1}{2u}\cdot\frac{1}{1+u}du}
I transformed this integral to...