b) Find the z- of the following 8z - 19 F(z) (z - 2)(z - 3)

Q: -2.7 -10w x'y 5.9 -7 2x' y'z

A: Consider the exponential rule as, aman=an The given equation is, -10w-2x7y32x5y-9z-7

Q: (b) Prove or disprove: Z10 ~ Z5 x Z₂.

A: We shall solve first question only as you have asked more than one unrelated question. For others…

Q: 5. For k(x) = 3 × - 6, determine kª(8) -

A: To find the required value we need to find the value of x for which k(x)= 8. 4x/5 -6 = 8 4x= 70…

Q: art of z- 2z, if z = a+ib ?

A:

Q: Find f-l (n) for 8ln) = n2-6n and its %3D domarn

A:

Q: Q4. Let flW=( Gué-4u-7) (4ax4 -8x#+15) Find tle regueetad closiuadtiul (10)

A: Given,

Q: 19z 1 Evaluate (5z 3)(x +2) + C

A: Let I=∫19x-15x-3x+2dx. Consider the fraction 19x-15x-3x+2 and take the partial fraction of it. The…

Q: 11. If AJKL - AMKN, find the value of x. 12 N 20 x+1 Зх - 2 J

A: It is known that in a pair of similar triangles, the corresponding sides are proportional. It is…

Q: 54, find r such that the m 5a. A -[ 3 -3 -2

A: A matrix 'A' is equal to its own inverse when  A2=I where I is the identity matrix.

Q: What is the value of Z if only 1.5​% of all possible Z values are​ larger?   The value of Z if…

A: From the provided information, The value of Z needs to be calculated if 1.5% of all possible Z…

Q: Differentiate the following by using product rule. (9x2-2)(3x+1) (3x+10)(6x2-7x)

A:

Q: -10 -8 -6 -4 -2 104 8 6 4 2 -2 -4 -6 -8 2 4 -10 y = -x - 2y = -2x + 1 6 8 00 X 10

A:

Q: * Q1 1 |1 2 31 -1 -1 0 21 3 -3 11 14 5 -71 -41 -7] -14] 2. -11 3. 5 -7 5] 5. 1 2 3 1. 4.

A:

Q: Expand f(2) = z-5)(=-15) in the domain 5 < |2 < 15 .

A:

Q: * Q1 [X1 x2 If 3 [x3 X4] 2 X1 + x2 -1 4x4 [x3+ x4 1. x1 = -2, x2 = 2, x3 = -2, x4 = -3. = -3 2. X1 =…

A:

Q: Give a counterexample to show that (A + B)-1 ≠ A-1 + B-1 in general.

A: Let  A and B be non singular matrix Determinant of A = 1 -0 =  1 Determinant of B = 1 -0  = 1…

Q: 8²z 8. If z = x + y Inxy, show that x- 8 z + x² 8²z 8y² 8x8y

A:

Q: Suppose z = 5 + -2i and w -5+ -4i. Then Im(zw) =?

A:

Q: Express y as a fiunetion af k if y - 2r+5, 1- V3t -1, and t- 3k - 5.

A:

Q: Explain why 3-1 does not exist in Z24.

A: Proposition: If is element in a ring then cannot be both zero divisor and unit. Given:

Q: Evaluate the indefinite wntegral 3tinigas 3. xIn X

A:

Q: Find The Maclausin besies funchlon. $2)= Z-7 2²22-3

A: Given that, f(z)=z-7z2-2z-3 The function can be written as, f(z)=z-7z2-2z-3=z-7(z+1)(z-3) Take,…

Q: 5.1. Show that y2 , V2 , and v3 + V2 algebraic. are

A: We will use definition of algebraic numbers

Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

Q: 1. x2 + 2x- 15 = 0 2. p? – 7p – 18 = 0 3. -3a2 + 27a - 54 0 4. 3x(2x + 5) = 0 5. 12x2 - 4x = 0 6.…

A: (1).             x2 + 2x - 15 = 0                     ⇒  x2 - 3x + 5x - 15 = 0                     ⇒…

Q: Q1\ Differentiate the following 1)2xsin-13x

A:

Q: The 4th term in the expansion of (2x -3x 10 is 10 C4 (2a) (-3x)³ O 10 C4 (2a2) (-32)4 10 C (2)…

A:

Q: Find the value of K by determines. |1 2 3 0 1 2- |2 1 3 3 4 3 kl

A:

Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3…

A:

Q: what is the characteristic of Z6xZ9

A:

Q: Suppose that X is a (A -e100, p 3e-100)-BCP. What is P(X(1)X (2)X(3) = 4)?

A: Answer is 4.

Q: diven that f(z) - S2-45 and g(z) - +2-9-9.

A:

Q: What is the coefficient of the term containing x^2*y^3 in the expansion of (2x-3y)^5?

A: In order to find the coefficient use binomial theorem, which is given below.

Q: 3. Which statement about k (z)= 3z -7z+2 is true?

A:

Q: Prove that if 8x-5=-2x-15 then -x=1

A:

Q: GIVEN: 2x - 3 = 7 PROVE: x = 5

A:

Q: Show that 1 -2 = R³. span 3 1

A: In R^3 if three vectors are linearly independent then they span the whole space R^3.

Q: Z4×Z6 has an element of order 24. true or false ?

A:

Q: 82z 82z 8. If z = x + y Inxy, show that x- 8x? δχδν

A:

Q: 6. Show that 2x-3- 2x - 5x-3 (a) , x e R, x ± 1. -1

A: Simplification

Q: b) Prove or disprove: Z10 ~ Z5 x Z₂.

A:

Q: If f1x2 = 2x3 + Ax2 + 4x - 5 and f122 = 5, what is thevalue of A?

A: The given function is: f(x)=2x3+Ax2+4x-5

Q: 8a+4=

A: Given : 8a+4=4+8a

Q: 1. Find z for x = 4.7 %3D 2. Find x if z = 3.2

A: Given  Sample is normally distributed with mean 5 and standard deviation 3.8

Q: ду Q5: A /Determine az if you knows that: z = (x2 + y2 - 2z Incos3x) дх ду %3D

A: To find the partial derivatives of given z=(x^2+y^2-2zlncos^3x)

Q: ( W + ) )² + (0-3679K - 1:3679 ) ( W + ₁) + 0-3679 +0-26421-0 -)

A:

Q: FIND B-A, GIVEN THAT A= {x ∈ z+ /2 <x<6}    B={x ∈ Z- / -6<x< - 2}

A:

Q: What is the coefficient of the term containing x^2y in the expansion of (4x+y)^3?

A:

Q: If 2sin-1x = n, what is x?

A:

Q: 4 Given that (5A ) -3 -17 52

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.