287) The specifications for machining a piece of metal state that it must be 12 cm long, within a 0.01-cm tolerance. What is the longest the piece is allowed to be? What is the shortest? Using l to represent the length of the finished piece of metal, write an absolute- value inequality that states these conditions.

288) Pat and Kim are operating a handcar on the railroad

tracks. It is hard work, and it takes an hour to cover each

mile. Their big adventure starts at 8 am at Rockingham

Junction, north of Exeter. They reach the Main St cross-

ing in Exeter at noon, and finish their ride in Kingston at

3 pm. Let t be the number of hours since the trip began,

and d be the corresponding distance (in miles) between the handcar and Main St. With t on the horizontal axis, draw a graph of d versus t, after first making a table of (t, d) pairs for 0  t  7.

These are two separate questions

Q. 287

Part A. longest = 12.01 cm. and shortest = 11.99 cm.

Part B.  | 12 - L | ≤ 0.01

Q. 288: See explanation.

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Step-by-step explanation:

Q. 287

Part A. What is the longest the piece is allowed to be? What is the shortest?

The specifications for machining a piece of metal state that it must be 12 cm long, within a 0.01-cm tolerance.

Let the length of the piece of metal = L

The perfect length is 12 cm.

And the tolerance is ± 0.01 cm.

∴ the longest the piece = 12 + 0.01 = 12.01 cm

And the shortest piece = 12 - 0.01 = 11.99 cm.

Part B. write an absolute- value inequality that states these conditions.

The inequality which represents the allowed length is:

shortest length ≤ L ≤ longest length

11.99 ≤ L ≤ 12.01

Subtract 12 from all sides

11.99 - 12 ≤ 12 - L ≤ 12.01 - 12

-0.01 ≤ 12 - L ≤ 0.01

The last inequality can be written as an absolute - value inequality:

| 12 - L | ≤ 0.01

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Q. 288

Let t be the number of hours since the trip began, and d be the corresponding distance (in miles)

The general form between d and t ⇒ d = mt

Where m is the rate miles/hours

it takes an hour to cover each mile. So, m = 1

∴ d = t

To graph the function in the range 0 ≤ t ≤ 7

Substitute with t and find the corresponding distance (d)

See the attache figure which represents the graph and the table between t and d.