1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Crank
9 months ago
13

At 8:00 am, here's what we know about two airplanes: Airplane #1 has an elevation of 80870 ft and is decreasing at the rate of 4

50 ft/ min. Airplane #2 has an elevation of 5000 ft and is climbing at a rate of 900ft/min. 1) let t represent the time in minutes since 8:00 am, and let E represent the elevation in feet. Write an equation for the elevation of each plane in terms of t. 2) at what time will the two airplanes have the same elevation. 3) what is the elevation at that time?.
Mathematics
1 answer:
wel9 months ago
6 0

Let's begin by listing out the information given to us:

8 am

airplane #1: x = 80870 ft, v = -450 ft/ min

airplane #2: x = 5000 ft, v = 900ft/min

1.

We must note that the airplanes are moving at a constant speed. The equation for the airplanes is given by:

\begin{gathered} E=x_1+vt----1 \\ E=x_2+vt----2 \\ where\colon E=elevation,ft;x=InitialElevation,ft; \\ v=velocity,ft\text{/}min;t=time,min \\ x_1=80,870ft,v=-450ft\text{/}min \\ E=80870-450t----1 \\ x_2=5,000ft,v=900ft\text{/}min \\ E=5000+900t----2 \end{gathered}

2.

We equate equations 1 & 2 to get the time both airlanes will be at the same elevation. We have:

\begin{gathered} 5000+900t=80870-450t \\ \text{Add 450t to both sides, we have:} \\ 900t+450t+5000=80870-450t+450t \\ 1350t+5000=80870 \\ \text{Subtract 5000 from both sides, we have:} \\ 1350t+5000-5000=80870-5000 \\ 1350t=75870 \\ \text{Divide both sides by 1350, we have:} \\ \frac{1350t}{1350}=\frac{75870}{1350} \\ t=56.2min \\  \\ \text{After }56.2\text{ minutes, both airplanes will be at the same elevation} \end{gathered}

3.

The elevation at that time (when the elevations of the two airplanes are the same) is given by substituting the value of time into equations 1 & 2. We have:

\begin{gathered} E_1=80870-450t \\ E_1=80870-450(56.2) \\ E_1=80870-25290 \\ E_1=55580ft \\  \\ E_2=5000+900t \\ E_2=5000+900(56.2) \\ E_2=5000+50580 \\ E_2=55580ft \\  \\ \therefore E_1\equiv E_2=55580ft \end{gathered}

You might be interested in
Mary is playing basketball. She scored 11 baskets in 15 free throws.What is the experimental probability that she will NOT score
Nina [5.8K]

Answer:

Her experimental probability of not scoring a basket would be 4/15

Around 26%

6 0
3 years ago
Math help algebra or algebra 2<br>1=k+14​
Maru [420]

Answer:

k=-13

Step-by-step explanation:

1=k+14

1) Subtract 14 from both sides to <u>ISOLATE</u> k:

k=-13

5 0
3 years ago
Read 2 more answers
NEED HELP ASAP WILL GIVE BRAINLIEST
luda_lava [24]
I think its D because don’t functions only have 1 equation?
5 0
2 years ago
Read 2 more answers
Please help me i need to do this fast
andrezito [222]

It would be answer A since moving it right from the axis makes the x part include a negative next to the number that's being shifted from the axis, and when reflecting it across the x-axis, the number outside of the parenthesis becomes negative

3 0
3 years ago
Which of the lines whose equations are given below is perpendicular to 3x - 12y = 10?
Dmitriy789 [7]

Answer:

1. 8x + 2y = 16

Step-by-step explanation:

3x - 12y = 10

12y = 3x - 10

y = 1/4 x - 5/6  .... slope: 1/4

perpendicular line slope: -4

8x + 2y= 16

2y = -8x + 16

y = -4x + 8  .... slope: -4

6 0
2 years ago
Other questions:
  • Factorise 15x+ 18y???
    8·2 answers
  • A bookstore owner has 48 science fiction books and 30 mysteries.He wants the most books possible in each package, but all packag
    15·2 answers
  • I need to find the experimental probability to this question in a fraction
    11·1 answer
  • In 2000, the population of Littletown was 17,000.
    7·1 answer
  • What is the value of x when 3^x=7?
    6·1 answer
  • Monica went shopping for holiday presents. She bought boxes of chocolates and boxes of ornaments for her
    12·1 answer
  • Can 10, 11, 2 be measures of the sides of a triangle
    11·1 answer
  • I want to find the side length and get the answer step by step
    12·1 answer
  • 10×3×4×4×4×4×4÷2 answer pls​
    10·2 answers
  • Solve for x. See picture for full problem. Please and thank you!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!