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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"
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How do you find the sum to n terms of a harmonic progression?
The sum of n terms in a harmonic progression is given by the formula ( S_n = \frac{n}{a_1+ \frac{ (n-1)d}{2}} ) where ( S_n ) is the sum of n terms, ( a_1 ) is the first term, d is the common difference.
How many numbers of n digits exist if the sum of all digits is s?
The number of n-digit numbers where the sum of the digits is s can be calculated using stars and bars method. It can be obtained by arranging (s - 1) + n stars and inserting n - 1 bars among them, which gives a total of (n + s - 1) choose (n - 1) possible numbers.
What is a real world application of Euler's formula?
One real-world application of Euler's formula is in electrical engineering for analyzing circuits. It can be used to understand the relationship between the voltage, current, and impedance in AC circuits, helping to calculate values such as power and phase angles.
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?
The size of the pipe needed for 1 cubic meter per second of water flow depends on the water velocity required and the material of the pipe. Generally, for water flow without excessive pressure drop, a pipe with a diameter between 0.2 to 1.0 meters is adequate. The specific pipe size can be calculated using hydraulic principles considering factors such as flow rate, pressure, and pipe material. Consulting with a hydraulic engineer or using specialized software can help determine the exact pipe size needed.
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 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)
What is the formula for percent of concentration?
M = n / V M = concentration of solution in mol/L, n = moles of substance, V = volume of solution in litres (L) the formula can re-arranged to V = n / M :)
What formula is n equals cV?
It's to find the number of moles n = moles c = concentration (in dm3) V = volume (in dm3)
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 is the definition of a perfect cube?
The definition of a perfect cube is the cube of a number n is its third power. This is formula that is used for finding volume.
The volume of any gas depends upon the size of the?
not size but value of the formula V=(nRT/P) where V is the Volume, T is the temperature, R is the gas constant and n is the amount of moles.
What is the formula for the volume of a gas?
PV=Nrt where P is pressure V is volume N is the number of molecules r is 8.314472 J/K(mol) ( gas constant) t is the temperature in Celsius.
What do you call the surface of a sphere?
The n-sphere is denoted Sn. It is an example of a compact topological manifold without boundary.
What is dimension of permittivity of vacumm?
The dimension of permittivity of any medium or vacuum (free space) is C2 N-1 m-2
