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