Time and Work Problem / Algebra – Mathematics Stack Exchange

I have this problem and I do not know how to handle it. It makes me stupid not to get it.

The first employee spends 4 hours less time producing 60 details than the second with making 80 similar details. The first worker makes 2 details more than the second within an hour. How many details make a second worker for an hour?

Combinatorics – Combinatorial Totals – Mathematics Stack Exchange

Calculation:

$ n choose 0 $+$ n choose $ 4+$ n choose $ 8+ …

The solution to this exercise:

let S1 =$ n choose 0 $$ n choose $ 2+$ n choose4 $$ n choose8 $+ …, S2 =$ n choose1 $$ n choose3 $+$ n choose5 $-…, S3 =$ n choose0 $+$ n choose4 $+$ n choose8 $+ …, S4 =$ n choose2 $+$ n choose6 $+$ n choose10 $+ … and we think (1 + i)$ ^ n $= S1 + iS2 =$ sqrt2 $$ ^ n $(cos$ frac {n pi} {4} $+ isin$ frac {n pi} {4} $) and 2$ ^ {n-1} $+ S1 = 2S3

The problem is that I did not get the part with (1 + i)$ ^ n $I've seen more exercises like these with combinatorial sums, the solution of which was complex numbers, and I'd like someone to explain that method to me. Thank you!

Mathematics – How to Implement the Meshlab Rotation Manipulator?

I want to implement a twist grip / manipulator mechanism that allows the user to rotate a 3D model just like Meshlab does.

Unfortunately, I do not quite understand how the rotation gizmo works. In particular, I do not understand how the model can only be rotated around the Z-axis. Open Meshlab and turn it just the blue circle to see what I mean. Rotations around the X and Y axis are easy for me to understand.

How to recreate the rotation mechanism of Meshlab, d. H. Like exactly Does horizontal and vertical panning shift into angle changes?

Meshlab-rotation Gizmo

Mathematics – Prediction of projectile flight time

I try to predict matematically how long the projectile will fly until it is reached
the goal. I try to implement this formula:

t = [V * sin(α) + √(V * sin(α))² + 2 * g * h)] / g

where I know V (velocity of the projectile), α (angle of the launch), h (height of the launch) The problem is, it shows some strange results. I'm not sure what's wrong (with ue4):

Flex Time = Velocity * FMath :: Sin (AngleDeg) + FMath :: Sqrt (FMath :: Square (Velocity * FMath :: Sin (AngleDeg)) + (2.f * Gravity * Altitude));
Time / = gravity;

For example, these test inputs:
Gravity = 9.8;
Height = 10;
Speed ​​= 10;
AngleDeg = 10;
shows 0.97 seconds, but the result should be 1.61 according to this calculator: https://www.omnicalculator.com/physics/projectile-motion … If I try different inputs, the result is always wrong … I also have the formula from this site so do not know what's going on. Thanks for any advice

Limit over another limit – Mathematics Stack Exchange

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Help with Calculus – Mathematics Stack Exchange

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