A machining company manufactures washers. The dimensions of the washer are 2cm for the inner circle and 4cm for the outer circle. And the inner and outer radii is positive and negative 2. The range of acceptable values is called the tolerance.
Write an equation for the area of the face of the washer in terms of r,R, and pi.
Write a compound inequality for the area, to the nearest tenth of a square centimeter, or the face of the washer.
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To find the equation for the area of the face of the washer, we can use the formula for the area of a ring or annulus.
The formula for the area of a ring is:
A = π(R^2 - r^2)
In this case, R represents the radius of the outer circle (4cm), r represents the radius of the inner circle (2cm), and π is a mathematical constant approximately equal to 3.14159.
Thus, the equation for the area of the face of the washer is:
A = π(4^2 - 2^2)
A = π(16 - 4)
A = π(12)
A = 12π
Now, let's move on to writing the compound inequality for the area of the washer's face.
Since we are looking for the range of acceptable values, which is the tolerance, we need to account for both the minimum and maximum acceptable areas.
Let's assume the tolerance is ±0.1 square centimeters. This means that the acceptable area should be within 0.1 square centimeters above and below the ideal value of 12π.
To write the compound inequality, we can use the following notation:
12π - 0.1 ≤ A ≤ 12π + 0.1
Rounding to the nearest tenth, we get:
37.7 ≤ A ≤ 37.9 (approximately)
Therefore, the compound inequality for the area of the face of the washer is:
37.7 ≤ A ≤ 37.9 (to the nearest tenth of a square centimeter).