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    Sum of Dice Rolls

    Haha me too. Thanks Ray for the help, I'll try to understand it :)
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    Sum of Dice Rolls

    Ok, what I did was to draw out two tables. The first one is here: 1st Dice 1 2 3 4 5 2nd 1 2 3 4 5 6 2 3 4 5 6 7 3 4 5 6 7 8 4 5 6 7 8 9 5 6 7 8 9 10 If Y = X1 + X2 So...
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    Sum of Dice Rolls

    Homework Statement There is a 5-sided fair dice with faces showing 1, 2, 3, 4, 5 dots. The dice is rolled four times. Find the probability of getting a total score between 10 and 15 (inclusive). Homework Equations If X is the score from one roll, then it follows a discrete uniform...
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    How much sleep do you need in school?

    Haha sadly this is so true
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    How much sleep do you need in school?

    Ok to clarify I meant, how much sleep did you get during your schooling years... :)
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    How much sleep do you need in school?

    Hi all, just out of curiosity, how much sleep did you get in school (high school, college etc.)? I'm a high school student from Singapore, and I average under 6 hours of sleep per day. But in my school, I get more sleep than probably about 80% of the student population. I know some who get...
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    Square a random variable

    yup. it's 0 for x < 0 and 1 for x > 25. Thanks for the help :)
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    Square a random variable

    Ah I see where I went wrong. But it should be 0.2\sqrt{x} and not \sqrt{0.2x} right? Thanks for the speedy responses!
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    Square a random variable

    Homework Statement Let the random variable X represent the length of the side of a square. It has a uniform distribution over the interval (0, 5). What is the cumulative distribution function for the area of the square, Y? Homework Equations F(x) = 0.2x (the cdf of the side). The...
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    3V Battery Indicator Circuit?

    Yup I'm looking at that schematic, which is for a 6V battery. Thanks Sciurus, I didn't think of that even though I have a few diodes lying around. So I guess instead of a Zener diode in reverse bias, I could just use (say 3) normal diodes in forward bias to get a 2.1V voltage drop, so the...
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    3V Battery Indicator Circuit?

    Hi, I'm not sure if this is the right place to post this, but here goes. I'm trying to build a battery indicator circuit for 2 AA batteries (3V). So far what I've read online is that I'd need to use a Zener diode to get a fixed voltage drop, then connect it to a transistor, like the...
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    Kinematics in Polar Coordinates

    Thanks ehild for pointing out my mistake :) I seem to be making alot of careless mistakes on this problem. So after correcting that cos in the denominator, I managed to get answers that sound reasonable, like 30 seconds. I think it should be right now. Thanks for all the help! Really...
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    Kinematics in Polar Coordinates

    Ok I tried using Wolfram Alpha to do the numerical integration. \frac{d\theta}{dt}=\frac{u \cos{\theta}}{r(\theta)} = \frac{u}{K}|\sec{\theta}+tan{\theta}|^{-\frac{v}{u}} So can I just separate the variables and get dθ|sec(θ)+tan(θ)^(v/u) = u/K dt? When I used Wolfram Alpha to perform the...
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    Kinematics in Polar Coordinates

    Yeah it is ugly, but I'm allowed to use numerical integration. Oh yeah I made a mistake in the signs, all of them should have been negative in the original expression for the velocity. So after integrating, I got r(θ) = K cos(θ)|sec(θ)+tan(θ)|^(v/u) The particle starts at (d, 0), and I...
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    Kinematics in Polar Coordinates

    Yup u and v are constant. Is this set of DE solvable? Edit: After looking at another problem from this forum, I think it would be possible to express it in terms of dr/dθ. \frac{dr}{d\theta} = \frac{dr}{dt} \frac{1}{\frac{d\theta}{dt}} = ur \tan{\theta} - \frac{vr}{u\cos{\theta}} And this...
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    Kinematics in Polar Coordinates

    Homework Statement A particle starts at (d, 0) in polar coordinates and has a velocity of \vec{v}=(u \sin{\theta} - v)\hat{r} + u \cos{\theta} \hat{\theta} where v > u Find the position vector of the particle as a function of time. Homework Equations \vec{v}=\frac{d\vec{r}}{dt}...
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    Work done in an accelerating frame.

    Ok I get it now :) Thanks vertigo!
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    Work done in an accelerating frame.

    So to clarify, the power output depends on the frame of reference? In a frame of reference inside the elevator, the rate of expenditure of energy should still be W(1+\frac{a}{g})(v) right? Since the man he has to exert a force of W(1+\frac{a}{g}) and is travelling at speed v. But from...
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    Work done in an accelerating frame.

    Homework Statement A man of weight W is in an elevator. The elevator accelerates vertically up at a rate a and at a certain instant has a speed V. The man then climbs a vertical ladder within the elevator at a speed v relative to the elevator. What is the man's rate of expenditure of energy...
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    Stability of a balanced plank

    Hmm ok I see that it should have been \frac{r+d}{\cos{\theta}} instead. But I'm not sure how to find the two lengths to add to get the correct answer still.
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    Stability of a balanced plank

    Homework Statement A uniform plank of thickness 2d and weight W is balanced horizontally across the top of a circular cylinder of radius r, whose axis is horizontal and perpendicular to the length of the plank. Prove that the gain of potential energy when the plank is turned without slipping...
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