2. munira is making custom kitchen cabinets. the front face of a drawer must have a width between 17 15/16\…

2. munira is making custom kitchen cabinets. the front face of a drawer must have a width between 17 15/16\ and 18 1/16\ and a height between 6 15/16\ and 7 1/16\.\n a) what are the nominal dimensions of the drawer face?\n b) what is the tolerance in the measurements?\n c) write the width and height in the form nominal value ± 1/2(tolerance).\n 3. a chemical mixture in a manufacturing process needs to reach a nominal temperature of 10.0°c, with a tolerance of 0.5°c.\n a) what are the minimum and maximum acceptable temperatures? write them in the form maximum value / minimum value.\n b) write the temperature in the form nominal value ± 1/2(tolerance).

2. munira is making custom kitchen cabinets. the front face of a drawer must have a width between 17 15/16\ and 18 1/16\ and a height between 6 15/16\ and 7 1/16\.\n a) what are the nominal dimensions of the drawer face?\n b) what is the tolerance in the measurements?\n c) write the width and height in the form nominal value ± 1/2(tolerance).\n 3. a chemical mixture in a manufacturing process needs to reach a nominal temperature of 10.0°c, with a tolerance of 0.5°c.\n a) what are the minimum and maximum acceptable temperatures? write them in the form maximum value / minimum value.\n b) write the temperature in the form nominal value ± 1/2(tolerance).

Answer

2.

a)

Explanation:

Step1: Find mid - point for width

The width is between $17\frac{15}{16}$ and $18\frac{1}{16}$. The nominal value for width is the mid - point. First convert to improper fractions: $17\frac{15}{16}=\frac{17\times16 + 15}{16}=\frac{287}{16}$ and $18\frac{1}{16}=\frac{18\times16+1}{16}=\frac{289}{16}$. The mid - point is $\frac{\frac{287}{16}+\frac{289}{16}}{2}=\frac{\frac{287 + 289}{16}}{2}=\frac{\frac{576}{16}}{2}=\frac{36}{2}=18$ inches.

Step2: Find mid - point for height

The height is between $6\frac{15}{16}$ and $7\frac{1}{16}$. Convert to improper fractions: $6\frac{15}{16}=\frac{6\times16 + 15}{16}=\frac{111}{16}$ and $7\frac{1}{16}=\frac{7\times16+1}{16}=\frac{113}{16}$. The mid - point is $\frac{\frac{111}{16}+\frac{113}{16}}{2}=\frac{\frac{111 + 113}{16}}{2}=\frac{\frac{224}{16}}{2}=\frac{14}{2}=7$ inches.

Answer:

Width: 18 inches, Height: 7 inches

b)

Explanation:

Step1: Calculate tolerance for width

The difference between the maximum and minimum width values is $\frac{289}{16}-\frac{287}{16}=\frac{2}{16}=\frac{1}{8}$ inches. The tolerance is $\frac{1}{8}$ inches.

Step2: Calculate tolerance for height

The difference between the maximum and minimum height values is $\frac{113}{16}-\frac{111}{16}=\frac{2}{16}=\frac{1}{8}$ inches. The tolerance is $\frac{1}{8}$ inches.

Answer:

Width tolerance: $\frac{1}{8}$ inches, Height tolerance: $\frac{1}{8}$ inches

c)

Explanation:

Step1: Write width in required form

The nominal width is 18 inches and the tolerance is $\frac{1}{8}$ inches. So the width is $18\pm\frac{1}{2}\times\frac{1}{8}=18\pm\frac{1}{16}$ inches.

Step2: Write height in required form

The nominal height is 7 inches and the tolerance is $\frac{1}{8}$ inches. So the height is $7\pm\frac{1}{2}\times\frac{1}{8}=7\pm\frac{1}{16}$ inches.

Answer:

Width: $18\pm\frac{1}{16}$ inches, Height: $7\pm\frac{1}{16}$ inches

3.

a)

Explanation:

Step1: Find minimum temperature

The nominal temperature is $10.0^{\circ}C$ and the tolerance is $0.5^{\circ}C$. The minimum temperature is $10.0 - 0.5=9.5^{\circ}C$.

Step2: Find maximum temperature

The maximum temperature is $10.0+0.5 = 10.5^{\circ}C$.

Answer:

$\frac{10.5}{9.5}$

b)

Explanation:

Step1: Write temperature in required form

The nominal value is $10.0^{\circ}C$ and the tolerance is $0.5^{\circ}C$. So the temperature is $10.0\pm\frac{1}{2}\times0.5=10.0\pm0.25^{\circ}C$.

Answer:

$10.0\pm0.25^{\circ}C$