23. Prove that (xo, Yo), (x1, y1), and (x2, y2) lie on a line if and only if (х — Хо)02 — Уо) - (*з — Хо)(ут — Уо) %3D 0.

Q: If u=f(x2+2yz,y2+2zx).Prove that

A: Given: u=fx2+2yz, y2+2zx Let u=fv, w where v=x2+2yz and w= y2+2zx. Now prove…

Q: - (m'n') m²n_> 14. (2xy)²(-3x²)(4) 15. (2ryz?)°(x²z}*, 21 im2, n (m35 m2).(nein (2)(x3(35 (2 243…

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Q: |=1|+ |= 2 | |- |- | 3. If z3 + z,, show that VI +

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Q: Prove that (RUS) (TUW), if we know as given from the problem that: RCT and SEW Justify each line of…

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Q: From (2) we get: 7h 1 (7g+7)n+1 - 2-(7g+6) (2 - N-(79+6) II ig+1)k-(a+1)t-q +1 h=0 k=1 7h 1…

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Q: 5.Use thelefinition to Rrave that Jw wh- 2

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Q: 25. If mRU = (16x - 13)', mSE (11x - 24)', and M2STU = (3x + 1)', find mŠU %3D Iex-13. mSU=

A: By visuals, we can say that RS is diameter in this circle.

Q: 3 Rnd the lineasion of the hunctran f(xLcos line asiz l

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Q: O max(x,z) О тах(хә 10xz + 3x + z suисh that 3 > 6х + 3z. О mincә 10xz+ 3x + z such that 3 6х + 3z

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Q: Show that =- 5)" /31 + 6. 1 = 2 ) /7! + () /9! – ... %3D | -- IN

A: We know that, from the Taylor's formula for power series expansion of sinx is given as…

Q: 7. Show for y = u.v that y"= uv"' + 3u' v'" + 3u" v' + u''' v.

A: The detailed solution is as follows below:

Q: 5. Determine mZU if mZR = 9x 10 and mZU = 3x + 4. %3D %3D R S T. mZU = 50.5° mZU = 35° %3D mZU = 75°…

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Q: A Moving to another question will save this respons Quèstion 1 If y = u - 4 and u = 3x2 + 10 , find…

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Q: д2 and дх дх Suppose y*2 — 118 — 4гу — 2. Compute 4.xy – z. Compute at the point (-3, 2, –2). ду д2…

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Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: If u = -12i - 6j and v = 9i + 9j, findu + v. O 21i - 4j O 21i + 3j O -4i + 3j O -3i + 3j

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Q: Express y as a fiunetion af k if y - 2r+5, 1- V3t -1, and t- 3k - 5.

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Q: A 6x 6 square is tiled by 2x 1 dominoes. Prove that it has at least one fault-line, that is, a…

A: Consider a 6×6 square which is tiled by 2×1 dominoes. Suppose the 6×6 square has no fault lines.…

Q: Prove that ifx > 3 and y> 4, then xy > 11.

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Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: 4: verify that wy = Wyx . ریاضيات المرحلة الثانية a w = In (2r + 3y) %3D

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Q: Find x, y, z and w if (::)-(; )-(.. ") 4 x + y 3 -1 2w z + w 3

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Q: 12 y' (12x +5) (4y* +3)° b. If y* +3y-4x' = 5x+1, then prove that y"(4y +3) = 24.x--

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Q: 4. Show that (1) SST = Cu – 9)* = vy - ng = v (1. -) (2) sSR= Em – )* = ³ X'y – ng° = v ( H - )v (3)…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 3. Evaluate Se(x² – iy²)dz along the straight lines from (1, 1) to (1, 8) and then from (1,8) to (2,…

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Q: Compute [rN (1- ) ]- d. K

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Q: 42. Show that S 4xys + %3D 1- x2 1- y? 1– 22 (1 – a²) (1 – 3²) (1 – 2²) if xy + xx yz = 1

A: Given that  xy+yz+xx=1 Prove that the expression

Q: (6) If w = f(u, v), where u = x + y and v = x – y, show that = 2 ди

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Q: (8) If w = 5x² + 2y², x= -3s+t, and y = s – 4t. Find and Əw as

A: The objective is to find the partial derivatives .

Q: 15. In AXYZ, if ZX =ZZ, XY = 13x – 21, YZ = 8x – 6, and XZ = x + 4, find x and the measure of each…

A: given: in ∆XYZ, ∠X≅∠Z XY=13x-21YZ=8x-6XZ=x+4 we have to find x and the measure of each side. that is…

Q: (2 Let xinN(0.1), n = 2 and T= Xx +X2 Show that Tis a Sufficiency Stakistic.

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Q: Evaluate ff xydxdy over the square with corners (0,0), (1,1), (2,0) and (1, –−1) (u + v) (u - v) 2 2…

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Q: Show that f10 fdx + gdy = S6 10 5a*y²dx + 2yx³dy is independent of path •(11,–7) ,-10) • (11,–7)…

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Q: 14) Find mzYIJ if mZHIY = 28°, %3D MZYIJ = 139x + 1, and mZHIJ= 168x. %3D Y

A: Given : m∠HIY = 28°m ∠YIJ = 139x + 1m∠HIJ = 168x

Q: Show that if 0 <y<1, and Y ~ N(0,1), we have that 9 6 3 P\Y + %(x² – 1) < =] × + (V +1). -

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Suppose X~N(112,16), and Z~N(0,1). Then x = 112, is equivalent to z = ______.

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Q: 5. Show that xZx + yZry = yezy if z= xy + y In xy

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Q: If W = 2x 2 + 3xy2 - 20y-2+ 6u; where x = 5u2 +4v 2 and y= u - 4v3 , find §W / §V.

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Q: Compute Projsw given by |2 -1 – 2 and S is defined by 8 [2 – 12]+t[-1 – 13], s,t e R. x = s ||

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Q: 15. In AXYZ, if ZX = Z , XY = 13r - 21, YZ = 8r – 6, and XZ = x + 4, find x and the measure of each…

A: Solve 15

Q: = 1, prove that 1. If a + u bě+ u Ć +U %3D ди ду du ди du - 2| х +y Əz

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Q: 2) Prove by using the pigeonhole principle that among any 17 points in a square of side one there is…

A: Given: A square of side one contains 17 points. To show: There is at least a pair whose distance is…

Q: List the sides of AFGH in order from least to greates if mZF=(5x+6)°, mZG=(12x-4)°, and m…

A: Consider the following △FGH: m∠F=5x+6°m∠G=12x-4°m∠H=4x+31° Sum of all angles of triangle is 180°.…

Q: -x+y<y. 2 If x < y, prove that x <

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Q: 10. If mZTSV= (6x + 17) and mSV = (15x + 13)', find mSUV. %3D T

A: A circle

Q: 2. 1. If UZ = x+ 21 and ZS = 3x – 15, find US.

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Q: 16 3. Show that for x2 + 2xy - 3y² = 4, y" (x-3y)3

A: We will find y" as following.

Q: 16) * Find y' if y In (x2-8), when x 4

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Q: a,b,x,y, are negative numbers a⁵ + b⁵<= 1 x⁵ + y⁵ <= 1 prove that a²x³ + b²y³ <= 1

A: Given information: The numbers a,b,x and y are negative numbers. The conditions are a5+b5≤1,…