If z = x + jy, where x and y are real, the value of lei is OA. 1 OC. ey OD. e-y

Q: [1 Given that A 1 1/3 and A = -I, d %3D C What is the value of C?

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Q: oS% (x? + y? + z*) dz dy dy

A: Solve the following

Q: Consider the relationship R CN x N, R(x, y) holds iff (/a /9) E N. True or False R is reflexive true…

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Q: When z = f(x,y), which of the following is true for the whole statement? %3D

A: We have given function z=f(x,y). We need to check which of the conditions are true for the given…

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: c1 f(x, y) dy da = F(z, 9) dz dy %3D O True O False

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Q: Given f(x, y) = 3x® – læ²y² – 5y³, find - fa(x, y) f„(x, y) = | fræ (x, y) = %3D fry (x, y) =

A: Given that, the function is fx,y=3x6-1x2y2-5y3. Obtain the value of fxx,y.…

Q: following (a) E(X) and E(Y) (b) Cov(X, Y) (c) Are X and Y independent? Justify your answer.

A: Solution

Q: If (x + iy)/3 = 3 - 4i , where x, y e R, evaluate O a. -50 O b. 50 O . -28 O d. 28

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Q: If f(x, y) dA > 0, then f(x, y) > 0 for all (x, y) in D. True False

A: Given statement, If ∫∫Df(x,y)dA≥0 then fx,y≥0 for all x,y∈D. The objective is tell whether the…

Q: Find r'(t), r(t,), and r'(t,) for the given value of to: r(t) = (e, e2t), to = 0

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Q: Show that for all formulas Y, Þ,0 € S(P), (y = 4) = -(4 ^ ¬b).

A: We need to prove that, φ⇒ψ≡¬φ∧¬ψ Now, constructing the truth table, φ ψ φ⇒ψ T T T T F F F T…

Q: SL (e,9) f(x, y) = dx dy f(x, y) dy da 0. 0. 0. O True O False

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Q: If X and Y are independent RVs, then E(YIX) - F(Y) nd F(Y10

A: X and Y are independent then joint distribution of X and Y is  f(x,y)=f(x)f(y)

Q: If A = and if xy = 1, then det ( AAT) is equal to y a

A: We have, A=axya As we know that, transpose of a matrix is obtained by changing rows to columns and…

Q: Given = = 2y, y and x = -금Find %3D = x+1 47 O A 2r –1 -8r C DI

A: We can solve this problem by substituting or by chain rule.

Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

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Q: iS (2) = (x + ay² – 2xy) + i(bx² – y + 2xy) is anal ytic, then the values ofa and b is

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Q: Again differentiate with sespect to x we e?+ cs(xe? +e?) +C2 e? cje + C2 ze+ 2C2e? dz2 from O : cze?…

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

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Q: Define h(*) = J¿r)d* . Then, which of the following are true?

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Q: If A = and if xy = 1, then det ( AAT) is equal to y

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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: a A = and if xy = 1, then det ( AAT ) is equal %3D to y a

A: Given:A=axyaif xy=1 then detAAT=?

Q: Q/ If the joint p.d.fof X and Y as f(x, y) = { Scx?y ,x² < y<1 ,0. W find the value of c and P(x 2…

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Q: Given f(x, y) = 2x* – 4xy – 2y?, find frr(x, y) = fzy(z, y) =

A: Solving the problem by finding the partial derivative.

Q: Find where . Vg r = |7| y g(r) = In(r") si = xi + yj + z 1) to be If you know that Vp x V¢ p = 3xy +…

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Q: If y = e3+, x = 0 when z = 1, z=1 z=1 = 3, then what is z=1? dy |3D O 1 O 3 O 21e4 O e30 O 19e30

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Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: Evaluate II, (z*y +) dz dz dy, where D = [0, 1] × [0, 1] × [1, 2]. %3D

A: Here we have to find the integration if triple integrate: ∭x2y+1zdzdxdywhere D=0,1×0,1×1,2Thus it…

Q: I= || elx²+y?)² dA, where R R={(x,v)E R² | x²+y²s 25, x2 0}, then 25 si 25 4 75 ne625 <IS 25ne625 4…

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Q: If z=u²+uv , u=x-2y, v=2x– y , find the value of when x=1 and y=-1. dx а. 13 b. 5 O c. 7 9

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Q: To evaluate y?csc2(y³) cor?(y³)dy, we let u =cse(y³)

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Q: Evaluate cz dz, where c is |z| = 1 zG-2) Inz %3D

A: Let

Q: Given f(x,y,z) = sin (2xy) + 2xyz3. Find fxzy(1,2,5). %3D

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Q: Let a,b be constants, a 0. If Y = aX +b, show that p(X, Y) = lif a > 0 p(X,Y) = –1 if a < 0

A: It is given that Y = aX + b We have to calculate the correlation coefficient between the variables X…

Q: RE YOUR CALCULUATOR IS ur answer to the nearest d

A: Angle B can be obtained as; tan B = AC/BC

Q: Given f(x, y) = x° + 3xy* – 5y', find fr(x, y) = | fy(x, y) = %3D

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Q: Given A= 3cosoà + 5sinoŷ, the value of A. ø at point P(1,70°,0) is dA dø %3D О a. 3.23 O b. 7.11 Oc…

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Q: Given f(x, y) = 2x? xy° + 4y°, find - fræ (x, y) = fay (x, y)

A: Consider  the given function. fx,y=2x3-xy3+4y6 The objective of the question is to find the value of…

Q: If // f(x,y) dA > 0. then f(x, y) ≥ 0 for all (x, y) in D. D

A: answer is in next step. please give a like !!

Q: If f(r, y) da dy = K, where K is a constant, then 5 f(x, y) dy da: %3D ок O-K

A: Solution: The objective is to find the value given integral

Q: If RX 16, XS 8, and XY 15, then ST %3D

A: A triangle RST with XY parallel ST

Q: Vy E R Ja E R [ (x² + y² + 1)ª+y+1 = 1] O True O False

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Q: Given f(x, y) = ex° fæy = fyx. ,8 x°yt, show that ,8,

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Q: If || f(t, y) dA > 0, then f(x, y) > 0 for al D (x, y) in D.

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Q: Let be Z= ax? yf +bx²y³ 9 and b que cors P is a pant givon by (-1,-1) qnd we Anaw dz (P) = -2 , &르…

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Q: Given f(x, y) = In Væ² y³. What is the value of fr (1, 2)? If the answer is a fraction, write your…

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Q: If w = f(x,y,z) = xz² + ye*z find the following %3D а. 8?w b. 8?w C. Ex8y

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Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.