Find free variables in the following formulas: i. ∀x(p(x) -> ∃y~q(f(x), y, f(y))) ii. ∀x(∃yr(x, f(y)) -> r(x, y)) iii. ∀z(p(z) -> ∃y(∃xq(x, y, z) V q(z, y, x))) iv. ∀z∃x∃y(q(z, u, g(u, y)) V r(u, g(z, u)))

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A: Let's find non zero unit vector.

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A: Given below clear explanation.

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Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y + z+ w= 6 3x…

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Q: How to solve this?

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Q: Show that if f(x, y) is homogeneous of degree n, then                                     xfx(x, y)…

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Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: 1- If z = 1+ y2, we can write: a) z = 1- (iy)?, b) z = 1- iy?, c) z = 1- iy, d) z 1 + (iy)? 2- If z,…

A: As you have posted multiple questions so according to our guidelines, I answered first three…

Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

Q: If w = f(u, v), u = x + y, and v = x - y, show that w,wy = w - w?. %3D %3D

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Q: L'équation 5xyz = 2x2 + y² +2z² + 6 définit implicitement z comme fonction de x et de y au voisinage…

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Q: Minimize c = s + t + 2u subject to s + 4t + 2u ≥ 95 4s + t + 3u ≥ 95 s ≥ 0, t ≥ 0, u ≥ 0. c= (s, t,…

A: the given simplex problem is as follows  Minimize c=s+t+2u subject to…

Q: 4. Find the work done by the force F(r,y,2) = (x,-z,2y) in moving straight from (0,0,0) to (1.1.0),…

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Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: Find the Jacobian of following functions f(x,y, z) = 3xy – yz + 2y z2 - 5xyz3 g(x,y, z) = xyz -…

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Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: (R, d), where d(r, y) = |r – y|, is separable. %3D

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Q: Let z = F(x , y) = xy2 + - , where x = u2 + v2 - 4 and y = uv . az Use the chain rule to find at (u…

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Q: Prove that the integral: √ [2xyz² dx + (x²z² + z cos yz)dy + (2x²yz + y cos yz)dz ] Is independent…

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