Thanks for the help! I definitely need to spend more time studying waves.
If anyone passes by this thread and knows of any good resources, could you reply to me with them, or PM me them? I looked all over Google trying to answer this question and didn't find many relevant sources.
So, is it as simple as saying that the waves are completely out of shift when 10,000πt - 8,000πt = π, meaning that t = 1/2,000? I must be oversimplifying this without fully understanding the fundamental ideas behind it. Am I evaluating the change in the cosine equal to π rads (cos(10,000πt) -...
Homework Statement
I'm given two frequencies: 4,000 Hz, and 5,000 Hz.
They are completely in-shift at time ##t=0##.
I am to find the time it takes them to get completely out of phase.
Homework Equations
The Attempt at a Solution
I've not gotten waves very well thus far in physics. My teacher...
OHH okay, I was skipping over a pretty fundamental idea there, but I think I get it now. Makes my question, about why we know it's a right triangle, seem pretty silly now.
Thanks for all the input in helping me find the answer, everyone!
Thanks a bunch for your response! First issue, I was so tired last night that I mixed up secant and cosecant. Correctly transforming secant into cosine (instead of sine) would let me use the sum-difference formula: \sin (x+y) = \sin (x)\cos (y) + \cos (x)\sin (y). I have values for \sin (x) and...
Homework Statement
\sin (x) = \frac{2}{3} and \sec (y) = \frac{5}{4}, where x and y lie between 0 and \frac{\pi}{2} evaluate \sin (x + y)
Homework Equations
Looked over some trig laws, don't think I saw anything that's too relevant. There \sec (x) = \frac{1}{\sin (x)}
The Attempt at a...
Homework Statement
A rectangular conducting loop of wire is approximately half-way into a magnetic field B (out of the page) and is free to move. Suppose the magnetic field B begins to increase rapidly in strength. What happens to the loop?
Homework Equations
Not sure which ones are relevant...
If the last image were correct, you could just solve it with the nominator equivalent to zero, and even if it weren't, you could still multiply through by the denominator leaving the nominator less than or equal to 0, right? Assuming what I said is correct, then it shouldn't be too difficult to...
Don't take my word for these, but consider that in a real life situation for 1, there would be friction in the moving turbine, and in situation 2 the energy that is moving them down the slope is coming from somewhere.
I don't answer often, so hopefully I've not given too little or too much...
Sorry I'm not replying until now, been busy.
Thanks! Guess I just needed to clear my head, now it makes sense. I appreciate the help!
Thanks a bunch! I don't know why I missed this the entire time, but it is indeed the solution. Of course, due to my organization on paper, I put b in instead of...
I could get the gradient of the tangent from the first derivative \frac{dy}{dx} = m = 24x^2 + 2bx + c, and I believe the equation of the line would then be y - y_1 = m(x - x_1), right? Sorry, I'm not picking up on where to go next.
Homework Statement
The cubic curve y = 8x^3 + bx^2 + cx + d has two distinct points P and Q, where the gradient is zero.
Show that b^2 > 24c
Homework Equations
None that I can think of.
The Attempt at a Solution
There's two distinct points where the gradient is zero, since it's third degree...
Thanks, I was able to figure it out! Once I recalled electrons were negative (maybe I shouldn't be doing this so late at night) the numbers made significantly more sense. I wrote up my original post a little hastily, but I do typically put in units. I was able to solve it using total energy...
Homework Statement
An electron moves from a point in space where the potential is 100 V to another point where the potential is 200 V. If it started from rest, what is its speed at the end of the trip?
Homework Equations
I'm not sure what's relevant and what's irrelevant at this point.
The...