2 $\begingroup$ I can prove that $x^3y^3 = (xy)(x^2xyy^2)$ by expanding the right side $x^3y^3 = (xy)x^2 (xy)(xy) (xy)y^2$ $\implies x^3 x^2y x^2y xy^2 xy^2 y^3$ $\implies x^3 y^3$ I was wondering what are other ways to prove that $x^3y^3 = (xy)(x^2xyy^2)$Graph y=x^23 y = x2 − 3 y = x 2 3 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 x 2 − 3 x 2 3 Tap for more steps Use the form a x 2 b x cX3 − x2y − xy2 y3 x 3 x 2 y x y 2 y 3 Factor out the greatest common factor from each group Tap for more steps Group the first two terms and the last two terms ( x 3 − x 2 y) − x y 2 y 3 ( x 3 x 2 y) x y 2 y 3 Factor out the greatest common factor ( GCF) from each group
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X 3 y 3 x y x 2xy y 2-Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!Factor x^3xy^2x^2yy^3 x3 − xy2 x2y − y3 x 3 x y 2 x 2 y y 3 Factor out the greatest common factor from each group Tap for more steps Group the first two terms and the last two terms ( x 3 − x y 2) x 2 y − y 3 ( x 3 x y 2) x 2 y y 3 Factor out the greatest common factor ( GCF) from each group
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X 3 y 3 = ( x y) ( x 2 − x y y 2) Use the distributive property to multiply xy by x^ {2}xyy^ {2} and combine like terms Use the distributive property to multiply x y by x 2 − x y y 2 and combine like terms x^ {3}y^ {3}=x^ {3}y^ {3} x 3 ySimple and best practice solution for x/y=2/3 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, Transcript Example 17 Solve the pair of equations 2/𝑥 3/𝑦=13 5/𝑥−4/𝑦=−2 2/𝑥 3/𝑦=13 5/𝑥−4/𝑦=−2 So, our equations become 2u 3v = 13 5u – 4v = –2 Hence, our equations are 2u 3v = 13 (3) 5u – 4v = – 2 (4) From (3) 2u 3v = 13 2u = 13 – 3V u = (13 − 3𝑣)/2 Putting value of u (4) 5u – 4v = 2 5((13 − 3𝑣)/2)−4𝑣=−2 Multiplying
If x 3 y 3 3axy = 0, then dy/dx equals If x x y y z z = c, then ∂z/∂x = If X1 X2 X3 As Well As Y1 Y2 Y3 Are In Gp With The Same Common Ratio Then The Points X1 Y1 X2 Y2 And X3 Y3 If Cos Pi By 2n Then X1 X2 X3 Infinity Equal If Xy Xe X Y 6 Then Dy Dx If y (x) is solution of x(dy/dx) 2y = x 2, y(1) = 1, then value of y(1/2)0 votes 1 answer Prove that the curves x = y^2 and xy = k intersect at right angles if 8k^2 =1 asked in Mathematics by Nisa (598k points)The normal to the ellipse at the point (x,y,z) is \nabla(x^2y^24z^2) = (2x, 2y, 8z) At minimum or maximum distance to the plane, This is easy if you don't insist on using Lagrange multipliers The normal to the ellipse at the point (x, y, z) is
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 byGet stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!Piece of cake Unlock StepbyStep Natural Language
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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 = y (x−y)(x2 xyy2) ( x y) ( x 2 x y y 2)Why does x y x y 2 x y 3 ⋯ = x y − 1?Piece of cake Unlock StepbyStep Natural Language
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Plot x^2 y^3, x=11, y=03 Natural Language;3x(x 2 2x – 5) Content Continues Below Factor 26 x sqrt9 y 3 – 13 y sqrt4 x 2 y xy sqrt169 x 4 y 3 , assuming that all variables are nonnegativeSince you are in high school, allow me to write an answer that is the an expanded version of the other answer, but perhaps, one that is written in a way that is more accessible to you
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2x35x2yxy26y3 Final result 2x3 5x2y xy2 6y3 Step by step solution Step 1 Equation at the end of step 1 (((2•(x3))((5•(x2))•y))(x•(y2)))(2Solution for xy2xy=3 equation Simplifying x y 2xy = 3 Reorder the terms x 2xy y = 3 Solving x 2xy y = 3 Solving for variable 'x' Move all terms containing x to the left, all other terms to the right Ex 57, 13 If 𝑦=3 cos〖 (log〖𝑥)4 〖 sin〗〖 (log〖𝑥 )〗 〗 〗 〗, show that 𝑥2 𝑦2 𝑥𝑦1 𝑦 = 0 𝑦=3 cos〖 (log
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Ex 25, 9Verify (i) x3 y3 = (x y) (x2 – xy y2)LHS x3 y3We know (x y)3 = x3 y3 3xy (x y)So, x3 y3 = (x y)3 – 3xy (x y) = (x y)3 – 3xyX^3 x^2 y x y^2 y^3 WolframAlpha Volume of a cylinder?1) Factor by grouping x^3 y^3 x^2y xy^2 = (x^3 y^3) (x^2y xy^2) The first is a sum of cubes (x y) (x^2 xy y^2) xy (x y) They both have an x y in common (x y) (x^2 xy y^2) (xy)
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Answer by You can put this solution on YOUR website!Find the condition that the curves 2x = y^2 and 2xy = k intersect orthogonally asked in Mathematics by AsutoshSahni (527k points) application of derivative;Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history
Implicit Differentiation
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Well, working backwards from (xy)(xy) you get x(xy)y(xy)=x 2xyxyy 2 For the difference of two cubes, x 3y 3 =(xy)(x 2 xyy 2) so again working backwards you get x(x 2 xyy 2)y(x 2 xyy 2) expanding, x 3 x 2 yxy 2x 2 yxy 2y 3 Transcript Ex 53, 6 Find 𝑑𝑦/𝑑𝑥 in, 𝑥3 𝑥2𝑦 𝑥𝑦2 𝑦3 = 81 𝑥3 𝑥2𝑦 𝑥𝑦2 𝑦3 = 81 Differentiating both sides 𝑤𝑟𝑡𝑥On the other hand, Mathematica gives an explicit solution for the original differential equation $$ y(x)=\frac{e^{3 x}}{96 \sqrt{(x6)^2}} $$ $$\begin{multline}\Biggl(\sqrt{2 \pi } c_2 \left(x^636 x^5519 x^ x^ x^ x\right)(x6)^2 \text{erfi}\left(\frac{\sqrt{(x6)^2}}{\sqrt{2}}\right)\\ 2 \sqrt{(x6)^2} \left(384
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Extended Keyboard Examples Upload Random 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 If √x √y = 5, then dy/dx at (4,9) is (a) 2/3 (b) 3/2 (c) 3/2 (d) 2/3 asked in Mathematics by KumariMuskan ( 339k points) bseb model setSimple and best practice solution for (3x^2y2xyy^3)dx(x^2y^2)dy=0 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework
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About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How works Test new features Press Copyright Contact us CreatorsSOLUTION 1 Begin with x 3 y 3 = 4 Differentiate both sides of the equation, getting D ( x 3 y 3) = D ( 4 ) , D ( x 3) D ( y 3) = D ( 4 ) , (Remember to use the chain rule on D ( y 3) ) 3x 2 3y 2 y' = 0 , so that (Now solve for y' ) 3y 2 y' = 3x 2, and Click HERE to return to the list of problems SOLUTION 2 Begin with (xy) 2 = x y 1 Differentiate both sides Here, by the Chain Rule, d/dx(y^3)=d/dy(y^3)*dy/dx=3y^2*dy/dx, &, by, the Product Rule, d/dx(xy)=x*d/dx(y)y*d/dx(x)=xdy/dxy*1 Therefore, 3x^23y^2dy/dx=2(xdy/dxy) (3y^22x)dy/dx=2y3x^2 dy/dx=(2y3x^2)/(3y^22x)
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43 x2 2xy y2 is a perfect square It factors into (xy)• (xy) which is another way of writing (xy)2 How to recognize a perfect square trinomial • It has three terms • Two of its terms are perfect squares themselves • The remaining term is twice theSolve 2xy/ X Y = 3/2 Xy/ 2x Y = 3/10 X Y ≠ 0 and 2x Y ≠ 0 CISCE ICSE Class 9 Question Papers 10 Textbook Solutions Important Solutions 6 Question Bank Solutions 144 Concept Notes & Videos 414 Syllabus Advertisement Remove all ads Solve 2xy/ X Y = 3/2 Xy/ 2x Y = 3/10 X Y ≠ 0 and 2x Y ≠ 0Y=2^x WolframAlpha Volume of a cylinder?
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You can put this solution on YOUR website!Use implicit differentiation to find the largest yvalue in the loop of the Folium of Descartes, which is given by x3 y3 − 3xy = 0 First, we do the implicit derivative to simplify our equation Because maxima/minima occur when f' (x)=0, we take the implicit derivative and set it equal to 0(xyz)^3 (x y z) (x y z) (x y z) We multiply using the FOIL Method x * x = x^2 x * y = xy x * z = xz y * x = xy
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Z = x 2 3 xy y 2 2 z = x y 2 − y x 2 3 z = sin 3 x cos 4 y 4 z = arctan (y x) 5 z = 2 x 2 − 5 xy y 2 6 z = xy x − y 7 z = xsin y ycos x 8 z = (x y) 3 9 z = x y x − y 10 z = e y Inx Total Differential We define the total differential dz as function z = f (x, y) by dz = ∂z ∂ x dx ∂z ∂ y dy A function of more x^3 x^2y y^3 xy^2=(xy)(x^2y^2) x^3 x^2y y^3 xy^2 = y^3((x/y)^3(x/y)^2(x/y)1) but z^3z^2z1 =0 has a root z = 1 making z^3z^2z1 = (z1)(b z^2c z d) equating the coefficients we find { (d1 = 0), (c d 1= 0),( b c 1= 0), (1 b = 0) } solving for b,c,d (b=1,c=0,d=1) so z^3z^2z1 = (z1)(z^2 1) and finally x^3 x^2y y^3 xy^2=(x1 {x2 y2 2x 2y = (x 2)(y 2) ( x y 2)2 ( y x 2)2 = 1 2 {x2 − 2xy − 6 = 6y 2x 3x2 y 1 = 4 − x 3 {x2 − y = y2 − x x2 − x = y 3 4 { x y 1 x 1 y = 9 2 xy 1 xy x y y x = 5 6 {x3(x − y) x2y2 = 1 x2(xy 3) − 3xy = 3 7 { x2 3y − 6x = 0 9x2 − 6xy2 y4 − 3y 9 = 0
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreWe think you wrote (x^3y^3)/(x^23xy2y^2)•(x^2xy6y^2)/(x^22xy3y^2)÷(x^2xyy^2)/(2x^22xy) This deals with factoring binomials as the sum or difference ofThe graph of mathx^2(y\sqrt3{x^2})^2=1/math is very interesting and is show below using desmos
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Y=x^2 3 This is an equation of a parabola y=ax^2bxc Here a=1 b=0 c=3 a=1>0 the parabola opens upwards The coordinates of the minimum point are x=b/2a = 0/2 =0 y(0)=0^23 y = 3 we need 2 more points to draw the parabola x=1 y=4 x=1 y = 4 Join the tree points together and you see the parabola y=3x This is the equation of a line thatMath Input NEW Use textbook math notation to enter your math Try it
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