Question

If u and v are functions of x and y defined by x = u + e^-v.sin u andy= v + e^-v.cos u, prove thatdu/dy=dv/dx.​

Answer 1

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Question 3.

Give the steps you will use to separate the variables and then solve the equation:

(a) 3n – 2 = 46

(b) 5m + 7 = 17

(c) 20p3=40

(d) 3p10=6

Solution:

(a) 3n – 2 = 46

⇒ 3n- 2 + 2 = 46+ 2 (adding 2 to both sides)

⇒ 3n = 48 Question 3.

Give the steps you will use to separate the variables and then solve the equation:

(a) 3n – 2 = 46

(b) 5m + 7 = 17

(c) 20p3=40

(d) 3p10=6

Solution:

(a) 3n – 2 = 46

⇒ 3n- 2 + 2 = 46+ 2 (adding 2 to both sides)

⇒ 3n = 48

⇒ 3n + 3 = 48 ÷ 3

⇒ 3n + 3 = 48 ÷ 3