Recent content by kastelian

so in the end there are two legitimate values of k, is that correct ?

Or you can imagine another hole, drilled symmetrically to the first, with the same mass taken out. The remaining cylinder will have 5 kg at x=0, one hole is actually filled with mass 1.5 kg at 2R/5. Then it shall be easy to calculate new xcom in terms of R. Also g shall be involved in the torque...

Yeah, but you need a picture to show that. It's not obvious. Sticking to algebra is a sure way to find a solution.

Found interesting that this problem even does not require algebra more than writing 2s=4c+104 and divide by 2. It gives s=2c+52. Drawing a picture makes it visible that unknown angle must be 52 :)

8x+20y=864 that is good for amount of alcohol but you are missing one more equation, what's the total amount of liquid that should be made ?

Given the a2, b2, c2 makes arithmetic progression that means b2 - a2 = c2 - b2. For \frac{1}{b+c}, \frac{1}{a+c}, \frac{1}{a+b} to make arithmetic progression it shall be enough to check if \frac{1}{a+c} - \frac{1}{b+c} = \frac{1}{a+b} - \frac{1}{a+c}. Thanks for the ordering already...

now I see, indeed haven't multiplied differences squared by number of people. It's the same as your result now. Thank you!

ehild: Grateful if you could share the formula please. I am still learning this stuff...

in my understanding (please correct if wrong): mean = (96*1+92*2+84*5+80*3+76*6+72*3+68*2)/sum(people) = 79.45 std deviation = sqrt( sum((score(i)-mean)^2) / (sum(people) - 1)) = 5.57 unbiased = sqrt( sum((score(i)-mean)^2) / (sum(people))) = 5.44 biased