The circumference,y, of a circle varies directly with the diameter,x, of the circle. Write an equation if y=44cm when x=14cm.

y = (22/7) x

is the equation they want you to write.

It is an approximation to the correct relationship, which is y = pi * x

22/7 = 3.14286..
pi = 3.14159..

To write an equation for the variation between the circumference, y, and the diameter, x, we can use the direct variation formula:

y = kx

where k is the constant of variation.

Given that y = 44 cm when x = 14 cm, we can substitute these values into the equation:

44 = k * 14

To solve for k, divide both sides of the equation by 14:

k = 44 / 14
k = 3.142857143

Now that we have the value of k, we can write the equation:

y = 3.142857143x

Therefore, the equation that represents the variation between the circumference, y, and the diameter, x, is y = 3.142857143x.

In this scenario, since the circumference of the circle varies directly with the diameter, we can use the formula for the circumference of a circle:

C = πd

Where C represents the circumference and d represents the diameter.

To find the equation that relates the circumference (y) to the diameter (x), we need to determine the constant of proportionality.

Given that y = 44 cm when x = 14 cm, we can plug in these values into the equation:

44 = π(14)

To solve for π, divide both sides of the equation by 14:

44/14 = π

Now, we can substitute the value of π back into the equation in terms of x and y:

y = πx

Replacing π with 44/14 (the value we found earlier):

y = (44/14)x

Simplifying,

y = (22/7)x

Therefore, the equation that relates the circumference (y) to the diameter (x) is:

y = (22/7)x