Question

the diameter of a value for the space shuttle must be within 0.001mm of 5mm. Write and solve an absolute value equation to find the boundary values for the acceptable diameters of the valve.

Answer 1

To find the boundary values for the acceptable diameters of a valve, we solve the absolute value equation |d - 5| = 0.001. The acceptable diameters are from 4.999 mm to 5.001 mm.

Step-by-step explanation:

The question requires solving an absolute value equation to find the boundary values for the acceptable diameters of a valve. If the diameter must be within 0.001 mm of 5 mm, we can write the absolute value equation as |d - 5| = 0.001, where d is the diameter of the valve. To solve for the boundary values, we split this into two separate equations: d - 5 = 0.001 and d - 5 = -0.001.

Solving the first equation, d = 5 + 0.001 = 5.001 mm. Solving the second equation, d = 5 - 0.001 = 4.999 mm. Therefore, the acceptable diameters of the valve are from 4.999 mm to 5.001 mm.

Answer 2

Since it is within 0.001mm, then that means that if the diameter is 5+x,
5+x>4.999 (due to that 5-0.001=4.999) and 5+x<5.001 (since 5+0.001=5.001 and therefore has to be less than that), getting 4.999<5+x<5.001. Subtracting 5, we get -0.001<x<0.001. If we get the absolute value of everything, that means that |-0.001|>|x|<|0.001| (Note that since getting the absolute value of a negative number requires you to multiply it by -1, we switch the inequality around).Adding 5 back to it, we get 5+|x|>5+|0.001|