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)Has degree 3 in x and degree 2 in y Degree function in abstract algebra Given a ring R, the polynomial ring Rx is the set of all polynomials in x that have coefficients in R In the special case that R is also a field, the polynomial ring Rx is a principal ideal domain and, more importantly to our discussion here, a Euclidean domain This is a semiimportant identity to know (x^3y^3)=(xy)(x^2xyy^2) Although it doesn't apply directly to this question, it's also important to know that (x^3y^3)=(xy)(x^2xyy^2) This gives us the rule (x^3y^3)=(xy)(x^2∓xyy^2)
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X 3 y 3 x y x 2xy y 2-X 2sin y x 22y ≤ sin2 y The limits of the outer two functions as (x,y) → (0,0) are both 0, and so the Squeeze Theorem tells us that lim (x,y)→(0,0) x2 sin2 y x2 2y2 = 0 The notion of the limit of a function of two variables readily extends to functions of three or more variablesUse the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the axis Sketch the region and a
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N x = y ( x 2 x y 1 ) e xy ( 2 x y ) e xy = ( x y 2 x 2 y 2 x 2 y ) e xy = m y The new equation is exact As was mentioned in class, there may be more than one integrating factor Here μ = (xy)1 will also work, although we have given no way to find this integrating factor, other than after solving the differential equationAnswer by lenny460 (1073) ( Show Source ) You can put this solution on YOUR website!Plot x^2 y^3, x=11, y=03 WolframAlpha Volume of a cylinder?
SOLUTION 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 The problem to solve is xyx3y3 Multiply y and x Multiply the y and x Multiply y and x The y just gets copied along The x just gets copied along The answer is yx yx x*y evaluates to yx x*yx evaluates to yxx Multiply y and 3 Multiply y and 1 The y just gets copied alongX 2 −xy, dy dt = 3y 1− y 3 −2xy To find the xnullcline, we solve2x 1− x 2 − xy = 0, where multiplying out and collecting the common factor of x gives x(2− x− y) = 0 This gives two xnullclines, the linexy = 2 and the yaxis By plugging in the points (1,0) and (2,2) into2x 1− x 2 − xy, we see that solutions
For example the command 2x @ 3 evaluates the expression 2x for x=3, which is equal to 2*3 or 6 Algebra Calculator can also evaluate expressions that contain variables x and y To evaluate an expression containing x and y, enter the expression you want to evaluate, followed by the @ sign and an ordered pair containing your xvalue and yvalueSystemofequationscalculator 3x^2=y, x1=y en Related Symbolab blog posts High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables In this blog post,Solution for x'y' 3xy = 10xy y = Cx3/2 Q Give the domain and the range of the function whose graph is shown to the rightWhen arrows are dra A • Domain is the set of all values of x for which the function f(x) is defined and takes a finite val
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We think you wrote 2xy^2y^22x^3x^2/2xy^32xy^2x^2y^2 This deals with reducing fractions to their lowest termsSolve $\left(xy^3y \right)dx2\left(x^2y^2xy^4\right)=0$ written 37 years ago by smitapn612 ♦ 90 modified 18 months ago by sanketshingote ♦ 640Extended 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
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Find the condition that the curves 2x = y^2 and 2xy = k intersect orthogonally asked in Mathematics by AsutoshSahni (527k points) application of derivative;(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 = xySimple and best practice solution for 3x2yxy(x3y)y^2= 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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First type the equation 2x3=15 Then type the @ symbol Then type x=6 Try it now 2x3=15 @ x=6 Clickable Demo Try entering 2x3=15 @ x=6 into the text box After you enter the expression, Algebra Calculator will plug x=6 in for the equation 2x3=15 2(6)3 = 15 The calculator prints "True" to let you know that the answer is right More ExamplesIf I couldn't do the above one, which looks a heck of a lot simpler, I doubt I'll get through this one x^ (6/7) y^ (8/5) = 16Uploaded By MateIron5245 Pages 27 This preview shows page 24 27 out of 27 pages View full document See Page 1 solution Here, M ( x, y ) = 3 xy y 2 , and N ( x, y ) = x 2 xy, 24 so that @ M ( x, y ) @ y = 3 x 2 y, and @ N ( x, y ) @ x = 2 x y Therefore, M y
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F(x,y)dydx = Z 1 0 Z 2 0 (cx2 xy 3)dydx = 2c 3 1 3, so c = 1 (b) Draw a picture of the support set (a 1by2 rectangle), and intersect it with the set {(x,y) x y ≥ 1}, which is the region above the line y = 1 − x See figure above, right To compute the probability, we double integrate the joint density over this subset of theXy − 3 x 2 ) dx ( x 2 2 y ) dy = 0 SOLUTION (a) M = 2 xy − 3 x 2 ; 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
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(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 2yzCho tam giác MNP vuông tại M,đường cao MH a, Chứng minh tam giác HMN đồng dạng với tam giác MNP b, chứng minh hệ thức M H 2 =NHPH c, Lấy điểm E tùy ý trên cạnh MP,vẽ điểm F trên cạnh MN sao cho góc FHE =90 độAnswer (1 of 3) x^3 x^2 x y x y 1 = x^2(x 1) x 1 (x y y) = x^2(x 1) x 1 y(1 x) = x^2(x 1) x 1 y(x 1) = (x 1)(x^2 1 y)
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Xy'y=x^{2}2x1 en Related Symbolab blog posts Advanced Math Solutions – Ordinary Differential Equations Calculator, Exact Differential Equations In the previous posts, we have covered three types of ordinary differential equations, (ODE) We have now reachedX 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 y3 < x < s 28 3 5 Problem 15 (xy2 bx2y)dx(xy)x2 dy = 0 First, for this to be exact M y = 2xy bx2 = 3x2 2xy = N x So b = 3 With this, find the solution to the DE f(x,y) = Z M dx = Z xy 23x2ydx = 1 2 x y2 x3y g(y) And solve for g(y) f y = x 2y x3 g0(y) = x3 x y So we didn't need g(y) This leaves 1 2 x 2y x3y = C 6 Problem
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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)))(2A first order Differential Equation is Homogeneous when it can be in this form dy dx = F ( y x ) We can solve it using Separation of Variables but first we create a new variable v = y x v = y x which is also y = vx And dy dx = d (vx) dx = v dx dx x dv dx (by the Product Rule) Which can be simplified to dy dx = v x dv dx∂ N ∂ x = 2 x Since the two partials are equal, the equation is exact (b) The solution is F (x, y) = C, where 1 F = ∫ M ∂ x f ( y ) F = ( 2 xy − 3 x 2 ) ∂ x f ( y ) F =
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Section 21 Limits In this section we will take a look at limits involving functions of more than one variable In fact, we will concentrate mostly on limits of functions of two variables, but the ideas can be extended out to functions with more than two variables∂M ∂ y = 2 x N = x 2 2 y;Answer (1 of 8) Given 2^x=3^y=6^z Lets assume that each and every term is equal to k Which implies 2^x=k Now by applying logarithm on both sides we get x=log k to base 2 and 1/x= log 2 to base k And 3^y=k Again by applying logarithm on both sides we get y=log k
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The simplified expressions are i) x 3 5x 2 5x ii) a 2 b 3 3a 2 5b 3 iii) t 3 st s 2 t 2 s 3 iv) 4ac v) 3x 2 y 2 4xy vi) x 3 y 3 vii) 225x 2 16y 2 viii) a 2 b 2 c 2 2ab ☛ Check NCERT Solutions for Class 8 Maths Chapter 9Simple 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, Stack Exchange network consists of 178 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack Exchange
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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)$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 nonnegativePiece of cake Unlock StepbyStep Natural Language
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Simplify (xy^2)^3 (xy2)3 ( x y 2) 3 Apply the product rule to xy2 x y 2 x3(y2)3 x 3 ( y 2) 3 Multiply the exponents in (y2)3 ( y 2) 3 Tap for more steps Apply the power rule and multiply exponents, ( a m) n = a m n ( a m) n = a m n x 3 y 2 ⋅ 3 x 3 y 2 ⋅ 3 Multiply 2 2 by 3 3Factor 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 Transcript Ex 53, 6 Find 𝑑𝑦/𝑑𝑥 in, 𝑥3 𝑥2𝑦 𝑥𝑦2 𝑦3 = 81 𝑥3 𝑥2𝑦 𝑥𝑦2 𝑦3 = 81 Differentiating both sides 𝑤𝑟𝑡𝑥
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This gives us the equations n = xy = yx x != y (Note that for this example, the != stands for not equal to similar to some programming languages) xy always equals yx due to the communtative property of multiplication So there are actually an infinite number of answers Some are given below 6 = (2)(3) = (3)(2), 2 != 3 12 = (3)(4) = (4)(3), 3(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) Now simplify (x y ( x^2 2xy y^2) 2) This is a difference of squares 81x^4 16y^4 = (9x^2)^2 (4y^2)^2 = (9x^2 4y^2)(9x^2 4y^2) But the first is a difference of squares, so that can be factored again (3x 2y)(3x 2ySolve 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 145 Concept Notes & Videos 431 Syllabus Advertisement Remove all ads Solve 2xy/ X Y = 3/2 Xy/ 2x Y = 3/10 X Y ≠ 0 and 2x Y ≠ 0
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