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OK, so I can't include MathML or images or TeX so I'm struggling to answer this question. Here's a verbal description of the equation V = ((PI^(n/2)) * r^n)/G((n/2)+1) where PI is 3.14159... G() is the Gamma Function (complex factorial) and ^ indicates "to the power of". Hope that helps. Source: Eqn 20 , p453 of Shannon's paper "Communication in the Presence of Noise"
What else can I help you with?
How do you find the sum to n terms of a harmonic progression?
Hey guys....There is no correct simple general formula for sum to n terms of the series1+1/2+1/3+1/4+ ............. + 1/nThe following expression is relatively a very good approximation.S = ln(n + 0.5) + 0.5772 + 0.03759/(n*n + 1.171)Deviation from the actual value fluctuates but remains relatively low.
How many numbers of n digits exist if the sum of all digits is s?
I've been trying to figure this out myself for a discrete structure class.From the digging I've done online I've found this formula thus far:if n is the number of digits, and s is the sum:C(n+s-1 , n-1) where C denotes "choose" as in C(n , k) "n choose k" which can be solved by(n! / [ (n-k)! * k! ] )this seems to work for situations where the sum is < 10, or so claims the forum I found.I whipped it all up into a scheme function if anyone wants to take advantage:;;factorial: num -> num;;finds factorial of num.(define (factorial num)(if (or (= num 1) (= num 0))1(* num (factorial (sub1 num)))));;==========================;;xchy: num num -> num;;the "n choose k" function(define (xchy n k)(/ (factorial n)(* (factorial(- n k))(factorial k))));;==========================;;n-dig&sum-s: num num -> num;;finds the number of n digit combinations with sum s;;C(n+s-1,n-1)(define (n-dig&sum-s n s)(xchy (sub1 (+ n s))(sub1 n)))
What is a real world application of Euler's formula?
Eulers can be used whenever ur bulding something n u need 2 know how the edges r going 2 be or wats the verticles n how many faces it has then ull be able 2 use it 2 help u figure it out n also if ur walking down the streets n ur wondering how many eges r there in the stairwall then ull know quiet easly!
What is the sum of the first forty positive integers?
The sum of the first forty positive integers can be calculated using the formula for the sum of an arithmetic series, which is (n/2)(first term + last term) where n is the number of terms. In this case, the sum is (40/2)(1 + 40) = 820.
How big pipe is needed for 1 cubic meter per second of water?
Let's say that in 1 second, n meters of water come out of the pipe.We have a cylinder of length n, and of an unknown radius.The volume of this cylinder is n*pi*r2, where r is the radius of the circle.We have our equation now: n*pi*r2=1.r2=1/n*pi.r=√(1/n*pi)So, if n meters of water come out of the pipe per second, then you will need a pipe of radius √(1/n*pi) to output 1 cubic meter of water per second.
Find the volume of a sphere with radius 2 units Use 22 7 for n?
The formula for the volume v of a sphere with radius r is 4/3 pi r3. Using 22/7 for pi results in a volume of 33.5 units, to three significant digits (which are probably more than justified by the statement of the problem.)
What does the variable n in the equation for the volume of a sphere stand for?
that is pi.there isnt really a variable there it just looks like n
What is the formula for calculating the electric field of a sphere?
The formula for calculating the electric field of a sphere is E k Q / r2, where E is the electric field, k is the Coulomb's constant (8.99 x 109 N m2/C2), Q is the charge of the sphere, and r is the distance from the center of the sphere.
What is the formula for calculating the electric field of a charged sphere?
The formula for calculating the electric field of a charged sphere is E k Q / r2, where E is the electric field, k is the Coulomb's constant (8.99 x 109 N m2/C2), Q is the charge of the sphere, and r is the distance from the center of the sphere.
How can one determine the volume of a gas using the formula for calculating gas volume?
To determine the volume of a gas using the formula for calculating gas volume, you would need to know the amount of gas in moles (n) and the gas constant (R), and the temperature (T) and pressure (P) of the gas. The formula for calculating gas volume is V (nRT) / P, where V is the volume of the gas. By plugging in the values for n, R, T, and P into the formula, you can calculate the volume of the gas.
What formula is n equals cV?
The formula n = cV is the ideal gas law equation, where n represents the amount of substance in moles, c is a proportionality constant, and V is the volume of the gas. This formula is commonly used to relate the amount of gas present to the volume it occupies under specific conditions of temperature and pressure.
What is the equation for surface area and volume of a sphere?
Volume of a sphereCircumscribed cylinder to a sphere. In 3 dimensions, the volume inside a sphere (that is, the volume of the ball) is given by the formulawhere r is the radius of the sphere and π is the constant pi. This formula was first derived by Archimedes, who showed that the volume of a sphere is 2/3 that of a circumscribed cylinder. (This assertion follows from Cavalieri's principle.) In modern mathematics, this formula can be derived using integral calculus, e.g. disk integration to sum the volumes of an infinite number of circular disks of infinitesimal thickness stacked centered side by side along thex axis from x = 0 where the disk has radius r (i.e. y = r) to x = r where the disk has radius 0 (i.e. y = 0).At any given x, the incremental volume (δV) is given by the product of the cross-sectional area of the disk at x and its thickness (δx):The total volume is the summation of all incremental volumes:In the limit as δx approaches zero[1] this becomes:At any given x, a right-angled triangle connects x, y and r to the origin, hence it follows from Pythagorean theorem that:Thus, substituting y with a function of xgives:This can now be evaluated:Therefore the volume of a sphere is:Alternatively this formula is found using spherical coordinates, with volume elementIn higher dimensions, the sphere (or hypersphere) is usually called an n-ball. General recursive formulas exist for deriving the volume of an n-ball.For most practical uses, the volume of a sphere can be approximated as 52.4% of the volume of an inscribing cube, since . For example, since a cube with edge length 1 m has a volume of 1 m3, a sphere with diameter 1 m has a volume of about 0.524 m3.Surface area of a sphereThe surface area of a sphere is given by the following formula This formula was first derived by Archimedes, a greek, based upon the fact that the projection to the lateral surface of a circumscribing cylinder (i.e. theGall-Peters map projection) is area-preserving. It is also the derivative of the formula for the volume with respect to r because the total volume of a sphere of radius r can be thought of as the summation of the surface area of an infinite number of spherical shells of infinitesimal thickness concentrically stacked inside one another from radius 0 to radius r. At infinitesimal thickness the discrepancy between the inner and outer surface area of any given shell is infinitesimal and the elemental volume at radius r is simply the product of the surface area at radius r and the infinitesimal thickness.At any given radius r, the incremental volume (δV) is given by the product of the surface area at radius r(A(r)) and the thickness of a shell (δr):The total volume is the summation of all shell volumes:In the limit as δr approaches zero[1] this becomes:Since we have already proved what the volume is, we can substitute V:Differentiating both sides of this equation with respect to r yields A as a function of r:Which is generally abbreviated as:Alternatively, the area element on the sphere is given in spherical coordinates by:The total area can thus be obtained by integration: +++++++++++++++++If you don't now anything about calculus & are looking for formulas, then use the following:V = (4/3) * (pi)*(r3)A = 4*(pi)*(r2)
Formula for normality to liquids?
Normality (N) of a liquid solution is calculated by dividing the number of equivalents of solute by the volume of solvent in liters. The formula for normality is N = (equivalents of solute) / (volume of solvent in liters).
What is the formula for molarity in writin form?
The formula for molarity (M) is: moles of solute (in mol) / volume of solution (in liters). It can be written as: M = n/V, where n is the number of moles of solute and V is the volume of the solution in liters.
Why sphere has minimum surface area for given volume?
The same volume of an object, The simplest regular tetrahedron polyhedron, calculate the surface area. The surface area is pentahedral small surface area than the regular tetrahedron Regular hexahedron surface area than the surface area is small pentahedral . . . . If it is known is N-face surface area of ​​the body, there are N +1 is smaller the surface area of ​​the surface When N tends to infinity for a long time, Serve the sphere surface. ------mecose
Suppose that each dimension of a prism is increased by ten percent by what percent does its volume increase?
When linear dimensions are increased by a factor of 'N', area increasesby the factor of N2 and volume increases by the factor of N3.(1.10)3 = 1.331 = 33.1% increase
What are two ways to remember density?
Two ways to remember density is to know the formula or always remember the norm always goes on top of the donkey ex) N/D=N divided by D = answer
