The diameter of a valve for the space shuttle must be within 0.001 mm of 5 mm. Write and solve an absolute-value equation to find the boundary values for the acceptable diameters of the valve.
| d - 5.000| = 0.001
d - 5 = 0.001
d * 1000 - 5 * 1000 = 0.001 * 1000
1000d - 5000 = 1
1000d - 5000 + 5000 = 1 + 5000
1000d = 5001
1000d / 1000 = 5001 / 1000
d = 5001/1000
and
d - 5 = -0.001
d * 1000 - 5 * 1000 = -0.001 * 1000
1000d - 5000 = -1
1000d - 5000 + 5000 = -1 + 5000
1000d = 4999
100d / 1000 = 4999 / 1000
d = 4999 / 1000
| d - 5.000| = 0.001
Wrongg
wrong
d = 5.001 mm and d = 4.999 mm are the boundary values for the acceptable diameters of the valve.
To find the boundary values for the acceptable diameters of the valve, we can write and solve an absolute value equation.
The equation representing the diameter of the valve is | d - 5.000 | = 0.001, where d represents the diameter we are trying to find.
To solve the equation, we need to isolate the absolute value expression and solve for d.
First, we can remove the absolute value signs by breaking the equation into two cases:
Case 1: (d - 5.000) = 0.001
By adding 5 to both sides of the equation, we get:
d = 5.001
Case 2: -(d - 5.000) = 0.001
By distributing the negative sign inside the absolute value, we get:
-d + 5.000 = 0.001
Subtracting 5 from both sides of the equation, we have:
-d = -4.999
Multiplying both sides by -1 (to isolate d), we get:
d = 4.999
Therefore, the boundary values for the acceptable diameters of the valve are 4.999 mm and 5.001 mm.