Problem #4: Let F(x, y, z) = (7x In(3y² + 6) + 8z7)i + (; 6yx? 6+ 62) j + (56xz6 + 6y – 87 sin z) k %3! and let r(1) = ( + 1)i + ( + 2)j + Pk, 0 sis 1. %3! Evaluate F.dr.

Q: Find the value(s) of z which satisfies the equation |z| 2 + 1 + 6i = 6z

A:

Q: Let A = [3 – 2i 4i 1+ 6i], and B = [5+i 2 – 3i 5]. Find (1 - 2i) A + (3 + i) B. %3D

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: 1-x 1 0 0x=x-7x denklemini sağlayan x değerlerini bulunuz. 21 -1 X 4

A:

Q: r(t) =(sin 3t, cos 31, V7t), 1. Let a) Find T(t) and N(t)

A:

Q: Evaluate: Jx?cos(2x)dx 2x2sin(2x) + 2xcos(2x) + sin(2x) A + C 4 2x2sin(2x) – 2xcos(2x) + sin(2x) В +…

A:

Q: If z = x sin y + y sin x a2z then дхду

A:

Q: 2x+3y -2 = 4 3X++22= 13 X+ 2y-s2=-

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: The f cos 5x cos x dx is 1 {A} = sin 4x - 12 1 1 {B} sin 4x + - 8 12 cos 6x + C cos 6x + C {C} {D}…

A: Given problem:-

Q: Question 12 Evaluate: J(7x3 + 4x²2)dx 7x4 4x2 +C 2 A 4 (B) None of the given choices 7x4. 4x3 + C 3…

A: The given integral,        ∫7x3+4x2dx

Q: Show that if an = 3n3-17n2 + 2n-6, then an = Θ(n3).

A:

Q: Use Cramer's rule to solve for y (y only) in x+y=z=6 3x - 2y+z=-5 x + 3y - 2z = 14

A: The given system of linear equations, x+y-z=63x-2y+z=-5x+3y-2z=14 We have to find the value of y…

Q: Consider statements p and q. p: It is summer. q: Rachel is wearing shorts. For parts (a) and (b),…

A:

Q: Find sun alpha and tan alpha if the terminal side of alpha lies along the line y=-8x in Q2

A:

Q: 3 1] -1 2 If A = show that A² - 5A + 7I = 0. %3D %3D

A: Introduction :We have given a matrix A. And we have asked to show

Q: Show that if an = 5n3 - 14n2 + 7n - 3, then an = Θ(n3).

A:

Q: (x - 1) If 1 / ² ) = = √ Ada² + √ dx [ B (x − 3)(x + 7) - 3 - then A+B = Bdx x +7'

A:

Q: 3 Evaluate: ₁ S 1²,₁ S² [(x²-x²)²] dx dy x+y

A: To evaluate the given double integral.∫-14∫03x2-y22x+y dx dy

Q: Show

A:

Q: 5. a. b. C. [1 2 ^= -√²-14 31²-432 B = = L2 0 Given A = 0 Find AB + (C-2A¹) T. Find the values of x,…

A: To solve the matrix. As per our guidelines we are supposed to answer?️ only one question. Kindly…

Q: Find the function f(x) = a + b cos Tx +csin 7x interpolating the data {(0,2), (1/2, 5), (1, 4)}.

A:

Q: If mZDFC = (11g 9), find g so that FC 1 FD. %3D D F

A: if two line are perpendicular then angle formed is of 90 degree

Q: Determine fe when f(x, y) = 2x - y x + 2y

A:

Q: 3(x-5) = 1 %3D 27 3. 3. 3D 3 = 3 X =

A: An exponential function is a one-to-one function. So if we have ax=ay then we have x=y. Solving an…

Q: Q.1) Evaluate # dydx 4

A:

Q: (xy ☺ Ty 5. Tyy Ty x 7) Tz ® Tzz 6. TzX

A:

Q: You are given that h (x) C = dh dx for a number c. You have to find c. = 6 sin (7x) + 5 cos(7x) 3…

A:

Q: 2 2y³) e³¹-7y²dy. Evaluate (7y - 2y³) (7y -

A: let ,  G=∫(7y-2y3)e(y4-7y2)dy

Q: 3 1 If A = show that A²- 5A + 7I = 0. %3D -1 2

A:

Q: (z+ 1)dz (z² + 2z + 2)3(z + 1)dz J Vzz + 2z + 2 1 (z2 + 2z + 2)3 +C 3 (z2 +2z+2)2 +C %3D Not Correct…

A: ∫xndx=xn+1n+1

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.