(c) Calculate the divergence (V.Ä = div Ã) and curl (V × Ā = rot Á). of the following vector fields. (i) Ã(x,y, z) = xē, + yēy + zē; (ii) Ã(x, y, z) = x²ē, + y?ē, + z²ē, en + Ey + ēz Vx² + y² + z² ex + ey (iii) Ã(x, y, 2) = + ēz x² + y? + z2 -yēr + xẽy x² + y? (iv) Ã(x, y, z) = (v) Ã(x, y, z) = (vi) A(p, Ф, г) — —ёр (vii) Ã(r, 0, ø) (viii) Ã(r, 0, ø)

Q: Six more than the quotent of a number and 4 is 8.

A: let that number is x and quotient of the number and 4 be x4

Q: Solve V8 - 3w = 4 www www www www ww www %3D wwww www

A: Isolate w to obtain its value.

Q: Зх + 2 9 3— 2х 4 4 6.

A:

Q: Solve the equation (1-5x)e¹-5 =0 for x. Give your answer as an integer or a fraction.

A: lne=1lnxn=nlnx

Q: how do i solve y?

A:

Q: Solve ex3+5 =13

A: We have to given x3+5=13

Q: Solve y2 + 25 = 8y

A: To solve the provided equation y2+25=8y for the value y. Now, use the quadratic formula to find the…

Q: y² +8y=-3

A:

Q: Solve 2 +125=0

A:

Q: ,2х 5. e3x.

A:

Q: e2x-3ex-4=0

A: Topic = Algebra

Q: Find a number for which of 13 less than the number is the same as 13 more than the number.

A: Find a number for which of 13 less than the number is the same as 13 more than the number.

Q: Solve. 9y-6(2y-14)=75

A:

Q: Solve 3/I + 10 – 5 = 4 for z न ]

A:

Q: -x-y=3 y=x-3 tell whether is a solution, one solution or infinitely many solutions.

A: Given equations are

Q: Please solve 5CA - 10A.

A:

Q: Solve for x+69=89

A: Here we want to solve  x + 69 = 89

Q: How to solve simultaneous equations?

A:

Q: Solve for the equation   2a²+ a – 10 = 0

A:

Q: 3x +1>-3 Solve for -4 Yes No

A:

Q: Solve the following. 8x + x = 2x + 7 x

A:

Q: Solve TB +4=AB+2F for B

A: To solve  for .

Q: e2x  -2ex -15= 0

A: Substitute ex by m then solve as following:-

Q: solve  (x+2)2=16 x=

A:

Q: Nine more than a number is 12

A: See this solution in below.

Q: e2x-3ex+2=0

A:

Q: 5x= 3y-21 7x-2y=-25

A: given equation    5x=3y-21       ...1   7x-2y =-25    ....2

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.