The joint p.m.f of (X,Y) is given by Px,y(x,v) = k(2x + 3y) x= 0,1,2, y = 1,2,3 .Find the value of k Select one: о а. 72 O . 1 36 72 d. 1 72

Q: Find u and v if u + v = (2,−3) and 3u + 2v = (−1, 2).

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Q: ir6 f(c)dz = 4 and , f(x)dr – 6, th then f(z)dz = Select one. O a -2 O b-10 Oc 2 Od. 10

A: We will let that the integration of the function f(x) is g(x) to solve the question.

Q: Find f'(÷) for f(x) = 2 sin z cos x

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Q: f(i) = 5, f'(i) = -3i, g(i) = 3i, and g'(i) = 4. Find (fg)'(i).

A: Given fi=5,f'i=-3i,gi=3i,g'i=4. Find fg'i.

Q: If u=2i + j -3k and v=i + 4j +k, find u x v.

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Q: Let u == (7,5,-5) and = (−1, −2, 2). Compute the following: u v . . = 2 7(ū. v) = (7) · v = ū. (77)…

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Q: Given u = (-2, 4) and = (1, 6), find 3(uw).

A: The vectors are given by u→ = -2, 4w→ = 1, 6 To evaluate: The value of 3u→·w→

Q: B|a- Find u.v and v xu if u=i+2j-k and v=-2i+2j+2k

A: We have to solve given problem:

Q: Let v = 2i - 5j and w = -4i + 3j. Find v . w

A: We have to find the dot product value v.w for given vectors: v=2i-5j and w=-4i+3j We know that for…

Q: Calculate v × w, where v = (−2, 1, 4) and w = (3, 2, 5).

A: Given: v = (−2, 1, 4) and w = (3, 2, 5)

Q: əz If z = f (x, y), find and for the following equation z=-2xy

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Q: Let f(x,y) = In ( x2+y ). If f,(2,a)=f,(- 1, 2), what is the value of a? O a. 8 O b.7 О с. -2 O d. 3…

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Q: Assume that u. v = 2, ||u|| = 9, and ||v|| = 3. What is the value of 1u (2u - 10v)?

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Q: u = [-5, –1] v = [9, –7) w = [8, 1] 5u + v – w = [ Ex: 6

A: We will use the co-ordinate wise vector addition definition in R² where, u, v, w are vectors in the…

Q: is a solution to the ODE a. x²y" - y = 0; b. x²y" + 6xy' + 4y = 0. Find the values of m for which…

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Q: Let F(x, y) = . Evaluate (3,2) SF.. (1,-1) F.dr

A:

Q: Let f(x.y) = In ( x? +y). If f,(2,a)=f,(- 1, 2), what is the value of a? O a. -2 O b. 8 O. 3 O d. 6…

A: First, let us calculate the partial derivative of the given function with respect to x and y as…

Q: ind V. (V × F), if F(x, y, z) = = V. (V X F) = ezi+ 6xe¹j - 3ek.

A: Topic:- vector algebra

Q: Given f(x, y) = values: fz(3, 2) = fy(3, 2) = - 5x³ + 5xy¹ + 2y2, find the following numerical

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Q: The domain and the range of z-cosh are represented respectively by D-(.)ER XR:20 and R= ( - c , 0 ):…

A: Use the following definitions, to obtain the solution. The domain of the function y=fx is a set of…

Q: et V xu u = (1,3,-3), v = (4,0,2) e l -3 %3D ......

A: Given:            u=1,3,-3            v=4,0,2 The cross product of two vectors is…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: