The variables x and y are proportional. Use the values to find the constant of proportionality. Then write an equation that relates x and y. Write any fractions in the simplest form. When y=20 , x=12.

Given:

y is proportional to x.

y=20 and x=12.

To find:

The constant of proportionality and the equation for the proportional relationship.

Solution:

y is proportional to x.

             ...(i)

Where, k is the constant of proportionality.

Putting y=20 and x=12, we get

Putting in (i), we get

Therefore, the contestant of proportionality is and the equation for the proportional relationship is  .

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

apex answer is: true.