Analysis and Calculus

Background - System of points a, b, c and q - a, b, and c exert a push on q moving it to the end of a vector that is 2 times the vector from a, b, or c to q. - a, b, and c do this at the same time, after each cycle the x and y values of q are the average of the end points of the vectors. - This happens n times First derivation The final x value is the sum of the averages of all the vectors endpoints divided by the number of iterations so n. Same goes for y I further thought why keep it at intervals when it can be a constant force. From this I derived The integral from 1 to n of the average of the averages of the vector endpoints in respect to the x valu…

I would appreciate very much your help or direction to solve the problem. ​ Looks like equation Q=SUM(ABS(B-Ai)) has got min and max values with the assumptions 0<B<1 0<=Ai<=1 SUM(A1:AK)=1 and i is a natural number from 1 to K Looks like the Qmax and Qmin depend on B and K only. I failed to find general solution for Qmax and Qmin. I attach the pdf with the problem written in Word Equation instead of Excel manner Q.pdf

Find integral from 0 to 2 of: X2 _______________ X2 - 2X + 2

when I tried to do: I came to the answer of 0 and I know this is not right. I do remember that you had to split the problem up and then integrate those or something like that. Could someone tell me the answer with their method.

I have reason to think that if A, B and N in the following equation are positive whole numbers then there is no solution. I would like either values of A, B and N which satisfy the equation or a reason why there is no solution. If you think it looks easy then give it a go - please.

In solving an integral of sqrt(9-x2), we substitute x=3sin(t) to get an integral of 3cos(t). Why does this work? In the original function, x can take on any value(if you include imaginary numbers), but the new function is equivalent to the original one even though sin(t) takes values only between its amplitudes. P.S. I remember a guide to writing math in this forum. Anyone have the link?

Want to ask a moronic question, can anyone answer me!! 48÷2y =24y or 24/y?

1-Even number 2-Prime number 3-Not prime 4-Non of these Please explain yor answer

according to the source* , this expression f(m) is a fact one "notices" in order to get the value for m infinite ...... which is 26 ! * les math au carré , by Marie-France Palissard

Has there ever been a formal proof of the following formula? [math]\sum_{n=0}^\infty {1\over (7n+1)^2}+{1\over (7n+2)^2}-{1\over (7n+3)^2}+{1\over (7n+4)^2}-{1\over (7n+5)^2}-{1\over (7n+6)^2} \stackrel{?}{=}{24\over 7\sqrt{7}}\int_{\pi/3}^{\pi/2} \! \log {|{\tan{t}+\sqrt{7}\over \tan{t}-\sqrt{7}}|} \mathrm{d}t \approx 1.15192[/math] The most recent result I can find is from Bailey&Borwein (2005), who have shown that the identity holds to at least 20,000 decimal places. Yet, no proof that it is exact has been known at that time. The Bailey&Borwein (2005) paper can be found here: http://crd-legacy.lbl.gov/~dhbailey/dhbpapers/math-future.pdf Thanks, Da…

links deleted The most difficult math problem of all time - solved in a perfunctory, concise way, an accepted way, consistently; and without error. Exposition And Sub-Proofs of Landau's Pole Prime Number Theory; Group Coordinates Magnitude Theory The Rho Function - Measure of density of prime number (and then general exponential) distribution; in the reals. A prime number is a foundational unit of arithmetic distribution (multiplication), and thus comprises the building-block root of Categorical Set Theory. Prime numbers are arbitrarily and relatively dipolar. Upon set-theoretic recombination (or substitution), this proves Goldbach's Conjecture for any set …

Can someone put up a tutorial on Integral Calculus just like there is one for differentiation? I need it.

I want to know about the functions which is path independent and path dependent. Please describe me about this.

from a high school level math book "les math au carré" by M-P. Falissard , page 133 n integer she uses the expression to deduce the limit of the sum as m approaches infinity (26) my gratitude to any solid help on this one !

lim (x-x) for x going to infinity equals? Is it simply 1? r

Taylor stated that: The curve is subjunctive to a partial of an infinite number of its differentials. So, we must be dealing with limited mathematics. Correct!

can some one help me with question 15. i am integrating it and trying this 1/3 (9)^3 -(1/3 (1)^3) and this gives me a answer of 242.66667 but the answer at the back of the book is 17 2/3

In proving that :[latex]x\leq y\wedge 0\leq z\Longrightarrow xz\leq yz [/latex] we have the following proof: Let ,:[latex]x\leq y\wedge 0\leq z[/latex] and let ,[latex]\neg(xz\leq yz) [/latex].......................................................1 But from (1) and using the trichotomy law we have :yz<xz.And using the fact [latex]0\leq z[/latex] we have for 0= z, y0<x0 => 0<0 , a contradiction since ~(0<0) Hence [latex] xz\leq yz[/latex]

The physics group have redirected me here. All parameters are constant save the Delta t terms. Related but a bit more involved is The divisor is essentially a large positive value with a small 'wiggle', but it would be nice to have an analytic solution. Many thanks for your time. Seth

Please describe me about simply connected and multiply connected curve.

A cylinder with radius r=0.75 m and height h = 1 m has to be covered by a cone. Find the minimal area for the cone. Surface Area of Cone: pi*r^2 + pi*r*L So, I figured out: H= Height of the cone R= Radius of the cone (H-1)/0.75 = H/R H=-4R/(-4R+3) To calculate L, I used the Pythagoras & substituted H from above: L = sqrt(R^2+H^2) L = sqrt(R^2+(-4R/(-4R+3)) L = (sqrt(16R^4-24R^3+25R^2)/(4R-3) I see I'm heading towards something really complicated... Could you please help me find the right way to do it? I have just started doing this.

For finding the volume between a multivariable line integral (x,y) and a single variable integral along the x axis, does this look right? ( Volume ∫0,0x+h,yf(x+h,y) ∫0,0x+h,0f(x+h) - Volume ∫0,0x,yf(x,y) ∫0,0x,0f(x) ) / h = ∫x,0x,y f(x,y) In particular I'm looking at f(x,y) parabaloids in the format z=axn+bym if that makes a difference; you can assume that f(x,y)-f(y)=f(x) I don't know if that's right or not, I was thinking of the volume as consisting of infinitesimal integral prisms, and following that the volume of a prism is its base multiplied by its height, the difference in volume from one of the infinitesimal integral prisms divided by h would equal the…

So, this pertains to a somewhat personal issue, but I have been freaking out over the possibility of my girlfriend's birth control malfunctioning. I'm worried because, though it's said that BC is 99% effective, there is a 1% chance of pregnancy. So, is there a law of probability that says in the occurrence of a scenario, that the 1% possibility HAS/WILL to happen? I doubt I'd be the unlucky 1% over the course of a month..but think of the amount of intercourse over a 10 year period using BC. You're going to have to be that 1% eventually, right? ~EE

The formula for 'n choose r' implies that r! divides n(n-1)(n-2)...(n-r+1). I seek a direct, arithmetical proof of this. Tbhank you.

Please see the attached file. Many thanks, T. question_max_functional.pdf