Formula Definition and 1000 Threads

I am making a Scratch 3.0 game. The shooter sprite is holding a gun slightly off-centre (see images), and I need the bullet to go to the end of the barrel of the gun before traveling forward (as so it would appear the bullet it leaving the gun). The issue is, to do this, I need to find the X and...

That's my attempting: first I've wrote ##e## in terms of the power series, but then I don't how to get further than this $$ \sum_{n=0}^\infty (-1)^n \frac {Â^n} {n!} \hat B \sum_{n=0}^\infty \frac {Â^n} {n!} = \sum_{n=0}^\infty (-1)^n \frac {Â^2n} {\left( n! \right) ^2} $$. I've alread tried to...

Hi everyone, while I was digging arima model I saw that BIC value is given as $k*log(n)-2*log(L)$ where $L$ is the maximized value of likelihood function whereas $k$ is number of parameters. I have found the proof of AIC but no any clue about that. I wonder how it is derived. Could you help me...

Hi All, Everyone knows so called "fictitious" forces, also known as "inertial" forces. They are forces felt by some mass point placed in a non-inertial frame. For example: a ball in a moving car or in a carousel. Maybe most intuitive fictitious forces are centrifugal forces, but there are also...

First, let me apologise if this is in the wrong thread, wrong place, or wrong forum. I've not had any good experiences so far getting an answer I can understand, because my maths education didn’t really prepare me to even begin to try to figure this one out! I'll try to explain the situation...

Hi everyone. I'm currently trying to master the use of the formula for nuclear masses from MYERS AND SWIATECKI (1969), https://www.sciencedirect.com/science/article/pii/0003491669902024. $$ E=[-a_1+J\delta^2+0.5(K\epsilon^2-2L\epsilon \delta^2 +M\delta^4)]A+c_2 Z^2 A^{1/3}...

I look though some algebra and calculus books but I didn't see any formula for this some, and I am stuck here. I can just represent it in a notation but I cannot think a formulation to obtain the result. ##\sum_{k=1}^{n=5}=\frac {n!}{n!k} ## Thank you.

It seems that Abel's theorem says that the quintic cannot be solved by arithmetic & root operations, but couldn't there be the situation where another function is used in concert with these operations?

Hi all, I am a self learner (graduated very long ago and rusty at math) working through the Riley, Hobson and Bence text, chapter 1. 1. Homework Statement Use the fact that ##sin(\pi/6) = 1/2## to prove that ##tan(π/12) = 2 − \sqrt{3}.## Homework Equations ##tan(2x) = \frac { 2 tan(x)} {1...

Does anybody know what the connection is between Wallis' formula for ##\pi## and quantum mechanics? There was an article about it: https://www.eurekalert.org/pub_releases/2015-11/aiop-ndo110915.php but like all articles for the lay public, all the details were left out. Wallis' formula is...

I thought this was "INTERESTing". You want to borrow a dollars, with monthly payment of p dollars, such that you'll owe f dollars after making n payments, at monthly rate r%. Example: MONTH PAYMENT INTEREST BALANCE 0 3000.00 1 -522.56...

Homework Statement A Varley Bridge is connected to a faulty three-core copper cable by two identical copper leads of resistance Rl. (a) Show that for the initial reading (connection to earth); 2Rx = 2Rc – Ri ........ 1 where Rc is the resistance of the cable core Ri is the initial reading...

I have a strange question. It's strange because I don't need a correct answer. I need an answer that seems correct and leads to predictable results. I'm making a multiplayer computer game where the players fire cannons in outer space. The cannon shells will move through the gravitational fields...

Found this formula on a whiteboard. I work in a financial institution. Can this mean something? (I may have transcribed the handwriting poorly. The d's might be a's.)

Hi, I am a makeup formulator and need to make a lipstick that would be stable at 50ºC. The stability is tested in a chamber with an inner temperature of 50ºC. The lipstick is in a plastic packaging - a regular one that can be seen in any store. The question is: Will the temperature of the...

Mentor note: moved from non homework thread to here hence no template. Hi, I wanted to calculate a non standard Cylinder. It have a Height (h), with a base radius of (r1) and a top radius (r2). It varies linearly along the height. How can I come up with a formula for that? Since my girlfriend...

Homework Statement In an organic compound "A" only C,H and O is present. 1.22g of A is completely burned and it gives 0.84g of CO2 and 0.54g of H2O. If the relative molecular mass of "A" is 123. Find the molecular formula of A. [/B] I have showed my attempt at solving this problem, but I think...

My chemistry teacher gave me this problem. I tried and tried, but I couldn't figure it out and the deadline is tomorrow. Please help me out here friends. 1. This is the problem : In a compound which is made of element Y, weight percentage of Y is 72% and N( Nitrogen) is 28%. Also, 3 Y atoms...

Homework Statement Consider a naked human body, with a surface area of 1.5 m^2 and an average temperature of 30° C (skin temperature), that stands at the middle of an empty breezy room whose surfaces have a temperature of 10° C. Assuming the human body as a blackbody (5% error), compute the...

Hey guys What's is the formula to find the force(torque) to throw a mass in the air that is 500kg/m(3) with 2 pulley and a belt. Thanks

Is the attached formula for covariance wrong? Fairly certain it is but want to double check as it seems an odd mistake to make in a paper. I am fairly certain it is wrong. The y_bar should be replaced with (y - y_bar) in the calculated of chi-squared.

I am not that smart when it comes to math. But I was wondering if there is a formula calculator or something online that would help me with the example of a problem. For instance if the attic is 130 degrees and I have a 14 inch round metal duct to my air conditioner in the Attic is there a way...

Hey! :o I want to calculate the integral $$\int_0^1\frac{1}{x+3}\, dx$$ with the Gaussian quadrature formula that integrates exactly all polynomials of degree $6$. The gaussian quadrature integrates exactly polynomials $\Phi (x)$ with maximum degree $2n-1$. In this case we consider $n=4$...

The equation ##x = x_0 + vt + at^2/2## is derived assuming a constant acceleration ##a##. My question is , from what frame is this path ##x(t)## described? Can I use it from a non inertial frame?

Hi all, I've been for quite a while trying to identify this formula. dV / V = β ΔT - κ Δp where β is the thermal coefficient of volume expansion and κ is the isothermal compressibility. I think it's related to thermodynamics applied to solids and I can understand relations between the...

If anyone side of a triangle cannot be derived from Euclid’s formula for pythagorean triples, is this sufficient to prove that a right triangle with integer sides is impossible? For example, let's take the leg expressed by k2mn in Euclid's formula,, where k,m,n, are integers. If one of the...

ETA. Read the bottom post first. Well, and.. Obviously mathematicians know this identity. At the x=b=c=n=2 point, pi exists. There are also connections to the Wallis product (pi/2). Anyway, I simplified it to the n=2 case. And re-remembered my fascination with the Pidentity, where...

Homework Statement A fairgrounds ride spins its occupants inside a flying-saucer-shaped container. If the horizontal circular path the riders follow has a 8.00 m radius, at how many revolutions per minute will the riders be subjected to a centripetal acceleration 1.95 times that of gravity...

*This is an introductory physics class for non-math majors. A typical jet fighter launched from an aircraft carrier reaches a take-off speed of 175mph over a distance of 310 ft. assuming the acceleration is constant, what is the jet's acceleration in (meters per second)? 2) how long does i...

Hi, I'm currently taking Chemistry 101 and came across this equation that seems to contradict what I've learned before. I don't know the name of it, but here is the equation and its implication. Now another equation we have learned is the Arrhenius equation, which is as follows: If I...

Hi guys I'm into rocks and minerals but I'm not a chemist I can't really find a definition between ... chemical formula and Idealised chemical formula ? example below of a mineral sample I purchased a few days ago part info from ... https://www.mindat.org/min-3760.html Chemical Properties of...

I've been researching for the calculus behind geodesic domes, and specifically calculus related to parametric surfaces. I've found http://teachers.yale.edu/curriculum/viewer/new_haven_06.04.05_u#f, but unfortunately, it comes short of providing me the most needed information, and so far I...

Simpsons formula and the volume of a pyramid frustum Normally I consider myself quite adept in mathematics, but I simply lack the right idea and/or the mathematical creativity to solve this assignmenent: "Prove that the Simpsons formula V = 1/6 * h * (Ab + 4Am + At) can be used to calculate...

Homework Statement : [/B] If the length of the filament of a heater is reduced by 10%, the power of the heater: Options are- a) increases by about 9%. b) increases by about 11%. c) increases by about 19%. d) decreases by about 10%. Homework Equations : P[/B]=I2R Or P=V2/R Where P=power...

Homework Statement An arrow of 2cm length stands about 6cm away from a convex lens (f = 2cm). How long is the image of the arrow? Homework Equations - The Attempt at a Solution Whenever I get homework regarding optics and particularly the lens formula, I never really know where to start. I...

Homework Statement A charge Q is uniformly distributed throughout a nonconducting sphere of radius R. Write the expression of the charge density in the sphere? Homework Equations Charge density ρ=dQ/dV Gauss's Law ∫EdA = E(4ϖr^2) The Attempt at a Solution If Q is uniform then ρ=Q/dV and the...

I want a clear formula for clear water (and salty water) penetration by giving only the radio wave frequency . I searched the web , the formulas on the web are so complicated . Are there any simple formula available for that ?

A constant tangential force of magnitude 12N is applied to the rim of a stationary, uniform circular flywheel of mass 100kg and radius 0.5m. Find the speed at which the flywheel is rotating after it has completed 25 revolutions? I know that this can be done using work-energy. But since a...

Homework Statement Hi, this is more of a review question and I'm just looking at solutions of natural cubic spline equations and some will give the cubic spline as: 1. s(x) = a + bx + cx^2 + dx^3 on Wolfram while other pages will give: 2. s(x) = a + b(x - t) + c(x-t)^2 + d(x-t)^3 where...

I have some question integrating between combinatorics and recursive formulas.Generally, I have some difficulty with the concept of recursion, as well as with the recursion in programming unfortunately.I have some question to solve, and maybe you can guide me:Find a recursive formula and a...

I'm trying to build an oval bicycle wheel and need a formula to calculate the radii so that I can use the results to calculate the length for each spoke. See diagram for details. Hope someone can help.

Hello, i have a sequence {1,2,13,62,313...} and I have to find out the rule for n-th number. I've found out that every next number is five times bigger but then is added or subtracted 3. For example 1x5 -3 = 2 and 2x5 +3 = 13 and so on. Can you please give me some advice how to create the...

Homework Statement Freezing point depression question[/B] student determines molar mass of acetone using the method used in this experiment. She found that the eq temp of water and ice was 1 deg C. She then adds 11.1g of the sample to mixture and temp falls to -3 deg C. Mass of solution was...

Homework Statement Two masses m1 and m2 are joined by a spring of spring constant k. Show that the frequency of vibration of these masses along the line connecting them is ω = √[ k(m1 + m2) / (m1*m2) ] (Hint: Center of mass remains at rest.) Homework Equations f = w/2π w = √(k/m) F = -kx a = -...

Homework Statement Consider two operators A and B, such that [A,[A, B]] = 0 and [B,[A, B]] = 0 . Show that Exp(A+B) = Exp(A)Exp(B)Exp(-1/2 [A,B]) Hint: define Exp(As)Exp(Bs) as T(s), where s is a real parameter, differentiate T(s) with respect to s, and express the result in terms of T(s)...

Kinetic Energy is defined as the product of half the mass of an object multiplied by the square of its velocity. Using this I derived the end formula. Work is as follows: KE = ½(m⋅v2) Because v = vi +at, if vi = 0, KE = ½(m⋅(at)2) KE = ½(m⋅a2⋅t2) KE = ½(m⋅a⋅a⋅t2) Substituting F for m⋅a...

I once drove my RC car in a vertical loop in a concrete drain pipe. If you know the diameter of the pipe, and the weight of the vehicle, what is the formula used to determine the minimum speed required for it to complete the loop?

I have been trying to find out how the cutoff equation for the T section LC Lowpass filter is derived. I remember from college that f=1/(2pi√(LC)) for an LC circuit. But, with the T section, the cutoff frequency is given by f=1/(pi√(LC)), with L being the sum of the two inductors. My math has...

Homework Statement You need to derive a formula for undamped pendulum simple harmonic motion; 1. Starting from the middle point 2. Starting from the extreme point Homework Equations The solutions are; 1. s = s0 sin(2 pi f t) 2. s = s0 cos(2 pi f t) The Attempt at a Solution I can derive the...

Hi all I was hoping someone could remove some doubt in my mind with regards to interpreting the Second Moment Of Area and Eulers formula for buckling. Am I correct in thinking that:- - The higher the Second Moment Of Area Value the more resistant to bending. - The lower the Second Moment Of...