In one revolution of the wheel, a point on the edge travels a distance equal to the circumference of the wheel.
The wheel has radius 1 ft, so its circumference is 2π (1 ft) = 2π ft.
Then the point has a linear speed of
(1/4 rev/s) * (2π ft/rev) = 2π/4 ft/s = π/2 ft/s
The answer is x=5. This is because you need to simplify both sides and then isolate the variable.
Answer:
![y=\frac{1}{2}x+6](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%2B6)
Step-by-step explanation:
Given:
The equation of the known line is:
![y=\frac{1}{2}x-4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx-4)
A point on the unknown line is (-4, 4)
Now, since the two lines are parallel, their slopes must be equal.
Now, slope of the known line is the coefficient of 'x' which is
.
Therefore, the slope of the unknown line is also ![m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B2%7D)
Now, for a line with slope 'm' and a point on it
is given as:
![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
Here,
. Therefore,
![y-4=\frac{1}{2}(x-(-4))\\\\y-4=\frac{1}{2}(x+4)\\\\y-4=\frac{1}{2}x+2\\\\y=\frac{1}{2}x+2+4\\\\y=\frac{1}{2}x+6](https://tex.z-dn.net/?f=y-4%3D%5Cfrac%7B1%7D%7B2%7D%28x-%28-4%29%29%5C%5C%5C%5Cy-4%3D%5Cfrac%7B1%7D%7B2%7D%28x%2B4%29%5C%5C%5C%5Cy-4%3D%5Cfrac%7B1%7D%7B2%7Dx%2B2%5C%5C%5C%5Cy%3D%5Cfrac%7B1%7D%7B2%7Dx%2B2%2B4%5C%5C%5C%5Cy%3D%5Cfrac%7B1%7D%7B2%7Dx%2B6)
Hence, the equation of the unknown line is
.