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Q: find ---y (a) u•v, (b) u•u, (c) ||v ||2, (d) (u• v)v, and (e) u • (3v).

A: Disclaimer: Since you have asked a question with multiple sub-parts, we will solve the first three…

Q: Solve for x, y, z and w. (Enter your ansv x + y y + z 3 5 z + w 8 5 (x, y, z, w) =

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Q: derrorsinx,y,zbe0.001.Find relative error when x = y = z = 1.

A: Given,                 U=z4                                                  ...(1)  x=y=z=1, and…

Q: A lacker 20 feet lon3 is Kanin3 azainst th Wall of a house, The base Of the ladder iS PUICA allay ot…

A: According to the question diagram will be as below Given: dxdt=3 ft/sec To find: dydt

Q: To check for the result, we have to prove that  d dt  8t6 + C   = 48t5.

A: We have to prove that d8t6+Cdt=48t5 This is differentiation of function with respect to 't' We know…

Q: if y = secx prove that y^2+y=2y^3

A: Equation relates the number of variables combined together by algebraic entities using equality…

Q: Verify that det A = det B + det C, where Uj + vj U2 + v2 Uz + V3 A = A22 аз1 A32 --EE-E: A12 A22 V2…

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Q: If WZ = 68 and UV = 94, what is XY? %3D V W Y U Z

A: Given ,  WZ = 68 , UV = 94  We have to find XY

Q: Wnete to y=2x=1 equotion for Hhe line Pacallel the Doinit 4,9) an and

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Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

Q: flt) = Ualt) U, It) (t -3)2 + o uslt) sinzlt-s)

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Q: a²u , a?u k x² ди at ax2 ' ay?, ||

A: In this question, we used the separation of the variable method to solve the 2-D heat flow.

Q: contides oolling 2 fair 6-wde duce Di. Dz define ditesete sandom vasiable as 2= Di +D9 Y-D.- D. -D.

A: (i). Determine the joint pmf of bivariate random variable (x,y): Here, two fair dice D1 and D2 are…

Q: for w = ze(zy²+2:). Do not include =" in your answer.

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Q: Show that Plx-1,y) = A(x, y) X+ y-1

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Q: If (x, y) > (x+3, y-7) maps TUVW to T'U'V'W', what is the algebraic description that will map…

A: x, y→x+3, y-7 maps TUVW to T'U'V'W'. That is, the x-coordinates of T, U, V and W are added by 3…

Q: Suppose V(x,y) = (2x, 2y) and W(x,y) = (x,y + 3). Is V o W = W o V? Justify your answer.

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Q: Let X=(1,0, – 1, - /2)'. Then, ||X||, =| Select one: а. -1- V3 b. -V3 O C. 2 +/2 d. -V2

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Q: The colder a substance gets the less its particles move. O True False QuickNav

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Q: Find ƒx (x, y, z), ƒy (x, y, z), ƒz (x, y, z), and ƒyz (x, y, z) for ƒ(x, y, z) = x4 + 2yz2 + z4

A: Consider the given function, fx, y, z=x4+2yz2+z4 now, use the partial derivative method to find the…

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

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Q: If x, +iy,=x,+ iv, then x =y,

A: Given x1 + iy1 = x2 + iy2

Q: ax + by + cz + dq = 0 ,ax + by + cz + d2 %3D

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Q: Solve the following IBVP: Utt = 4uzz 0 0, u, (0, t) = u,(27, t) = 0, t>0, u(x,0) = 0, 0<I< 2n, T.…

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Q: Evaluate |/I. ze*+ydV where B is the box determined by B 0 <x < 4, 0 < Y < 3, and 0 < z < 3. The…

A: We have to evaluate the integral

Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

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Q: Making use of the fact that ˆα = y − βˆx and βˆ = SxySxx, show thatni=1[yi − (αˆ + βˆxi)] 2 = Syy −…

A: Given

Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: af(x, y) If f(x, y, z) = , then is equal to dz (y – 2)² (y – 2)? O 1 2z – x – y (y – z)?

A: Given problem:-

Q: If W= Wly,, Y2, Y3] where y1, y2 , y3 are twice diffferentiable, W" = W. Select one: O True O False

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Q: In Exercises 53-58, compute the derivatives indicated.

A: Here given as fx, y=3x2y-6xy4 Now ∂f∂x=∂∂x3x2y-6xy4=6xy-6y4∂2f∂x2=∂∂x6xy-6y4⇒∂2f∂x2=6y

Q: 4) Lett =,u = x? - y² ,v = 4xy³. Find %3D ax ду

A: t=uv

Q: R is The lowey timit topolygy Pimer than the strmdard topoleoy てom

A: The given question is related with topology. Let Τ' be the lower limit topology on ℝ and Τ be the…

Q: Let V, 3 V3 = Vz= -3 8. %3D 131 2- -5 does { Vi,UeiVa} span R3?

A: Given vectors, v1 = 06-2 , v2 = 0-38 and v3 = 4-1-5 These vectors will span ℝ3 if they are linearly…

Q: O show thet fu) =2a +3b is Candin Uous where a, b are Constants.

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Q: noger whare : y's Fl7. ) Homogencus writter us Example 2: y'- 3yay %3D

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Q: a?u at (r,y)=(2,2), when Evaluate u = In vr² + .

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Q: prove in words: If {X, Y, Z} ` A ∧ ¬A, then {Y, Z} ` ¬X ` = derivability

A: Use the deduction theorem: Deduction theorem states that, If ┌ A⊦B then ┌⊦ A→B

Q: Suppose T(x,y) = (2x, 2y) and U(x,y) = (x, -y). Is T∘U=U∘T?  Justify your answer.

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Q: C) prave that sbatz = Clnrtt - an for all nE B, Nzl. %3D |

A: We will prove the relation of part c by mathematical inducation.

Q: z+i dz = + ni. 23 + 2z2 Select one: True False

A: According to the given information, it is required to check whether the given integral is true or…

Q: f Shoo that the interior operat1on has the tollouni ng Propeities. if E, CE2, then interier (E) C…

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Q: SU SW. Complete the proof that ASTW ASXU. T. V W Statement ZW ZU SU N SW ZS ZS 4 ASTW ASXU 2.

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Q: Evaluate Js I | ix, v, z) ds. Ах, у, 2) - Ху S: z = x2 + y2, 9 sx² + y2 < 81

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Q: (d) Could p(y) for y = 1, ..., 6 be the pmf of Y? 92 --Select-- , because p(y) : y = 1

A: The given function is P(y) =y2 /92         y=1,2,3,4,5,6

Q: When u × v = 0 and u ∙ v = 0, what can you conclude about u and v?

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Q: Calculate az/ax, where xez + zeY = x + y.

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Q: ,whue •dd fimcden. 2prove that S fiss da ニ0 -- つ

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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,…