math – Calculate value of bitcoin holdings at hypothetical bitcoin price different to current market price

Hey guys got a question for you, I’m sure its really simple but I’ve gone blank on the formula for excel spreadsheet.

Calculate value of bitcoin holdings at hypothetical bitcoin price different to current market price

i.e a btc holding of 0.09999 at a bitcoin price of 40000usd is worth what, as opposed to the market price which is easy to find an online calculator

data structures – How can I calculate the time complexity of T(n) = 2T(n-1) – 1 using recursion tree?


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graphics – BodePlot to calculate the amplitude and phase at a specific frequency

I have transfer function:

$W=frac{1}{s+1}$

tf = TransferFunctionModel({{1/(s + 1)}}, s)
BodePlot(tf, {.01, 100})

It is very simple to construct a Bode diagram, but how to calculate the amplitude and phase shift with the help of ‘BodePlot‘ at a selected frequency, for example $omega=2pi$, is not clear…

Will be glad to advice.

calculated column – Calculate business days between start date and end date

BLUF: I would like to create a calculated column in SharePoint that looks at the (Start Date) and (Provisioned Date) and know how many business days it took between the two.

I am very new to SharePoint and so far I have the following formula that gives me the full count of days between, I just am not sure how to add the BD function into it. Bonus, I would love for it to say either 1 Day(s) and if more than a month, show as X Year, X Months and X Days.

=Provisioned-(Start Date)

How do I calculate YTD pay in google sheets?

I have a sheet like this to track the salary and amount paid each month to my employees.
enter image description here

I run a small company but as it got bigger I decided to give pay stubs to each employee.enter image description here

How do I make it so when I input a Emp ID# the Year-to-date pay pops up?

integration – Calculate the volume (double or triple integral) with boundaries

Suppose we have the following boundaries:

$x^2+y^2 le a^2$

$x ge 0$

$y ge 0$

$0 le z le sqrt{x^2+y^2}$

I need to calculate the volume of the figure which is bounded by these conditions. So I know that the most obvious way would be to use a triple integral with the following boundaries:

$$ int_{0}^{a}int_{0}^{sqrt{a^2-x^2}}int_{0}^{sqrt{x^2+y^2}}{dzdydx}$$

However, after solving the first integral I get $$int_{0}^{a}int_{0}^{sqrt{a^2-x^2}}{sqrt{x^2+y^2}dydx}$$

but the next integral seems kinda hard to solve which makes me wonder if the volume should be calculated by another method (for example a substitution).

Can anyone help? Thanks!

sharpness – How to calculate MTF ? Need help with the formula

I’m trying to reproduce MTF chart programmatically but I’m stuck at some point.

I’m starting with a clean bar chart like this:
enter image description here

I then take a picture of this pattern with a smartphone (printed on HD quality paper, no gloss, no texture, …) and I get something like this: (there is a big of distortion)
enter image description here

I used the following page to understand how MTF is calculated:
https://www.imatest.com/docs/sharpness/

With my script, I’m basically scanning all vertical lines one by one, I scan pixels one by one from top to bottom for each line and I get the min and max value for luminance (I get the LAB value for each picture and I take the “l” value).

For the first step (amplitude), I get the following graph for my “perfect” example:
enter image description here

And when I do the same with the picture I took, I get something like this:

enter image description here

So far, it seems to be in line with what I see on the Imatest page except that my values seem inverted and that I go above 100 while I only apply the following formula: C(f)=Vmax−Vmin/Vmax+Vmin

Now my problem is that I can’t get to the MTF formula, if I apply MTF(f)=100%×C(f)C(0), I get exactly the same graph. My maths are rusty and maybe I’m missing something somewhere.

What I’m trying to achieve is to give a easy to understand score to sharpness. MTF is a good starting point but in the end, I would like to give a score like an average. I know it’s not accurate because the center is sharper than the edge but at least it would allow to rank sharpness in a more or less neutral way.

Any idea on how I can build the MTF chart or how I could assign a final score?

Thanks

microsoft excel – Calculate when a business makes profit

I’m not an accountant, but asked to prepare a simpel report about starting a business.

The initial investment is $2400 in the first two months ($4800 total) while the sales amount is $0. The cost is also $470 starting from first month onwards.

Starting from 3rd month, the sales amount is $2000 increasing by $2000 each month ($4000, $6000, $8000, …).

Of course calculating the benefit is very easy, only if I knew how to apply the initial investment (return on initial capital).

Please assist.

3d – Calculate coordinates of boundaries containing group of objects

I would like to understand how to calculate coordinates of boundaries group of objects as a parallelepiped in 3D game?

Let’s say for simplicity we have spheres randomly slowly moving in 3d space some of them cross each other from time to time and forming groups from 2 or more object locating very close to each other. Now I need to create dynamic parallelepiped surrounding this formed group as long as this group still formed because spheres moving constantly and such groups may appear and disappear chaotically.

So how to calculate coordinates of this parallelepiped faster? The naive approach I was thinking is just calculate distance of each object from each other individually to know to which group each sphere belongs which is slow O(n^2) time complexity. Is there more efficient solution to solve this problem?

Sorry if already similar question answered. I couldn’t find answer to my question so far.

How to calculate the complexity of summation

I am trying to calculate the computation complexity of an algorithm and I have reached the following summation (that shows the number of operations) and I don’t know how to find the Big O. (H is constant value)
enter image description here