[1 1 3] Let A = |2 3 5|. Then the adjoint of A is given by: 3 9 7.

Q: If f = xi + yj + zk, l7I = r,and i=, then show that grad () =

A: 1. Gradf=(dfdxi^ + dfdyj^ + dfdzk^ )      2.  dxndx = n xn-1 3. r = x2+ y2 +z2

Q: In AFGH, FG || IJ. Given that HF= 24, FG=32, and IJ 20, find HI. G HI%3D H. %3D

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Q: If C is the z-axis from the origin to the point (0,0, 2), then So(3j – 3k) - d - dr |

A: If C is the z‐axis from the origin to the point 0, 0, 2, then ∫C 3j→-3k→.dr→=?

Q: Find the real component if mid 09.png s(e)= a in vbet is evaluated at z = 9 + 4i when a=8 , b = 7,…

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Q: Hw÷ find the Voctor Peralle I to the line intersedbetween the two flane 3X-6y-2Z=5 and 2x+4-27=5

A: The equation of the given planes is, 3x-6y-2z=52x+y-2z=5 If n1 and n2 are the normal to the planes,…

Q: where C is rE by the lines X

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Q: A E F B CD 1 AB, BE I AC AC = AB, AD = 4x-5 AE = 2x + 7, mZA = 3x +8. 9. Find m2C 10. AAEB = AADC by…

A: This question can be solved by applying ASA congruency.

Q: Let T: P2(IR) → P2 (R) be defined by T(p(x)) = p(x) – 3p'(x). Given that %3D - T(1+x + x?) = a + bx…

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Q: If u(x,y) =3x2y+2x2-y3-2y2, then u is harmonic %3D

A: A function u(x, y) is said to be harmonic if it satisfies the differential equation uxx+uyy=0. The…

Q: Find the value of c such that P(Z > c) = 0.28 %3D O a. 0.3 O b. 0.58 O c. 0.85 O d. 0.22

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Q: 0(x. y) y= Vuv , then find 2. If x=, at (1,1) O(u.v)

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Q: Consider the two relations R and S, as given below: R S A 1 A 1 в 2 C 2 D 3 D 3 F E 4 E 5 Solve the…

A: Given that R = { ( A, 1 ) , ( B , 2 ) , ( D , 3 ) , ( F , 4 ) , ( E , 5 ) }  S = { ( A, 1 ) , ( C ,…

Q: dz where C is the bo + 6)

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Q: (a) Find x, y el such that x+y || x || .. = 1 = || y || = || ** ||**y. ∞o 2

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Q: b) Find the work done along AB A(1,-1, 2) F=5i + 3j + 2k B(3, 2, -4)

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Q: Find a linear transformation T:

A: Consider the provided information, T11=23   and T1-1=05 Find a linear transformation T. We can put…

Q: 2. Find the correct value of c such that P (Z < c) = 0.4. %3D C =

A: According to the provided information, P(Z&lt;c) = 0.4

Q: Let a b A =| d f e i and 2g B = -2d -2e -2f 2h 2i 2a 2b 2c Given that det(A)=1/24, what is det( B-)?…

A: Let A be a determinant of the order: n×n. Using the properties of the determinants, it can be…

Q: evaluated at fo as follows. 1 0.5 0.2

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Q: Evaluate fr z sin(z2) dz where I is the union of the directed line segment that joins the origin to…

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Q: 5. Find which of the following quadrature formulas are of the interpolatory type. Show your…

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Q: 2 W = Span- - 1 1 .Then, the distance and y = 1 -3 -21 3 11 ny to W is

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Q: Let f(z,y) = z* + y° – 2r° - 4y be given. Which of the following statements is correct? %3D

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Q: Consider P2 with the inner product 2 = | f(x)g(x) dx. Then d(x, 2) = a) b) c) 2 d) c) 152

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Q: Find f, and f, and evaluate each at the given point. fx, у) - arctan(), (2, -2) fx(x, y) = ,(x, y) =…

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Q: Which of the following is a secant? G A C D @ EF ® GH © AB O ĒF E,

A: Secant

Q: If u -x2 + y? + z² be such thatr u,+ yu, + zu̟ = Àu, then A is equal to %3D + A.1 В.2 C.0 D. none of…

A: Given that, u=x2+y2+z2 Then xux+yuy+zuz=λu The aim is to find the λ value, ux=2xuy=2yuz=2z

Q: Suppose that a?y +xz? = 3 and let u = -r³. Find the value of du when (x, y, z) = (1, –1,2). dz A) –2…

A: Given that: x2y + xz2= 3 and u=-x3 and (x,y,z)=(1,-1,2). We find du/dz ot differential with respect…

Q: Let a = (x + y)i + 2j + yk and b = 3i+ (4.x + y + 1)j + 4k. Find values of x and y such that a l b.…

A: Givena=(x+y)i+2j+ykb=3i+(4x+y+1)j+4k

Q: Consider P2 with the inner product 2 = f(x)g(x) dx. Then d(x, 2) = %3D b) e) 2 d) 18 13

A: Distance between x,y is given by d(x,y)=&lt;x,y&gt;12and in the question given that…

Q: Find b∈R so that ∫C4x^2dy − 2xydx = 53, where C is the segment from (1, −5) to (−2, −3), followed…

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Q: a. R1 is defined on R by x R1 y if x² + y? = 1. b. R2 is defined on R by x R2 y if 4x² + 3y² = 1. c.…

A: (a) Given relation is xRy⇔x2+y2=1 The relation is not a function because Take x=1/2,…

Q: If f(r, y) = (3r" + 21 – 12)', then fy is given by : %3D

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Q: Find a and b such that v au + bw, where where u (1, 2) and w - v- (0, 6)

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Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

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Q: The value of a that makes the given fuction continous fx)=Sx -2 x22; x)~lax²+2x<2 3 3 2 2.

A: A function f(x) is continuous at x=a if the left-hand limit, the right-hand limit, and the values of…

Q: Write a in the form a = arT + aN N at t-0 for R(t) = t2i + %3D (t+r) + ( -r°*

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Q: If f(1) = 4, f'(1) = 2 and g(x) = lInf(e*), then g'(0) is : %3D %3D %3D А. О в. O C. 2 С.2 D. 1 18…

A: Given: if f1=4, f'1=2 and gx=lnfex To Find: g'0 Concept: (i). Chain Rule for…

Q: If z=x+iy where x and y are real, find the real and imaginary parts of:- Z+1

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Q: If z = x + y, x = 2t, y = 3t, then %3D %3D 1 5 II

A: Recall:    If f(t) and g(t) are two function of 't' and h(t)=f(t)+g(t) then…

Q: Q5: Let A = 7i – 4j + 2k and B -3i + 6j – 2k. %3D %3D - Find A + B, |A – 2B|, A × B?

A: Given: A=7i-4j+2k  and B=-3i+6j-2k

Q: IF| = r r) = -i = 5xi + 2yj – 2zk so be it where div() , grad(f find all of

A: Solution:

Q: C. Prove the Converse of the Hinge Theorem. Given: AB = DE, BC = EF, and AC > DF Prove: m1 > m/2

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Q: Let z = 3+ 4i and w = -2 + i. Find the following and express your %3D answer in the form a + ib. (a)…

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Q: Use the diagram to answer the following question. Which parts must be congruent to prove APQR APSR…

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Q: 4. and A= Find flA) where f lt) = t"-2t+3t+ 3t +2 て %3D %3D て

A: Given,  A=124-1 f(t)=t4-2t3+3t2+3t+2 Find: f(A)

Q: Find f, and f and evaluate each at the given point. 2xy KX, y) = + 2y (1, 1) ,(X, y) = F,(1, 1) =…

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Q: Let Find in terms of x and y. x=1+3a+6a² +10a³+, |a|<1 y = 1+ 4b+10b² + 206³ +.., |b|<1…

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Q: Another change of variables that can beinterpreted geometrically is the scaling u = cx, where c is a…

A: To prove: ∫abfcxdx=1c∫acbcfudu         ...(1) For fx=sinx where a=0, b=π and c=12.