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 Answer The formula of x 3 y 3 z 3 – 3xyz is written as Let us prove the equation by putting the values of x = 1 y = 2 z = 3 Let us consider LHS of the equation LHS = x 3 y 3 z 3 – 3xyz LHS = 1 3 2 3 3 3 – 3 (1 × 2 × 3)Now, to return to 3 dimensions Lines in 3 dimensions also have implicit equations, but now it takes two equations to characterise a line One equation alone would characterise a plane, not a line To find these equations, you proceed as above the coordinate equations for (x,y,z) = (1,6,3) t(7,4,4) are x = 1 7t, y = 6 4t, z = 3 4t(x y) 3 = x 3 3x 2 y 3xy 2 y 3 Example (1 a 2 ) 3 = 1 3 31 2 a 2 31(a 2 ) 2 (a 2 ) 3 = 1 3a 2 3a 4 a 6 (x y z) 2 = x 2 y 2 z 2 2xy 2xz 2yz

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(x y z)^3 formula-Answered 1 year ago Author has 44K answers and 14M answer views (XYZ)^3 Put XY = A (AZ)^3= A^3 Z^3 3AZ ( AZ) = (XY)^3 Z^3 3 A^2 Z 3A Z^2 = X^3Y^3 Z^3 3 X^2 Y 3 X Y^2 3 (XY)^2 Z 3 (XY) Z^2 =X^3 Y^3 Z^3 3 X^2Y 3XY^2 3 ( X^2 Y^2 2XY ) Z 3X Z^2 3YZ^2Relplot a general equation plotter black blue red green orange purple magenta cyan yellow solid dashed dotted 07pt 1pt 2pt 3pt 5pt Tip Relplot allows equation (s) such as y=x^2 , not just formulas like x^2

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3D Function Grapher To use the application, you need Flash Player 6 or 7 Click below to download the free player from the Macromedia site Download Flash Player 7Differentiating equation (1) partially wrt x & y, we get Eliminating a and b from equations (1), (2) and (3), we get a partial differential equation of the first order of the form f (x,y,z, p, q) = 0 Example 1 Eliminate the arbitrary constants a & b from z = ax by abX y is a binomial in which x and y are two terms In mathematics, the cube of sum of two terms is expressed as the cube of binomial x y It is read as x plus y whole cube It is mainly used in mathematics as a formula for expanding cube of sum of any two terms in their terms ( x y) 3 = x 3 y 3 3 x 2 y 3 x y 2

 Ex 31 , 6Find the value of x, y, and z from the following equation(i) 8(4&3@x&5) = 8(y&z@1&5) 8(4&3@x&5) = 8(y&z@1&5)Since matrices are equalTheir corresponding elements are equalHence, 4 = y 3 = z x = 1Hence x = 1, y = 4 & z = 3To sum numbers based on other cells being equal to either one value or another (either x or y), you can use the SUMIF function In the example show, we are summing all sales from either the West OR North region The formula in cell H6 is Where region \f\left( {x,y,z} \right) = z g\left( {x,y} \right)\ In terms of our new function the surface is then given by the equation \(f\left( {x,y,z} \right) = 0\) Now, recall that \(\nabla f\) will be orthogonal (or normal) to the surface given by \(f\left( {x,y,z} \right) = 0\) This means that we have a normal vector to the surface

6x 2 y 6x 2 z 2y 3 6y 2 z 6yz 2 2z 3 = 2 • (3x 2 y 3x 2 z y 3 3y 2 z 3yz 2 z 3) Trying to factor by pulling out 22 Factoring 3x 2 y 3x 2 z y 3 3y 2 z 3yz 2 z 3 Thoughtfully split the expression at hand into groups, each group having two terms Group 1 3y 2 z 3yz 2 Group 2 3x 2 y 3x 2 z Group 3 y 3 z 3 Ex 31 , 6Find the value of x, y, and z from the following equation(iii) 8( @ ( @ )) = 8(9@ (5@7))Since matrices are equalTheir corresponding elements are equal x y z = 9 x z = 5 y z = 7 Solving these equationsFrom (2) x z = 5 x = 5In a form for us to enter in CalcPlot3D these are z = sqrt(C x^2 y^2) z = sqrt(C x^2 y^2) For \(C = 2\text{,}\) we enter z = sqrt(2 x^2 y^2)in the 1st function and z = sqrt(2 x^2 y^2)in a 2nd function Figure561Level surface, \(C = 2\) For \(C = 2\text{,}\) we enter

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X y z = 1 0 0 It is given that x, y and z should be positive integers ie, x 1 , y 1 , z 1 Let x 1 = x − 1, y 1 = y − 1 and z 1 = z − 1 Now equation becomes, x 1 y 1 z 1 = 9 7 Now the total number of solution is = 9 7 3 − 1 C 3 − 1 = 9 9 C 2 = 4 8 5 1 Hence, option 'C' is correct Google describes this as "Accomplished X as measured by Y, by doing Z" But just to make it easier to remember, let's shorten it to XYZX^3y^3z^33xyz=(xyz)(x^2y^2z^2xyyzzx)a^3b^3c^33abc=(abc)(a^2b^2c^2abbcca)a^3b^3c^33abc formula proofx^3y^3z^33xyz formula proofa

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  The answer is z = 0 Remember that an horizontal plane is tangent to a curve in the space in its points of maximum, minimum or saddle We can answer in two ways The first this function is the equation of an elliptic paraboloid with concavity upwardsOn x^3 x y^3 y = z^3 z Suppose we wish to find an infinite set of solutions of the equation x^3 x y^3 y = z^3 z (1) where x, y, z are integers greater than 1 If z and x are both odd or both even, we can define integers u and v such that z=uv and x=uvIn similarity with a line on the coordinate plane, we can find the equation of a line in a threedimensional space when given two different points on the line, since subtracting the position vectors of the two points will give the direction vector Q = ( − 3, 0, 1) Q= (3,0,1) Q = (−3,0,1)

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Generic formula = IF(AND(OR( A1 = x, A1 = y ), B1 = z ),"yes","no") Summary To apply more complex logic like "if cell is (x OR y) AND z", you can embed the AND and OR functions directly in the logical test of the IF function In D5, the formula is = IF(AND(OR( B5 = "red", B5 = "green"), C5 > 10),"x","") This formula returns "x" if the color in Consider the random variables X, Y and Z, which are given to be pairwise uncorrelated (ie, X and Y are uncorrelated, X and Z are uncorrelated, and Y and Z are uncorrelated) Suppose that E X4=E Y4=E Z4=3 Let W=abXcX2 and V=dX, where a,b,c, and d are constants, all greater than 0Click here👆to get an answer to your question ️ The number of solutions of the equation x y z = 10 in positive integers x,y,z is equal to Join / Login Question The number of solutions of the equation x y z = 1 0 in positive integers x, y, z is equal to A 3 6 B 5 5 C 7 2 D 4 5 Hard Open in App Solution

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 You can substitute these formulas for y and z into the second equation This gives a single equation, in a single variable (x) The single equation can be simplified, by letting v = x 1, and substituting v1 in for x Then you can multiply through by v² Notice that you are assuming that v ≠ 0 Then you can solve for vEquationcalculator xyz=6, 2xyz=3, 3xz=0 en Related Symbolab blog posts High School Math Solutions – Quadratic Equations Calculator, Part 1That is, a surface that may be defined as the zero set of a polynomial of degree two in three variables Among quadric surfaces, an ellipsoid is characterized by either of the two following

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Multiply each term in y z = x y z = x by z z Cancel the common factor of z z Tap for more steps Cancel the common factor Rewrite the expression Rewrite the equation as x z = y x z = y Divide each term by x x and simplify Tap for more steps Divide each term in x z = y x z = y by x x A function of two variables z = (x, y) maps each ordered pair (x, y) in a subset D of the real plane R2 to a unique real number z The set D is called the domain of the function The range of f is the set of all real numbers z that has at least one ordered pair (x, y) ∈ D such that f(x, y) = z as shown in Figure 1411There are two formula of it x^3 y^3 z^3 3xyz = (xyz) (x^2y^2z^2xyyzzx) 2 x^3 y^3 z^3 3xyz = (1/2) (xyz) {xy)^2(yz)^2(zx)^2}

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Factor x^3y^3 x3 − y3 x 3 y 3 Since both terms are perfect cubes, factor using the difference of cubes formula, a3 −b3 = (a−b)(a2 abb2) a 3 b 3 = ( a b) ( a 2 a b b 2) where a = x a = x and b = y b = ySolve x y z = x 3 y 3 z 3 = 8 in Z First I tried to transform this equation, substituting x = 8 − y − z So I end up with Using Wolfram Alpha I expanded this equation and tried to factorize it so finally I got z ∈ Z, which implies z − 8 is an integer implying that the second term is also an integerYou can reduce the first equation to x^3 = y^3, z = 1 with obvious infinite solutions This paper details other families of solutions The second equation has solutions (x,y,z)\equiv (6t^31, 16t^3,

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W L A Tafelmacher, La ecuación x 3 y 3 = z 2 Una demonstración nueva del teorema de fermat para el caso de las sestas potencias 17, Ann Univ Chile, Santiago 97, 6380 Advertisement Explanation (x −y)3 = (x − y)(x −y)(x −y) Expand the first two brackets (x −y)(x − y) = x2 −xy −xy y2 ⇒ x2 y2 − 2xy Multiply the result by the last two brackets (x2 y2 −2xy)(x − y) = x3 − x2y xy2 − y3 −2x2y 2xy2 ⇒ x3 −y3 − 3x2y 3xy2X2 z2 1 Example 3612 Reduce the equation to one of the standard forms, classify the surface, and sketch it 4y2 z2 x16y 4z =0 To solve this, we will have to complete the square The first step is to organize the equation by variable and factor out coecients of the highest degree term 4(y2 24y)z 4z x=0

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The domain of a function of several variables is the set of all inputs for which the function is defined In , R 3, the distance between points P = ( x 0, y 0, z 0) and Q = ( x 1, y 1, z 1) (denoted as P Q ) is given by the formula P Q = ( x 1 − x 0) 2 ( y 1 − y 0) 2 ( z 1 − z 0) 2 and thus the equation of a sphere withSteps for Solving Linear Equation x y z = x y z x y z = x y z Subtract xyz from both sides Subtract x y z from both sides xyzxyz=0 x y z − x y z = 0 Subtract y from both sides Anything subtracted from zero gives its negationLXXIII3 (1995) Solutions of x3 y3 z3 = nxyz by Erik Dofs (Stockholm) Introduction The diophantine equation (1) x3 y3 z3 = nxyz has only trivial solutions for three (probably) infinite sets of nvalues and some other nvalues (7, Chs 10, 15, 3, 2) The main set is characterized by n2 3n 9 is a prime number, n−3 contains no prime factor ≡1

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 Example 1 Find each of the directional derivatives D→u f (2,0) D u → f ( 2, 0) where f (x,y) = xexy y f ( x, y) = x e x y y and →u u → is the unit vector in the direction of θ = 2π 3 θ = 2 π 3 D→u f (x,y,z) D u → f ( x, y, z) where f (x,y,z) = x2zy3z2 −xyz f ( x, y, z) = x 2 z y 3 z 2 − x y z in the direction of →vGeneral form P(R)y= Q(R)x ztransform P(z 1)Y = Q(z 1)X xis called the input and yis the output or response Example Example 3 above has (1 8R 7R2)y= (1 R )x Using the formula for the ztransform of Rwe get (18z 17z 2)Y = (1 z )X System (or transfer) function Theorem The di erence equation P(R)y = Q(R)x with initial conditionsA solution to a system of three equations in three variables latex\left(x,y,z\right),\text{}/latex is called an ordered triple To find a solution, we can perform the following operations Interchange the order of any two equations Multiply both sides of an equation by a nonzero constant

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 An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation An ellipsoid is a quadric surface;Solution for xyz=3 equation Simplifying 1x y z = 3 Solving 1x y z = 3 Solving for variable 'x' Move all terms containing x to the left, all other terms to the right Add '1y' to each side of the equation 1x y 1y z = 3 1y Combine like terms y 1y = 0 1x 0 z = 3 1y 1x z = 3 1y Add '1z' to eachSolution Here f(x;y;z) = x2 y2 z2 is the function to be minimized and the constraint is g(x;y;z) = y2 xz= 9 LaGrange's method gives us the four equations in four unknowns 2x= z 2y= 2 y 2z= x y2 xz= 9 From the second equation we obtain two cases (1) y= 0 Then x;zand are all nonzero and we can divide the rst equation by the third to

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To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW Verify that `x^3y^3z^33x y z=1/2(xyz)(xy)^2(yz)^2(zx)^2`Solution for y=xz/3 equation x in (oooo) y = xz/3 // xz/3 yx(z/3) = 0 yx1/3*z = 0 // y1/3*zx = (y1/3*z) // * 1 x = y1/3*z x = y1/3*z The formula for the equation of a sphere We can calculate the equation of a sphere using the formula ( x − h) 2 ( y − k) 2 ( z − l) 2 = r 2 (xh)^2 (yk)^2 (zl)^2=r^2 ( x − h) 2 ( y − k) 2 ( z − l) 2 = r 2 where ( h, k, l) (h,k,l) ( h, k, l) is the center of the sphere and r r r is the radius of the sphere

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In threespace, the most general equation of the second degree in x, y and z has the form A x 2 B y 2 C z 2 D x y E x z F y z G x H y K z L = 0 , {\displaystyle Ax^{2}By^{2}Cz^{2}DxyExzFyzGxHyKzL=0,}

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