For how many different pairs of positive integers (a, b) with greatest common factor 1, and with a>b, does ab=30!

4 pairs

Step-by-step explanation:

Given

ab = 30

Where

a > b

Required

Determine number of pairs (a,b)

To do this, we simply test values for a and b that satisfy the required condition.

First,

Take a = 30

Substitute 30 for a in ab = 30

30 * b = 30

b = 30/30

b = 1

The pair is (30,1)

Take a = 15

Substitute 15 for a in ab = 30

15 * b = 30

b = 30/15

b = 2

The pair is (15,2)

Take a = 10

Substitute 10 for a in ab = 30

10 * b = 30

b = 30/10

b = 3

The pair is (10,3)

Take a = 6

Substitute 6 for a in ab = 30

6 * b = 30

b = 30/6

b = 5

The pair is (6,5)

There exist no other pair that satisfy the given condition.

Counting the above pairs, there are just 4 pairs.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47