The sum of two numbers, one is as large as the other is 24. Find two numbers

4 and 20

Step-by-step explanation:

The sum of two numbers is 24.

One of the numbers is 5 times larger than the other.

Let x be the first number.

Let y be the second number.

x + y = 24

x = 5y

Put x as 5y in the first equation.

5y + y = 24

6y = 24

y = 4

Put y as 4 in the second equation.

x = 5(4)

x = 20

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

19

step-by-step explanation: