. Suppose that n is a three-digit natural number, and 3 | n. If x is the 100s digit of n, y is the 10s digit of n, and z is the 1s digit of n, show that 3 | (x y z). (Hint: To understand the notation x, y, and z, suppose, for example, that n is the number 153. In this case, we get x

Proof is shown in the Explanation

Step-by-step explanation:

Suppose that you have a three-digit number natural number n that is written xyz. Then

So when we divide n by 3, we obtain:

The remainder is clearly going to come from the division , since 33x+3y is an integer.

Since 3 divides n, the remainder is going to be a multiple of 3 and so we have shown that 3|(xyz).

Example:

Consider the number 336

80 the answer is 80

step-by-step explanation:

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