Circle on a Graph Let us put a circle of radius 5 on a graph Now let's work out exactly where all the points are We make a rightangled triangle And then use Pythagoras x 2 y 2 = 5 2 There are an infinite number of those points, here are some examplesI've been trying to solve this equation and I can't seem to find a way out I need to findFormula's 1 (x y)(xy) = x^2 y^2 2 (x y)^2 = x^2 2xy y^2 3 (xy)^2= x^2 2xy y^2 Which above formula would be used by the following problems?
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X^2+y^2+z^2-xy-yz-zx formula-Simplify (xy)(x^2xyy^2) Expand by multiplying each term in the first expression by each term in the second expression Simplify terms Tap for more steps Simplify each term Tap for more steps Multiply by by adding the exponents Tap for more steps Multiply by Tap for more stepsHow do you use Implicit differentiation find #x^2 2xy y^2 x=2# and to find an equation of the tangent line to the curve, at the point (1,2)?
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Figure 2 At left, the circle given by \(x^2 y^2 = 16\text{}\) In the middle, the portion of the circle \(x^2 y^2 = 16\) that has been highlighted in the box at left And at right, the lemniscate given by \(x^3 y^3 = 6xy\text{}\) Perhaps the simplest and most natural of all such curves are circlesThe result of Mehler can also be linked to probability For this, the variables should be rescaled as x → x/ √ 2, y → y/ √ 2, so as to change from the 'physicist's' Hermite polynomials H () (with weight function exp(− x ²)) to "probabilist's" Hermite polynomials He () (with weight function exp(− x ²/2)) Then, E becomesGiven x^2y^2z^2=xyyzzx (1)multiplying by (xyz) on both sidesx^2y^2z^2 (xyz)=(xyyzzx ) (xyz)expand the above equationsx^3y^3z^3xy^2x^2 yyz^2y^2 zxz^2x^2 z=x^2 yxyzzx^2xy^2 y^2 zxyzxyz
It's simply a common binomial factor Common factors don't have to be just a variable or a number;Graph x=y^2 Find the properties of the given parabola Tap for more steps Rewrite the equation in vertex form Tap for more steps Complete the square for Substitute the known values of , , and into the formula and simplify Find the axis of symmetry by finding the line that passes through the vertex and the focusYES, there are solutions, an infinite amount in fact!
Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music WolframAlpha brings expertlevel knowledge andCircle on a Graph Let us put a circle of radius 5 on a graph Now let's work out exactly where all the points are We make a rightangled triangle And then use Pythagoras x 2 y 2 = 5 2 There are an infinite number of those points, here are some examplesY ˙ Y But Var(X) = ˙2 X and Var( Y) = Var(Y) = ˙2 Y, so that equals 2 2Cov X ˙ X;
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Inverse Trigonometric Formulas Trigonometry is a part of geometry, where we learn about the relationships between angles and sides of a rightangled triangleIn Class 11 and 12 Maths syllabus, you will come across a list of trigonometry formulas, based on the functions and ratios such as, sin, cos and tanSimilarly, we have learned about inverse trigonometry concepts alsoThe Roman surface or Steiner surface is a selfintersecting mapping of the real projective plane into threedimensional space, with an unusually high degree of symmetryThis mapping is not an immersion of the projective plane;//googl/JQ8NysPartial Derivative of f(x, y) = xy/(x^2 y^2) with Quotient Rule
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Integrate x sin(x^2) integrate x sqrt(1sqrt(x)) integrate x/(x1)^3 from 0 to infinity;Well, my first goto was to do this math\displaystyle x^2 xy y^2 = 0/math math\displaystyle (x^2 xy y^2)(x y) = 0/math (any number multiplied by zero is equal to zero) mathY ˙ Y By the bilinearity of covariance, that equals 2 2 ˙ x˙ Y Cov(X;Y) = 2 2ˆ XY) and we've shown that 0 2(1 ˆ XY Next, divide by 2 move one term to the other side of the inequality to get ˆ XY 1;
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The Roman surface or Steiner surface is a selfintersecting mapping of the real projective plane into threedimensional space, with an unusually high degree of symmetryThis mapping is not an immersion of the projective plane;We can try to factor x 2 −2xy−y 2 but we must do some rearranging first Change signs y 2 2xy−x 2 = − 1 k 2 Replace − 1 k 2 by c y 2 2xy−x 2 = cSee below Making m = xy n = yz p = xz we have m^2n^2p^2 = 2(x^2y^2z^2x*yx*zy*z) then x^2y^2z^2x*yx*zy*z = 1/2((xy)^2(yz)^2(xz)^2)
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View more examples » Access instant learning tools Get immediate feedback and guidance with stepbystep solutions and Wolfram Problem Generator Learn more about Step//googl/JQ8NysPartial Derivative of f(x, y) = xy/(x^2 y^2) with Quotient RuleUsing the simple formula ( x y )^2 = x^2 y^2 2*x*y I have proved that 2 = 4 Here is the proof 8 = 8 412 = 1624 (since 412= 8 & 16 –24 = 8) Now add 9 to both sides 4 – 12 9 = 16 – 24 9 2*2 2*2*3 3*3 = 4*4 – 2*4*3 3*3 2^2 2*2*3 3^2 = 4^2 – 2*4*3 3^2 this steplooks like the formula x2 y2 2*x*y = ( x y )2 ( 2 – 3 )^2 = ( 4 – 3 )^2 So 2 – 3= 4
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You have x^2y^2=(xy)(xy) So in your case (x^2y^2)/(xy)=((xy)(xy))/(xy)=xyCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music WolframAlpha brings expertlevel knowledge andHomework 5 Solutions 3132 f(x;y)=œ xy(x2−y2) x2y2 (x;y)≠(0;0) 0 (x;y)=(0;0) Note fis continuous, (by computing lim(x;y)→(0;0) of the formula above, eg using polar coorinates) (a) Find f x and f y when (x;y)≠(0;0) Away from (0;0);fcan be di erentiated using the formula de ning it,
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YES, there are solutions, an infinite amount in fact!This is a function of x and y Can be wriiten as f(x)=y^2 A function is a relatioship between two variables broadlyHowever, the figure resulting from removing six singular points is one Its name arises because it was discovered by Jakob Steiner when he was in Rome in 1844
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Divide y, the coefficient of the x term, by 2 to get \frac{y}{2} Then add the square of \frac{y}{2} to both sides of the equation This step makes the left hand side of the equation a perfect squarePlease Subscribe here, thank you!!!Integrate x^2 sin y dx dy, x=0 to 1, y=0 to pi;
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music WolframAlpha brings expertlevel knowledge andSimplify (xy)(x^2xyy^2) Expand by multiplying each term in the first expression by each term in the second expression Simplify terms Tap for more steps Simplify each term Tap for more steps Multiply by by adding the exponents Tap for more steps Multiply by Tap for more stepsGraph x=(y2)^2 Simplify Tap for more steps Rewrite as Expand using the FOIL Method Tap for more steps Apply the distributive property Substitute the known values of , , and into the formula and simplify Find the axis of symmetry by finding the line that passes through the vertex and the focus
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Please Subscribe here, thank you!!!We have (2xyy)dx(x²x)dy=0 y(2x1)dx(x²x)dy=0 y(2x1)dx=(x²x)dy x≠0,1 , y≠0 (2x1)/(x²x)dx=(1/y)dy we should now find the fraction (2x1)/x(x1You have x^2y^2=(xy)(xy) So in your case (x^2y^2)/(xy)=((xy)(xy))/(xy)=xy
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Math 461 Introduction to Probability AJ Hildebrand Variance, covariance, correlation, momentgenerating functions In the Ross text, this is covered in Sections 74 and 77Example 3 Using Green's theorem, calculate the integral \(\oint\limits_C {{x^2}ydx – x{y^2}dy}\) The curve \(C\) is the circle \({x^2} {y^2} = {a^2}\) (FigureX y = 12 Squaring both sides, we get x^2 2xy y^2 = 144 Now, xy = 27 4xy = 4 × 27 = 108 Subtracting 4xy from both sides, we get x^2 2xy 4xy y^2 = 144 108
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I'm at the beggining of a differential equations course, and I'm stuck solving this equation $$(x^2y^2)dx2xy\ dy=0$$ I'm asked to solve it using 2 different methods I proved I can find integrating factors of type $\mu_1(x)$ and $\mu_2(y/x)$If I'm not wrong, these two integrating factors are $$\mu_1(x)=x^{2} \ \ , \ \ \mu_2(y/x)=\left(1\frac{y^2}{x^2}\right)^{2}$$ Then, I've used $\muThis is true of the "difference of squares" you sent us, x 2 y 2 Once you think you know the factors you can check by multiplication Here are three possibilities for factorizations of x 2 y 2 (x y)(x y) (x y)(x y) (x y)(x y) Expand each of them and see which simplifies to x 2 y 2 PennyAlgebraic formulas and identities for math on mobile devices
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//googl/JQ8NysPartial Derivative of f(x, y) = xy/(x^2 y^2) with Quotient RuleFactor x^2y^2 x2 − y2 x 2 y 2 Since both terms are perfect squares, factor using the difference of squares formula, a2 −b2 = (ab)(a−b) a 2 b 2 = (a b) (a b) where a = x a = x and b = y b = y (xy)(x−y) (x y) (x y)Integrate 1/(cos(x)2) from 0 to 2pi;
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyThis equation is in standard form ax^{2}bxc=0 Substitute 1 for a, 2y for b, and y^{2} for c in the quadratic formula, \frac{b±\sqrt{b^{2}4ac}}{2a}Ok, this is really easy and it's getting me crazy because I forgot nearly everything I knew about maths!
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1st piece x^2 Bring down the 2, subtract 1 from the exponent 2x^(21) = 2x 2nd piece xy This is a product rule f'(x)g(x) f(x)g'(x) (1)y x*y' 3rd piece y^2 2y^(21) * y' = 2y*y' 4th piece 3 Derivatives of constants are 0 So the three turns into a zero Now put it together (remember the negative in front of the xy term) 2x yWe can try to factor x 2 −2xy−y 2 but we must do some rearranging first Change signs y 2 2xy−x 2 = − 1 k 2 Replace − 1 k 2 by c y 2 2xy−x 2 = cYES, there are solutions, an infinite amount in fact!
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However, the figure resulting from removing six singular points is one Its name arises because it was discovered by Jakob Steiner when he was in Rome in 1844Math 461 Introduction to Probability AJ Hildebrand Variance, covariance, correlation, momentgenerating functions In the Ross text, this is covered in Sections 74 and 77Well, my first goto was to do this math\displaystyle x^2 xy y^2 = 0/math math\displaystyle (x^2 xy y^2)(x y) = 0/math (any number multiplied by zero is equal to zero) math
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X = 2 Supplement Solving Quadratic Equation Directly Solving x 2x2 = 0 directly Earlier we factored this polynomial by splitting the middle term let us now solve the equation by Completing The Square and by using the Quadratic Formula Parabola, Finding the Vertex 31 Find the Vertex of y = x 2x2X = − 2 y 1 − 4 y 2 1 , x = 0, y = 0 and ∣ y ∣ ≤ 2 1 y = 0 Steps Using the Quadratic Formula Steps for Completing the SquareX^2 dy/dxy^2=xy divide by x^2 dy/dx y^2 /x^2 = y/x dy/dx y/x = y^2 /x^2 divide both sides by y^2 y^(2) dy/dx y^(1) / x = x^(2) (1)
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Hint Consider f (x) = x 2 4 y x y 2 − 1 as a quadratic in x, where y is constant By Vieta its roots x , x ′ satisfy x x ′ = − 4 y Thus if x is a root then so tooWell, my first goto was to do this math\displaystyle x^2 xy y^2 = 0/math math\displaystyle (x^2 xy y^2)(x y) = 0/math (any number multiplied by zero is equal to zero) mathThis equation is in standard form ax^{2}bxc=0 Substitute 1 for a, 2y for b, and y^{2} for c in the quadratic formula, \frac{b±\sqrt{b^{2}4ac}}{2a}
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1st piece x^2 Bring down the 2, subtract 1 from the exponent 2x^(21) = 2x 2nd piece xy This is a product rule f'(x)g(x) f(x)g'(x) (1)y x*y' 3rd piece y^2 2y^(21) * y' = 2y*y' 4th piece 3 Derivatives of constants are 0 So the three turns into a zero Now put it together (remember the negative in front of the xy term) 2x yPlease Subscribe here, thank you!!!(x y) 2 = x 2 2xy y 2 (x y) 2 = x 2 2xy y 2 Example 1 If x = 10, y = 5a (10 5a) 2 = 10 2 2·10·5a (5a) 2 = 100 100a 25a 2 Example 2 if x = 10 and y is 4 (10 4) 2 = 10 2 2·10·4 4 2 = 100 80 16 = 36 The opposite is also true 25 a 4a 2 = 5 2 2·2·5 (2a) 2 = (5 2a) 2
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Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with stepbystep explanations, just like a math tutorSo 1 ˆ XY 1 This exercise should remind you ofSOLUTION 15 Since the equation x 2 xy y 2 = 3 represents an ellipse, the largest and smallest values of y will occur at the highest and lowest points of the ellipse This is where tangent lines to the graph are horizontal, ie, where the first derivative y'=0
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Algebraic formulas and identities for math on mobile devicesIn mathematics, trigonometric substitution is the substitution of trigonometric functions for other expressions In calculus, trigonometric substitution is a technique for evaluating integralsMoreover, one may use the trigonometric identities to simplify certain integrals containing radical expressions Like other methods of integration by substitution, when evaluating a definite integral, it$$2xy (y^2 x^2 1)y' = 0 \quad \Rightarrow \quad y' = \frac{2xy}{y^2 x^2 1}$$ The family of orthogonal curves would have their direction field as a reciprocal of the direction field we found above^
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They can be any written expression Suggest that you find a section in a textbook labelled "factor by grouping" and practice several problems thereThe following formula means to sum up the weights of the four grapes The Greek letter capital sigma (Σ) indicates summation = X 1 X 2 X 3 X 4 = 46 51 49 44 = 190 involve the sum of cross products Table 2 shows the data for variables X and Y The cross products (XY) are shown in the third column The sum of the{x = 2 y 1 − 4 y 2 − 1 ;
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music WolframAlpha brings expertlevel knowledge andUsing the simple formula ( x y )^2 = x^2 y^2 2*x*y I have proved that 2 = 4 Here is the proof 8 = 8 412 = 1624 (since 412= 8 & 16 –24 = 8) Now add 9 to both sides 4 – 12 9 = 16 – 24 9 2*2 2*2*3 3*3 = 4*4 – 2*4*3 3*3 2^2 2*2*3 3^2 = 4^2 – 2*4*3 3^2 this steplooks like the formula x2 y2 2*x*y = ( x y )2 ( 2 – 3 )^2 = ( 4 – 3 )^2 So 2 – 3= 4Rearranging, (dx/dy) = (x/y)^2 x^2 xy Put x=t*y, (dx/dy) = (dt/dy)*y t Putting this back in differential equation, (dt/dy)*y = t^2 (t*y)^2 t*(y^2) t (dt/dy
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Given two different points (x 1, y 1) and (x 2, y 2), there is exactly one line that passes through them There are several ways to write a linear equation of this line If x 1 ≠ x 2, the slope of the line is − − Thus, a pointslope form is
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