The sum of three numbers is 98. if the ratio of the first to second is 2: 3 and that of the second to the third is 5: 8; then the second number is

30

Step-by-step explanation:

Since the ratio between the first/ second number is 2 : 3

Let them be represented by

2x : 3x

The ratio between the second/ third numbers is 5 : 8, then

third number = × 3x = x = 4.8x

We have the 3 numbers in the ratio 2x : 3x : 4.8x

Sum the numbers and equate to 98

2x + 3x + 4.8x = 98

9.8x = 98 ( divide both sides by 9.8 )

x = 10

Hence the 3 numbers are

2x = 20, 3x = 30 and 4.8x = 48, that is

20, 30, 48 ← sum = 98

Thus the second number is 30

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

8

step-by-step explanation: