(a) (i) If (a + b)2 = -5 + 12i, find a and b given that a, b € R.

Q: | V1 – 47² dx.

A: We know that sin2(u)+cos2(u)=1   ⇒ 1-sin2(u)=cos2(u) cos2(u)=121+cos(2u) sin2 sin-1y = 2y1-y2

Q: Find [4x³ (In x)² dx. O A. 1.4 X x In²x + In x + O B. x² ln² x - ln x + O C. x ln x O D. x ln x X 2…

A: Note : according to our gauideline, i can solve oy first so please reroute the remaining question.…

Q: (Vx – 1)5

A:

Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: x? + y? – 2x – 8y + 19 = 0

A: x2 + y2 - 2x - 8y +19 = 0 Repositioning x and y accordingly we get x2 - 2x + y2 - 8y +19 = 0…

Q: 3 2. x1 + x² dx

A: Definate integration

Q: g(x.y)-xn (x-y), as(-2,3) Pind vg ?

A: Given the given function is gx,y=xlnx+y,    x,y=-2,3. Apply gradient formula ∇f=∂f∂xi+∂f∂yj

Q: Find mZA. (5x - 1) A D (2y + 1° (4x+17)° B C (3y - 20)

A: We can find the value of angle A as below.

Q: 2. Find the value of x (3r - 7) 29 D

A:

Q: (x+8)2=7

A: Given: (x+8)2=7

Q: - - simplify the following: 3(6-x) + 4(2x − (m — 2))

A: Use the given information.

Q: (2+1) x (9-?)=12

A: Just try to simplify and that's easy.

Q: Let a = 5j + k and b - 27 + 3 + 2k. Find - 3ā – 36.

A: We can find the given vectors.

Q: Let A=(¹). 3¹). Find 3A³2A² + 5A - 12.

A: Given: A=1-123 We are required to find: 3A3-2A2+5A-I2

Q: Simplify (ex)5 . e(7x + 6) to the form eA x + B) = eC. eDX where %3D A = B = C = D =

A:

Q: If (n, 15) = 1 and o(n) = 56, find o (75n).

A: Given: n, 15=1 and σn=56.To find: σ75n

Q: Let à = 27 - 5j + 4k and b = − − 5j + 4k. Find -a + b. -ā +b =

A:

Q: 8. Find the value of t. (94 + 31)" (7t + 2) B

A: We have given the arc length BC = (7t + 2)° And arc length DE = (94 + 3t)° And length BC = DE We…

Q: Does each of the following series converge or diverge? Why? Show all your work and MUST include the…

A: To determine whether the series ∑n=1∞​(3+8n2)(2n2+1)​​ converges or diverges, I'll use the Direct…

Q: Find the 4** x³ dx А. + c 4 In 4 В. + c 4 In 4 С. + c 3 In 3 D. 24 2 In 2

A:

Q: R. (3x + 5) (91- 17)*

A: We know sum of opposite interior angles of parallelogram is equal to 180°

Q: = B=( nds 2A – 38. Sean A %3D y B = Finds 2A 3B.

A:

Q: √x√√7-x² d dx - S

A:

Q: S7=1−1/√2+1/2−12/√2+14−14/√2+1/8.

A: Given:

Q: Exl show that 9dx (x²+4)² 97 16 H.W

A: Here we have to show the above integral.

Q: VA – 3 4 2x + 1 X

A: To find the value of the given integral by substitution method. Here we change the dx to dz and then…

Q: If n(A) = 105, n (A ⋃ B) = 142, and n (A ⋂ B) = 46, find n(B)

A: This question is about set

Q: (b) Simplify, 2n > (5r + 2) r=1

A: See the detailed solution below.

Q: 2(7)+8y=23

A:

Q: Determine the value of 7A+6B if 19x2 + 41x + 16 A (x+ 1)² Cx +B (x – 1)(x +1)2 Answer:

A:

Q: If a 10î + 10f + 5k, b = 5i – 2j – 14k, è = 4î + 7j – 4k , find the value of å x (b x 2).

A: The cross product of two vectors a=a1i+a2j+a3k ,b=b1i+b2j+b3k can be calculated using determinant…

Q: If x=2 and t= 4, what is the value of (x² – 4)(t² +8)? -144 O- 72 4 O 12

A:

Q: i (d) What is Arg(-,- 2 ? -2-2i

A:

Q: ( x + 3 ) 2 + ( y − 6 ) 2 = 104

A: We have to draw the curve using the equations

Q: Express in the form (a+bj): (4+7j)-j) (2–5 3.1 3.2 e

A: The complex numbers are usually represented in the form of z=a+bj , where, a is the real part and b…

Q: 1 da (2a + 1) +1) 1. 8.

A: