Assume x, y, z E R³. and x · y= x · z = y• z = 0. If ||æ|| = 3, ||y|| = 12, ||2|| = 4, what is || – æ + y – 2||?

Q: If f(x,y) = x In(2y³ – 5) + y e* , find ! of and ôx ây

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Q: 4. Suppose is a discrete rv with E(9X + 2) = 20 and E(X²) = 13. (a) Find E (X) (b) Find V (X)

A: a) We will use the formula E(aX+b)=aE(X)+b E(9X+2)=20E(9X)+E(2)=209E(X)+2=209E(X)=18E(X)=2   Answer:…

Q: Suppose E(X) = 1, V(X) = 2, E(Y)= 3, V(Y) = 4, and E(XY)= 5. (1) Сov (X, Y) (2) Corr(X,Y) (3)…

A: 1) COV(X,Y) =E(XY)-E(X)E(Y)                    = 5-1×3                    = 2

Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: The solution of the IvP Elb+2)jl&+2)y=t", yL3)=o exists in the interval O 6, 00). noncof the giren…

A: given differential equation is t(t+2)y'+(t+2)y=t2,y(-3)=0

Q: Given, f(x, y, z) = xln(x?y)+ x*y – e a2. Compute fa, f, fry, fayz-

A: If f(x,y,z) is a multivariable function, then the variables x,y, and z are called the input of the…

Q: If r(t) = (V10 – t, In(t – 1), sin(2t)) - then the domain of r is О 11, 10] (1, 0) O [1, 10) O…

A: Explanation of the answer is as follows

Q: 17. AABC - AXYZ (not shown). If AB = 5, BC = 8, XY = y, and YZ= 2y – 3, find y. 17. y = P Type here…

A: We have to find y from the given information

Q: If the joint p.m.f. of X and Y is given byh(x , y) = k(x+ y)2, x = -1, 0, 1 and y = 0, 2, 4.where k…

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Q: Given w = xysin(z²), x= s-t, y = s², z= t². Find ay

A: Explanation of the answer is as follows

Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

A: See the attachment

Q: 4. Given that T : R² → R* and is defined as T(x, y) = (x + a, y + b) . Prove that

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Q: If r(t) = (e³t, e-4t, t), find r'(0), T(0), r"(0), and r'(0) x r"(0). r'(0) = II T(0) = r"(0) =…

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Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: (a) (x² + y² + z² + w?)3/2 = 4

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Q: If (x, y) = (-V3, 1) , then find r and 0.

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Q: Given f(x, y, 2) = In(x² + y? + z?), show that 2 dy? x² + y² + z²

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Q: 6) Given that h(x,y) = e**y® _ ¥² Find hxx, hxy, hyy, hyx

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Q: 25. Which of the following is the answer for secx = V2 A. E + 2nk|k E Z}U {+ 2rnk|k € Z} 3 B. G+…

A: We will solve the problem

Q: R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 =…

A: Given : R2=SSRSSTr=∑xi-x¯yi-y¯∑xi-x¯2∑(yi-y¯)2r=SxySxxSyy

Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf (2,-1, 1) = =, then %3D A) B) 11 C) D) E)

A: The function is given by fx, y, z = ln2+x2-2y2-3z The vector is given by u→ = 1, 1, -1 To evaluate:…

Q: A If w= f (x, y), where x = rcos 0 and y = rsin 0 , show that 2 1 + 2 +

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Q: Let a,be Z-{0}. Then one of the following statements is false A)lf ax+by=1 with x,y eZ, then…

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Q: . If x, y E R with x < y, prove that x < tx + (1 – t)y < y for all t e (0,1).

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: af af e. Find g(x,y,z) = af +: az if f = xy²(z³ – 1) | ax ду

A: Given:    f = xy2(z3 - 1)   To find :  g(x, y, z) = ∂f∂x + ∂f∂y + ∂f∂z

Q: (1,1) S[3x*+5y+i(x°-y°)] dz along y=x Evaluate (0,0)

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Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<1 0; otherwise. Compute E(X | y), Var(X) and Var(Y).…

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Q: Let  z=xln(x2+y2−e4)−176xy, x=tes, y=est.  If the value of    ∂z ∂t   when  s=2 and t=1  is equal…

A: z=xlnx2+y2-e4-176xy x=tes,     y=est use the chain rule to find the partial derivative…

Q: Ifx.y,z are real numbers satisfying the equation 25(9x + y) +9:*–15(5xy + yz + 3:x)= 0 then prove…

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Q: 1. If x, y, z E R, prove that (c) ||x| – |y|| < |x –yl. (d) \xy| < }(x² + y²)

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Q: QUESTION 5 Complete the proof using the drop-down menu. Prove: (A xB)N(C×D)c(ANC)x(B ND). VE(AXB)N(C…

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Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

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Q: Given y = Va In æ , what is dy dr In z+2 In z+y7 dy dr dy dr In z-2 dy In z-I dr ||

A: Given,

Q: If f(z) = 6tan(z) , then f'(r) = (A) In(6) 6tan(2) (B) sec2(z) 6tan(2) (C) In(6) sec2() 6tan(z) (D)…

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Q: Let f(x, y, 2) = eF tan(x² 2) . Compute fay: (x, Y, z) . Simplify your final answer.

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Q: The solution for the IVP: Uxi u(x, 0) =2 x u,(x, 0) -ex. ux, () - 2x + (*-0-(**) O b. u(x,…

A: Consider the given information. utt=uxx                 -∞&lt;x&lt;∞t&gt;0ux,0=2xutx,0=e-x D…

Q: 3. If (x, y, z) = xy²z find grad 6 at (2,−1,3).

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Q: Determine C, and C, so that y(x) = C, e²* + C,e* + 2sinx will satisfy the conditions y(0) = and…

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Q: If A = ze?xVi VxA at the point (2,0,3) is + 2xycosy j+ (x + 2y) k then the valueof

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

Q: If X is a RV with f(x) = 0, when x 0, P(X 2 a) <u/a. %3D

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Q: 1),Given: AB || CD; AC 1CD Find: x and y A, ax ay by 4,

A: Here given as Given  CD||AB Also given ∠ACD=90Then∠CAB=909x=90⇒x=10

Q: z=xln(x2+y2−e4)−176xy, x=tes, y=est.  If the value of    ∂z ∂t   when  s=2 and t=1  is equal to…

A: we have to partial derivative by using chain rule

Q: he joint pmf of X and Y is given below. What is E()XI-M)? Y -1 1 X 1/16 1/16 1/16 1/8 1/16 1/8 1/8…

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Q: (a) z, and z4 where z = sin(2x) + y, x = s² – t², and y = s² + t² (b) z, and z4 where z = e*+y, x =…

A: We need to find the partial derivatives z.

Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: Given that {x, e) is a fundamental solution set to y'"+p(x) y' +q(x) y = 0. Find a particular…

A: Please see the answer below

Q: Find f, and f and evaluate each at the given point. F(x, y) = e*y?, (In 4, 2) f(x, y) f,(x, y) =…

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Q: Suppose that a) b) f(x, y) = [15x²y; 0<x<y<l 0; 0; otherwise. Compute E(X|y), Var(X) and Var(Y).…

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Q: Which of the following is a general solution to the followin x²y"+xy'+ (x²– 1)y=0 y=c,(x) +cY_,(x) O…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.