Explore a wide range of topics and get answers from experts on IDNLearn.com. Get accurate and detailed answers to your questions from our knowledgeable and dedicated community members.

9. An airplane is flying at [tex]35,000[/tex] feet above sea level. The airplane starts to descend at a rate of [tex]2,500[/tex] feet per minute. Let [tex]m[/tex] be the number of minutes. Which of the following expressions describes the height of the airplane after any given number of minutes?

A. [tex]2,500 - 35,000m[/tex]
B. [tex]2,500 + 35,000m[/tex]
C. [tex]35,000 - 2,500m[/tex]
D. [tex]35,000 + 2,500m[/tex]

10. Create a storyline (word problem) using the following algebraic expressions:
Part A: [tex]\frac{1,000}{r}[/tex]
Part B: [tex]75 - 3m[/tex]
Part C: [tex]30 + 2d[/tex]


Sagot :

Let's break down the given problems and present detailed step-by-step solutions.

### Problem 9:

The airplane is flying at an initial height of 35,000 feet above sea level. It starts to descend at a rate of 2,500 feet per minute. We need to find an expression that describes the height of the airplane after any given number of minutes, denoted by [tex]\( m \)[/tex].

1. Identify the initial height:
[tex]\[ \text{Initial height} = 35,000 \text{ feet} \][/tex]

2. Identify the rate of descent:
[tex]\[ \text{Rate of descent} = 2,500 \text{ feet per minute} \][/tex]

3. Determine the height change over time:
- As the airplane descends, it loses height.
- After [tex]\(m\)[/tex] minutes, the airplane will have descended [tex]\( 2,500 \times m \)[/tex] feet.

4. Formulate the expression for the height after [tex]\( m \)[/tex] minutes:
[tex]\[ \text{Height after } m \text{ minutes} = \text{Initial height} - (\text{Rate of descent} \times m) \][/tex]
[tex]\[ \text{Height after } m \text{ minutes} = 35,000 - 2,500m \][/tex]

Thus, the correct expression is:
[tex]\[ 35,000 - 2,500m \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{C. \; 35,000 - 2,500m} \][/tex]

### Problem 10:

We need to create a storyline (word problem) using the given algebraic expressions:
- Part A: [tex]\(\frac{1,000}{r}\)[/tex]
- Part B: [tex]\(75 - 3m\)[/tex]
- Part C: [tex]\(30 + 2d\)[/tex]

Let's construct a cohesive storyline involving these expressions:

Storyline:

John runs a transportation company that deals with shipping packages.

- Part A: John charges a rate for each package he ships based on the speed of delivery, represented by [tex]\( r \)[/tex]. The cost to ship a package with priority delivery is given by [tex]\(\frac{1,000}{r}\)[/tex] dollars, where [tex]\( r \)[/tex] is the speed in miles per hour. Faster deliveries are more expensive.

- Part B: John has a driving route that covers multiple stops each day. He starts his daily route with 75 packages. At each stop, he delivers [tex]\( 3 \)[/tex] packages. If [tex]\( m \)[/tex] is the number of stops he makes, the number of packages remaining to be delivered after [tex]\( m \)[/tex] stops is given by [tex]\( 75 - 3m \)[/tex].

- Part C: John often needs to hire temporary workers for sorting packages at different locations. The total number of hours he needs for sorting packages, depending on the number of days [tex]\( d \)[/tex] the workers are hired, is represented by [tex]\( 30 + 2d \)[/tex]. This means he starts with a base need of 30 hours and hires for 2 additional hours per day.

This storyline tying together the expressions provides a realistic scenario that involves transportation logistics, package delivery, and temporary manpower allocation in John's business operations.