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Chapter 1 (maths 3) 1 CHAPTER 1PARTIAL DIFFERENTIAL EQUATIONS A partial differential equation is an equation involving a function of two ormore variables and some of its partial derivatives Therefore a partial differentialequation contains one dependent variable and one independent variable Here z will be taken as the dependent variable andAnswer to If P(x) = x2 x2 and Q(x) = 4x2 2 find P(6) P(6)=0 (Type an integer or a fraction)Simple and best practice solution for p^2x^2(p^2q^2)xq^2=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
This is an example of completing the squareIf we expand (x p)^2 q, we will have x^2 2px p qNow we can use algebra to work out what p and q are from the following equation x^2 7x 2 = x^2 2px p^2 q 7x 2 = 2px p^2 q We can force an answer because 7x must equal to 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 Solve the PDE $$ x(y^2z)py(x^2z)q=(x^2y^2)z$$ where, $ p=\displaystyle \frac{\partial z}{\partial x}$ and $ q=\displaystyle \frac{\partial z}{\partial y}$ My attempt I
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= 2xy −x2p2 −xypq −2xy y2q2 xypq = y2q2 −x2p2 = 0 So the equations are compatible • Next step is to determine p and q from the two equations xp−yq = 0, u(xpyq) = 2xy Using these two equations, we have uxp uyq −2xy = 0 =⇒ xp yq = 2xy u =⇒ 2xp = 2xy u =⇒ p = y u = φ(x,y,u) and xp −yq = 0 =⇒ q = xp y = xy yuSolve p 2 q 2 = x 2 y 2 The given equation can be written as p 2 –x 2 = y 2 –q 2 = a 2 (say) p 2 –x 2 = a 2 Implies p = Ö (a 2 x 2) andy 2 –q 2 = a 2 Implies q = Ö (y 2 –a 2) But dz = pdx qdy Standard IV (Clairaut's) form Equation of the type z = px qy f (p,q)#14 Report 4 years ago #14




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Check x 2 is the square of x 1 Check y 2 is the square of y 1 Factorization is (x y) • (x y) Trying to factor as a Difference of Squares 12 Factoring p 2 q 2 Check p 2 is the square of p 1 Check q 2 is the square of q 1 Factorization is (p q) • (p q) Equation at the end of step 1\left(qx^{2}2qx2q\right)p\left(x1\right)p^{2}q^{2}xq^{2}=0 (q x 2 − 2 q x 2 q) p (− x 1) p 2 − q 2 x q 2 = 0 All equations of the form ax^{2}bxc=0 can be solved using the quadratic formula \frac{b±\sqrt{b^{2}4ac}}{2a} The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction Solve for y, then find the value of y when given x = 2 6x = 7 4y 12 7/4 19/4 24 I need help solving these Can you please explain how to solve these problems?




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MATHEMATICS2 Que 6 Solve the equation x 2 p 2 y 2 q 2 =z 2 Solution PreviousSimple and best practice solution for Px^2(2pq)x2q=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 If it's not what You are looking for type in the equation solver your own equation and let us solve itSolve the following quadratic equations equation by using formula (xii) x^210x2=0




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Justify your answer Solution Yes, x 2 – 4x 1 = 0 is a quadratic equation with rational coefficients Question 8 Write the set of values of k for which the quadratic equation 2x 2 kx 8 = 0 has real roots Solution For real roots, D ≥ 0 ⇒ b 2 – 4ac ≥ 0 ⇒ k 2 – 4 (2) (8) ≥ 0= (m)^2 (m^2 a) = m^2 m^2 a = a Hence, the value of p^2 q^2The question has no unique answer math\begin{align}3x \dfrac{2}{1\dfrac{2}{x}}\\3x\dfrac{2x}{x2}\\\dfrac{3x^24x}{x2}\end{align}/math and therefore mathP




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The PDE p^2 q^2 = x^2 y^2 for the function U(x,y) with p =U_x , q =U_y written as p^2 x^2 = q^2 y^2 suggests to assume U(x,y) = F(x) G(y) From the equation obtain the separation F'(x)^2 x^2 = G'(y)^2 y^2 =K with K co 8 Follow 6 Certified by MeritNation Expert Shraddha, added an answer, on Shraddha answered this here p 2 x 2 (p 2 q 2 )xq 2 =0 D=b24ac = (p 2 q 2 )2 4p2 x q2 =p4q42p2q2 4p2q2Solve a quadratic equation by factoring and applying the zero product property




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Solve the following quadratic equation for x p2x2 (p2 q2)x q2 = 0 Solve the following quadratic equation for x p 2 x 2 (p 2 q 2)x q 2 = 0Solve x^2 p^2 y^2 q^2 = 1, where p=∂z / ∂x and q = ∂z / ∂y MATHEMATICS2 question answer collectionThe actual question I'm trying to tackle is express 3x^2 5x1 in the form p(xq)^2r and to be honest I don't know where to begin!



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The quadratic formula is a fine way to solve this problem, but if we want to find the roots of #q#, when #q(x)=0#, this problem is already set up very well for a quick and easy algebraic manipulation to find the roots If you're familiar with completing the square to find the roots of a quadratic equation, this is essentially already in the "completed square" formMath Use your knowledge of exponents to solve a) 1/2^x=1/(x2) b) 1/2^x>1/x^2 So I know that these functions are rational functions and I am trying to solve for x I tried toQ (x) is quadratic so would be a u shape (as x^2 is positive) It would also have y intercept of as when x=0, q (x) would be X^210x can be written as factories but won't be whole numbers The turning point is when x=5 as the differential is 2x10 When this is 0, that's the turning point




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Let's solve the first one for y y 2x = 5 y = 2x 5 Now let's substitute 2x 5 for y in the second equation to solve for x math What is the first step in solving the linear system {2x−3y=11 {−x5y=−9 by the substitution method in the most efficient way? We have the quadratic equation in x, x^2 mx m^2 a = 0, and its given that it has roots p and q So, sum of roots = p q = m/1 = m product of roots = pq = m^2 a We have to find the value of p^2 q^2 pq p^2 q^2 pq = (p q)^2 pq Now, we'll use the values of (p q) and pq we calculated above;Math, 1300, ashiii12 P^2x^2(p^2q^2)xq^2=0 using quadratic formula solve the equation



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