Calculation Definition and 1000 Threads

A calculation is a deliberate process that transforms one or more inputs into one or more results. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people.
For example, multiplying 7 by 6 is a simple algorithmic calculation. Estimating the fair price for financial instruments using the Black–Scholes model is a more complex algorithmic calculation.
Statistical estimations of the likely election results from opinion polls also involve algorithmic calculations, but produces ranges of possibilities rather than exact answers.
To calculate means to determine mathematically in the case of a number or amount, or in the case of an abstract problem to deduce the answer using logic, reason or common sense. The English word derives from the Latin calculus, which originally meant a small stone in the gall-bladder (from Latin calx). It also meant a pebble used for calculating, or a small stone used as a counter in an abacus (Latin abacus, Greek abax). The abacus was an instrument used by Greeks and Romans for arithmetic calculations, preceding the slide-rule and the electronic calculator, and consisted of perforated pebbles sliding on iron bars.

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  1. hraghav

    How to show 400 neutrinos are present?

    Number of neutrinos detected per kg of water = 12/3*10^6 kg = 4*10^-6 neutrinos Neutrinos detected by 1 eyeball = 4*10^-6 neutrinos * 0.01kg = 4*10^-8 neutrinos I am not sure how to scale this to get 400 neutrinos. I did try multiple ways but either ended up with 3.69*10^9 or 4*10^-8 neutrinos...
  2. L

    Calculate E and B fields when given A

    Hi I'm not sure if I calculated the magnetic field from task a) correct? for calculatin ##\vec{B}## i used, the formular ##\vec{B}=\vec{\nabla} x \vec{A}## $$\vec{B}=\left(\begin{array}{c} \frac{\partial}{\partial x_1} \\ \frac{\partial}{\partial x_2} \\ \frac{\partial}{\partial x_3}...
  3. gabe99

    Why am I calculating the unknown mass of ice incorrectly?

    The answer should be around 39g. I keep getting around 45g. This is the calculation I tried Any feedback on what I am doing wrong ? Regards!
  4. 1

    I Different Substitution for Solving an Integral

    I have a question about how to solve the following integral: ##\int \frac 1 {x\sqrt{3x^2+2x-1}}dx##, I know how to get the right answer (which agrees with WolframAlpha and the book I got the question from) through substituting ##\frac 1u## for ##x##, completing the square and finally doing a...
  5. L

    Is the sequence (0,0,1,0,0,0,0,1,1,1,..) a valid subsequence?

    For example ##(0,0,1,0,0,0,0,1,1,1,..)## is a subsequence? I think it is not a subsequence and a rule must be given? İs it true? Thank you.
  6. S

    Derivative Problem: f’(1), f’(2), f’(3), and f’(5)

    1. How to get f’(1), f’(2), f’(3), and f’(5) 2. How to calculate average speed change of y to changes in x in the interval [0,6] 3. Estimate value of f’+(0) and f’-(6) pls help me about this graph, i dont know how to read this 🙏
  7. Morle

    Is My Calculation of Work Along a Defined Curve Correct?

    I created a problem for myself, which I have documented in LaTeX. I hope it's acceptable that I included snapshots of my pages. I would like to calculate the Work W along curve C1. I have solved the problem as shown below. Is my solution correct (see Equation 1.11)? The pictures I included...
  8. chwala

    Find the distance ##d## to a point in the given problem

    My problem is on how to arrive at ##d=\dfrac{mx-y}{\sqrt{1+m^2}}## My working steps are as follows; ##d^2=(x_1 - x)^2+ (y_1-y)^2## ##d^2=(\dfrac{y}{m} -x)^2+ (mx-y)^2## ##d^2=\dfrac{(mx-y)^2}{m^2} + (mx-y)^2## ##m^2d^2=(mx-y)^2(1+m^2)## ##d=\dfrac{mx-y\sqrt{1+m^2}}{m}## ...unless they...
  9. hraghav

    Find the mass of odium for both solid and liquid state

    Mass of honorite initially: 4.51 kg at 261.2 K Additional mass of honorite added: 3.75 kg at 261.2 K total mass of honorite is 4.51 kg + 3.75 kg = 8.26 kg Mass of liquid odium: 14.69 kg at 391.14 K Q melt = m honorite × L honorite Qmelt = 8.26kg × 15500J/kg Qmelt = 128030 J Q cool = (m odium)...
  10. I_Try_Math

    Finding the angular velocity of a pendulum

    My answer disagrees with the textbook and I have a feeling it may be due to how I calculated the moment of inertia. Is there anything obviously wrong with my calculation? Any help is appreciated. ## I_{sphere} = \frac{2}{5}MR^2 + Md^2 ## ## I_{rod} = \frac{1}{3}ML^2 + Md^2 ## ## I_{sphere} =...
  11. L

    I Calculation of absorption edges of Niobium

    I want to calculate the K and L absorption edges for Niobium (Nb). Could anyone explain the steps to calculate these absorption edges? I don't know how to use the Moseley law to calculate those values: https://en.wikipedia.org/wiki/Moseley%27s_law For reference, Niobium has: Shielding...
  12. MatinSAR

    Measurement of the Stefan-Boltzmann constant

    I've written it as : The mentor indicated that this is incorrect. How can I write it correctly? My try: $$ \sigma = 1.07 \times 10^{-8}W.m^{-2}.k^{-4} \pm 0.0243 \times 10^{-8} W.m^{-2}.k^{-4} $$
  13. L

    Surface integral - question about "restrictions"

    source: https://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceIntegrals.aspx I am not sure why the question had to say "in front of the yz-plane". If I understand correctly, that means x >= 0. However, isn't this restriction already accounted for by saying "in the first octant" which means x...
  14. A

    How Do You Calculate Component Forces in an Automotive Drum Brake?

    I'll try and keep this as easy as I can. The Right Triangle above represents the forces acting through the trailing shoe of a automotive drum brake. Point A is the central position of the brake expander. When the foot brake is depressed, a force is created that pushes the brake expander piston...
  15. N

    Find the Period of Oscillation for a Mass Falling Through a Tunnel Through the Earth

    I'm trying to solve it by 2 methods(screenshot below). However, I'm getting 2 different answers. I'm not able to find out the error in method 1. Method 2 gives the answer correctly. Kindly help. P. S: If the pics are not clearly visible enough, kindly let me know. I'll try to either improve the...
  16. Biscuit_Jones

    Formula Needed for Role Playing Game

    Hello, Great Minds and Fellow RPG Enthusiasts! I play and moderate a role-playing game and am seeking your brilliance. Can anyone provide me with a formula to calculate how far a person can throw and object based on how much they can lift and how much the object weighs? For example, if a...
  17. I_Try_Math

    Classical Mechanics: Rocket Propulsion Calculation

    My textbook says the correct answer for #79 is 1551 kg but I get 1600 kg. I just attempted to solve it using conservation of momentum. Can't see where the math is incorrect.
  18. S

    A How to do Convergent-Close Coupling (CCC)

    Is there an online source where I can learn how to calculate cross-sections and rates using CCC? More specifically, I want to calculate the dissociation rate of the molecular hydrogen ion due to electrons and ions, but I don't know how to do it numerically. Is there a resource available where I...
  19. chwala

    I Understanding the given transformation - PDE

    My interest is on how they arrived at ##r^2 \sin θ## My approach using the third line, is as follows ##\cos θ[r^2 \cos θ \sin θ \cos^2 ∅ + r^2 \sin θ \cos θ cos^2∅ ] + r\sin θ [r\sin^2 θ \cos^2∅ + r \sin^2 θ \sin^2 ∅]=## ##\cos θ[r^2 \cos θ \sin θ[\cos^2 ∅+ \sin^2 ∅]] + r\sin θ [r\sin^2 θ...
  20. V

    I Normal Mode calculation steps

    Can someone please explain me the steps of calculation of X1:X2 after putting in the lower value of W^2 in equation 9.9 in "Riley, Hobson, Bence - Mathematical Methods for Physics and Engineering 2006 - pg 319"? I have attached the page as a PDF file. Thank you.
  21. Robbie E Sayers

    Simple lever calculation- help with giving it notations

    My course has a module in mechanical engineering. The handout i was given for this one is: Effort = (Load x Load to fulcrum distance) / Effort to fulcrum distance my problem is memorising the formula, I am not used to formulas that use sentences to denote a variable. I am simply here to ask...
  22. T

    Medium Hard continuity proof Tutorial Q6

    I am trying to solve (a) and (b) of this tutorial question. (a) Attempt: Since ##c'## is at ##c'(0) = 1##, then from the definition of continuity at a point: Let ##\epsilon > 0##, then there exists ##d > 0## such that ##|x - 0| < d \implies |c'(x) - c'(0)| < \epsilon## which is equivalent to...
  23. chwala

    How long is the longest piece of the given Rope?

    I do not seem to understand why the ms answer is (C) 45 m unless i am missing something, In my working i have the longest piece being; ##x+0.5x+0.25x= 95## ##x=\dfrac{380}{7}= 54.28 ##m
  24. M

    B Energy required to bring 1 kg 1000 meter above the surface of the Earth

    How can i calculate the Energy required to bring 1 kg 1000 meter above the surface of the earth ?
  25. S

    Minimum force to tip the bin over

    I am stuck on part b) i). I understand that there is no normal force from the ground as the bin is on the point of being lifted off the ground, that is all fine. That leaves R, F and W. I know W is 40g, and I am required to calculate F, therefore it makes most sense to take moments about the...
  26. L

    Help calculating this limit please

    Hi, I have problems with task b, more precisely with the calculation of the limit value: By the way, I got the following for task a ##f^{(n)}(x)=(-1)^{n+1} \frac{(n-1)}{x^n}## Unfortunately, I have no idea how to calculate the limit value for the remainder element, since ##n## appears in...
  27. N

    Resistivity calculation from two-probe resistance measurement of sheet

    I'm really not sure. Obviously I can get the units right with Resistance * thickness, but I assume there's a correction factor here that I can't find anywhere?
  28. A

    Measurements Calculation Problem

    I have done this problem three times now, and keep coming up with an answer that is a factor of 10 off from the answer in the solutions manual. The way I'm doing it is MUCH different than how they did it, so I can't use their method to see where I'm going wrong. I want to find out what I'm...
  29. Dries vanlandschoot

    Does the Modified Collatz Conjecture Always End in 1, 5, or 17?

    Did some calculations and with 3×-1 i Always get 5.is this correct?
  30. C

    B Question about the fundamental theorem of calculus

    Hello everyone, I've been brushing up on some calculus and had some new questions come to mind. I notice that most proofs of the fundamental theorem of calculus (the one stating the derivative of the accumulation function of f is equal to f itself) only use a limit where the derivative is...
  31. MatinSAR

    Please check my calculations with these complex numbers

    $$Re(e^{2iz}) = Re(\cos(2z)+i\sin(2z))=\cos(2z)$$$$e^{i^3} = e^{-i}$$ $$\ln (\sqrt 3 + i)^3=\ln(2)+i(\dfrac {\pi}{6}+2k\pi)$$ Can't I simplify these more? Are they correct? Final one:## (1+3i)^{\frac 1 2}## Can I write in in term of ##\sin x## and ##\cos x## then use ##(\cos x+i\sin x)^n=\cos...
  32. M

    Help calculating force required to flange a cylinder

    Need help in calculating the force required to flange a cylinder outwards around the perimeter by approx. 5mm. Cylinder is either Aluminum or standard Mild Steel. Thank you.
  33. S

    B Calculating shaded area: I'm getting discrepancies between methods

    **EDIT** Everything looked good in the preview, then I posted and saw that some stuff got cropped out along the right edge...give me some time and I'll fix it. Hello all, I"m trying to calculate shaded area, that is, the area bounded by the curves ##x=y^{2}-2, x=e^{y}, y=-1##, and ##y=1##...
  34. I_Try_Math

    Using energy considerations to determine speed

    $$K_i + U_i = K_f + U_f$$ $$K_i = \frac 1 2 m(15)^2$$ $$U_i = 196m$$ $$U_f = 0$$ $$K_f = K_i + U_i - U_f$$ $$=\frac {15^2} 2 m + 196m$$ $$=\frac 1 2(15^2m + 98m)$$ $$=\frac 1 2m(15^2 + 98)$$ $$=\frac 1 2m(323)$$ $$=\frac 1 2m(17.97)^2$$ $$v=17.97 m/s$$ Not seeing where I'm...
  35. A

    Torque calculation based on distributive load

    The following images contain the question as well as my solution. I am not sure whether my solution is correct or not. Please help.
  36. M

    Centrifugal Compressor: Absolute Velocity Calculation

    How can I calculate the absolute velocity of air at the outlet of a centrifugal compressor if I have: Diameter of impeller RPM Slip factor I've been reading for weeks and cannot seem to find the answer to this question. For anyone who is familiar with the subject, I'm sure you know about the...
  37. S

    Circuit calculation practice: voltage dividers, series, parallel

    Hi, I'm teaching Engineering (honors) and want to drill the students on series, parallel resistors in circuits and voltage dividers. does anybody a have a worksheet with lots of samples? Thanks!
  38. KnightTheConqueror

    B Confused about this force calulation in Resnick Halliday Krane Electrostatics

    I'm confused in the calculation for R/2. The author took in account that the charge will change by a factor 1/8. But how does it show that the coloumbic force will become 1/8th. The distance will also reduce by half shouldn't that also be taken into account? Or am I missing something here?
  39. S

    Trying to calculate motor kW/reduction drive for lift of 100kg at 0.8m /sec

    Hi need to calculate 240v/315v motor size attached to reduction gearbox (reduction unknown) to lift a weight of 100kg on cable drum .8mtr/sec. Drum dia not determined yet. motor size not determined yet. any help is greatly appreciated as this seems to be out of depth of many motor drum winch...
  40. cxza

    Is the Final Velocity of a Fly Impacted by an Elephant's Mass?

    My solution was that the final velocity of the fly is equal to the mass of the elephant divided by the mass of the fly, and then multiplies by the delta in the elephant's velocity. My teacher said it was the wrong answer and that the calculations are presumably pretty long
  41. narrator

    Trying to resolve a volume calculation

    Hi all, I've made errors in my calculations and need help. I'm trying to calculate the volume of a layer above sea level to the height of Flight Level 300 i.e. 30,000 feet. Next, I want to subtract the volume of land within that layer. Here are my calculations. Purely for the sake of my...
  42. Z

    B How Do We Calculate the Number of Atoms in the Universe?

    hi, how do we calculated the number of atoms at the start of universe i.e, after big bang?
  43. J

    Calculating components of a third-quadrant vector

  44. L

    What is the derivative of ln(x)^e ?

    Can't figure it out, here's a screenshot with better typography.
  45. B

    Conservation of Momentum Calculation Woes!

    Alleyway kick The kicker weighs approximately 64kg or 140lb and the gentlemen holding the air shield is approximately 73kg or 160lb. How far does the kickee travel before hitting the chair and boxes and what speed is he travelling at? The practice kick prior to the actual kick puts the men...
  46. S

    Dose calculation for oscilloscope

    If pulse source output is recorded by a detector on oscilloscope, is it possible to calculate dose from this output voltage pulse?
  47. S

    Calculation of the orbital period for a binary star system

    Hello guys, Would it be possible to get some help on how to approach this problem? I don't really understand it. do I need to look at the orbital motion of the center of mass here or? If so how should I start? Thanks in advance.
  48. Edy56

    What Are Vout Values for Open and Closed Switch?

    TL;DR Summary: I need to calculate Vout when the switch Is closed and open. I need to calculate Vout when the switch Is closed and open. Is my work correct?
  49. H

    Calculation of Box's Acceleration on a Trailer with Friction

    Question picture: My solution: Where: S is the lineforce Ff is the force as a result of friction a is the resulting acceleration F is the acting force The answear is supposed to be a=(F-2mg(mu))/(m+M) Any idea what i could have missed? Thanks for your help on beforehand!
  50. P

    I Prony brake calculation help (for determining engine horsepower)

    I need some help here. I'm trying to determine how to use the numbers I'm getting for my pony break to determine horsepower at the axle of my engine. Right now I'm getting a reading of six pounds of torque, 4 in off of the center line of the axle at a rate of 30 rpms. Can someone help me...
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