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
faust18 [17]
3 years ago
6

An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each oth

er. One airplane is 150 miles from the point and has a speed of 600 miles per hour. The other is 200 miles from the point and has a speed of 800 miles per hour.
(a)At what rate is the distance between the planes changing?

(b) How much time does the controller have to get one of the airplanes on a different flight path?
Mathematics
1 answer:
sattari [20]3 years ago
7 0
They are traveling at right angles to each other so we can say one is traveling north to south and the other west to east.  Then we can say that there positions, y and x are:

y=150-600t  x=200-800t

By using the Pythagorean Theorem we can find the distance between these two planes as a function of time:

d^2=y^2+x^2, using y and x from above

d^2=(150-600t)^2+(200-800t)^2

d^2=22500-180000t+360000t^2+40000-320000t+640000t^2

d^2=1000000t^2-500000t+62500

d=√(1000000t^2-500000t+6250)

So the rate of change is the derivative of d

dd/dt=(1/2)(2000000t-500000)/√(1000000t^2-500000t+6250)

dd/dt=(1000000t-250000)/√(1000000t^2-500000t+6250)

So the rate depends upon t and is not a constant, so for the instantaneous rate you would plug in a specific value of t...

...

To find how much time the controller has to change the airplanes flight path, we only need to solve for when d=0, or even d^2=0...

1000000t^2-500000t+62500=0

6250(16t^2-8t+1)=0

6250(16^2-4t-4t+1)=0

6250(4t(4t-1)-1(4t-1))=0

6250(4t-1)(4t-1)=0

6250(4t-1)^2=0

4t-1=0

4t=1

t=1/4 hr

Well technically, the controller has t<1/4 because at t=1/4 impact will occur :)


You might be interested in
Choose the following which is COMPLETELY correct:
Vlada [557]

Answer:

D

Step-by-step explanation:

Mean = (4+4+5+8+9) / 5

            30 / 5

             6

Median = put them in order and the one in the middle is the median.

                4, 4, <u>5</u>, 8, 9

Mode = the most common

            <u>4, 4</u>, 5, 8, 9

     

5 0
3 years ago
eight hundred ninety-one billion, nine hundred sixty-two million, one hundred seventy-two thousand, four hundred nine in standar
ahrayia [7]

Answer:

891,962,172,409

Step-by-step explanation:

4 0
3 years ago
jake spends 2 hours on each homework assignment and he had 3 assignments each day.orlando spend 2 hiurs on each homework assignm
Andrej [43]
Ok so u have to multiply for this one

Work *Jake*:

So he spends 2 hours on each assignment. He has 3 assignments so u have to do :
2*3=6
 
He spend 6 hours a day doing home work so now u have to multiply that by 30:
6*30=180

Work *Orlando*:

So he spends 2 hours on each homework. He has 2 sheets each do so u have to multiply 2 and 2: 
2*2=4

He spends 4 hours a day doing homwork so u  have to multiply it by 30: 
4*30=120


Answer:
 

So Jake spends 130 hours
Orlando spends 120 hours 

Add both together:
120+130=250

They spend 250 hours together on work in 30 days/
4 0
3 years ago
Read 2 more answers
2. Order the numbers from least to greatest.
kari74 [83]

Answer:

-5, -2, -1, 0, 7

the answer is D

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
2(x+1) please do full steps and answer thank you i will give brainlist
alisha [4.7K]

Distribute the parentheses:

2(x + 1)

2 · x = 2x

2 · 1 = 2

2(x + 1) = 2x + 2

7 0
3 years ago
Other questions:
  • NEED HELP IN MATH . THANKS FOR ALL HELP .
    11·1 answer
  • Is 35% greater than less than or equal to 3.0​
    10·2 answers
  • The perimeter of a rectangular playing field is 280 feet. The length of the field is 20 feet more than the width. What are the d
    5·2 answers
  • Write the equation of the line that passes through the points (3,-2) and (5, -1).
    11·1 answer
  • The length of needles produced by a machine has standard deviation of 0.04 inches. Assuming that the distribution is normal, how
    15·1 answer
  • When using a power tool, never engage the?
    9·1 answer
  • I only need the explanation
    9·1 answer
  • Select ALL of the lines that contain the point (1,6)
    9·1 answer
  • 1+1+8 what's the best answer to this question ​
    13·1 answer
  • A ball is thrown in the air from a platform that is 96 feet above ground level with an initial vertical velocity of 32 feet per
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!