## Why use discrete mathematics to understand algorithms?

I'm new to algorithms. I need to know if you need to study discrete math to understand algorithms. If yes why? In particular, it is necessary for understanding algorithms or just creating your own algorithms (if you need to prove algorithm correctness).

## 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?

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?

## 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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