u = [8, 3] v = [4,0] 2u + v = [ Ex: 5 :

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

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) =

A:

Q: Use Cramer's rule to solve for y without solving for x, z, and w. y + 5x + 3y 5х + z + w = -7 z + =…

A: Given:

Q: ху f(x,y,z) =- х+у+z

A:

Q: Find the component of u along v. u - (-2, 4), v- (1//7, 1/v2)

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Q: f(x, y, z) = x – Vy² + z

A: Take the partial derivative ony by one with respect to x, y & z considering other as constant at…

Q: Find the average value of f(x, y) over the plane region R.

A:

Q: f Vf(x, y) = 0, then Duf(x, y) = 0 for all u. %3D %3D

A: True

Q: (d) u =-,v = xy, = a' ху, 21

A: Consider the given information. (d) Consider the given values. u=12-12x2v=xy The equation of the…

Q: Ut + 4tuz – 2u e', x E R, t > 0 u(x, 0) xe- , x E R. Find u(x, 1).

A:

Q: "en J(2, 9) 5y), find =(z, y) = (z, y) = -(z, y) = %3D

A: We wil find the second order partial derivative.

Q: U = kuzx for 0 0, u(0, t) = u(L, t) = 0, u(x, 0) = x(L – x)

A: Given that, ut=kuxx , 0<x<L, t>0u0, t=uL,t=0ux, 0=xL-x This is  the heat conduction problem…

Q: If u * v = 2i - 3j + k, what is v * u?

A: As we know a×b = - b×a

Q: Let = (0,- 2)v=(3,2) and w=(-2,1) Then the dot product u. (V w) is equal to

A:

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y w = 3 5x + 2y 4 4x 2 y 5z +…

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Q: Find ||u||, ||v ||, and ||u + v||. -(-1. 금), v-(2.-3) v = (2 - ± ) u = 4 (a) ||u|| (b) ||v|| (c) ||u…

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Q: Condition JW=3.6, j0=0.4

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Q: mTQ = %3D mQR = %3D U 44 mTS %3D T. R 25 MSQR %3D MRQT %3D

A: Problem 1   Problem 2

Q: Prove or disprove: Vx € Q, Vy e Q, 3z E Q, (x < y) → (x < z< y).

A:

Q: f (x, y, z, u, v, w) 3æyzuvw + x²y²w? – 7cz° + 3yvw Calculate [af af af af af af + for a = y= z = u…

A: Solution

Q: Let X and Y be iid N(1,3). Let U = 4X + Y and V V_dependent or independent? Justify your answer. 2X…

A: Given X  and Y be iid with N(1,3). Mean, μ=1 Standard deviation, σ=3  U = 4X + Y and V = 2X — 3Y

Q: c) 0 0, Ut = Uxx; u (x, 0) = x, 0 0.

A:

Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: Evaluate f(х, у) ds. f(x, у) %3D у + 3 s: r(u, v) = ui + vj + 4vk, 0 sus 1, 0svs 4

A: Given: fx,y=y+3 S:ru,v=ui+vj+4vk, 0≤u≤1, 0≤v≤4 Differentiating r with respect to u, ru=1,0,0…

Q: b) If x = u(1 + v) and y = v(1+u), find vx, Ux and a(u,v) a(x.y)

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Q: Use Cramer's rule to solve for x, y and Z 2х + у — 3z %3D 0 | 4х + 5y + Z %3D 4 %3D

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Q: 8. % = () Given that u = and w = calculate the values of x and y if 2u = v - w. %3D

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Q: Repeat Exercise 27 for the forces KX = (2, – 3) and KY = (- 2, 3).

A: The given two force vectors are, KX→=2,-3KY→=-2,3 When we find the addition of two vectors, then the…

Q: f(x, y, z) = 2 ≤ x ≤ 10,0 ≤ y ≤ 4,0 ≤ z ≤4

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Q: If VW = -2z + 29, UX = z + 9, and ST = z + 13, what is UX? %3D V U UX w/ ト

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Q: O Civen w (2-31, XL-4,9),Y(S,y) and z(-1,1) find the Value so that ux LYZ

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Q: solve for w where u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v w=?

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Q: Find Duf at P f(x,y,z)=4x^3y^3z^3;  P(1,−2,1);  u=1/3i+2/3j−

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Q: Solve for w where u = = (0, 1, 1, –1) and v = (0, -1, 2, 3). %3D 5w = u - 4v W =

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Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: Determine D,f (4,-1,6) for f(x,y,z) = ery + 4zx in the direction of (-3,2,6).

A: Given fx,y,z=ex2y+4zx3 in the direction of -3,2,6

Q: Calculate f,e,5 as if f(x,y, z) = z In Vxy

A: here we have to find the functional value

Q: 26 + 4z4 – 2z2 +1 dz (z – 2i)6

A:

Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

Q: Find the component of u along v. 3(5,2), v = (3, -4)

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Q: Let C: |z-i=3 and I = §. dz 2z dz. Then %3D

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Q: I ntegrate: Sv V v+2dv HIN T: If u =x+Q, then × = U-a

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Q: Be u = x2 + yz, where x = rsin(t), y = rcos(t) and z = rsin2(t), calculate: ∂u/∂r and ∂u/∂t

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Q: a(x, y) r = u? -v,y =ue". Compute ô(v,u)

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Q: f(x, y) = e&z– 4y af af ду

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Q: Let f (z) =iz - 7x. Which of the following is correct ? oi4 = - 7 v, и 3D — olu =7 v oi4 = - 7 v,…

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Q: z = f(x, y) = r* – x²y+ 4y, r= g1(u, v) = u² + v², y = 92(u, v) = = uv.

A: Let's find.

Q: O eiz dz < z2 – i e2 , 3 - z(t) = 2e", t e [0,27]. true False

A:

Q: aw Find ди dw. and if w = x³ + In (-) + y, x = u? dv -+ 5 and %3D wwww y = 3v + 5u and point…

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.