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
tamaranim1 [39]
2 years ago
12

A plane flying horizontally at an altitude of 1 mile and a speed of 570 mi/h passes directly over a radar station. Find the rate

at which the distance from the plane to the station is increasing when it has a total distance of 3 miles away from the station. (Round your answer to the nearest whole number.)
Mathematics
1 answer:
valina [46]2 years ago
4 0

The rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.

We assume the station to be at point A.

The plane when directly over the station, takes point C.

As it is flying horizontally continuously at an altitude of 1 mile, AC = b = 1 mile.

The plane flies continuously, and when it is at a distance of 3 miles from the station, it is at point B.

The distance between the plane and the station of 3 miles can be shown as AB = c = 3 miles.

The movement of the plane from C to B can be shown as BC = a.

Now, from the given case, we get a right triangle ABC.

By Pythagoras' Theorem,

a² + b² = c² ... (i).

or, a² + 1² = 3²,

or, a² = 9 - 1 = 8,

or, a = 2√2 miles.

We are told that the plane is moving at a speed of 570 miles/hour.

This can be shown as, da/dt = 570 miles/hour.

As the plane is moving horizontally, the vertical distance between the plane and the station doesn't change, that is, db/dt = 0.

In the question, we are asked to find the rate at which the distance from the plane to the station is increasing, that is, we are asked to find dc/dt.

Differentiating (i), with respect to time t, we get:

2a(da/dt) + 2b(db/dt) = 2c(dc/dt).

Substituting values of a = 2√2 miles, b = 1 mile, c = 3 miles, da/dt = 570 miles/hour, and db/dt = 0, we get:

2(2√2)(570) + 2(1)(0) = 2(3)(dc/dt),

or, 2280√2 + 0 = 6(dc/dt),

or, dc/dt = 380√2 miles/hour = 537.40 miles/hour ≈ 537 miles/hour.

Thus, the rate at which the distance from the plane to the station increases is 537 miles/hour. Computed using Pythagoras Theorem and Differentiation.

Learn more about the Pythagoras Theorem and Differentiation at

brainly.com/question/15291822

#SPJ4

You might be interested in
Solve the equation 4x^2-12x=7 algebraically for x.
ss7ja [257]
                            4x² - 12x = 7
                                      - 7  - 7
                       4x² - 12x - 7 = 0
                4x² + 2x - 14x - 7 = 0
2x(2x) + 2x(1) - 7(2x) - 7(1) = 0
          2x(2x + 1) - 7(2x + 1) = 0
                    (2x - 7)(2x + 1) = 0
       2x - 7 = 0    or    2x + 1 = 0
           + 7 + 7                 - 1  - 1
             2x = 7                 2x = -1
              2     2                  2      2
               x = 3¹/₂      or       x = ⁻¹/₂
7 0
3 years ago
Read 2 more answers
It’s kinda urgent lol
ladessa [460]

Answer:

60m²

Step-by-step explanation:

my dude you need to know this. A=bh. A=10(6).

7 0
3 years ago
Find the number of liters in 12.8 gal of gasoline. Round to the nearest hundredths
masya89 [10]

Answer:

48.45

Step-by-step explanation:


7 0
3 years ago
Jack's overtime wage is $3 per hour more than his regular hourly wage. He worked for 5 hours at his regular wage and 4 hours at
tamaranim1 [39]
Jack's regular wage is $6 per hour.
3 0
3 years ago
What does a isosceles triangle look like
S_A_V [24]
Can i also have a 5 star rating and can you press the Thanks button

4 0
3 years ago
Read 2 more answers
Other questions:
  • Joseph and Tyler went to the hobby store. They each bought a race car for $15.99. Joseph bought a blue race car for $2.99 and Ty
    13·1 answer
  • The Cia estimates the world population is growing at a rate of 1.167% each year.the world population for 2007 was about 6.6 bill
    12·1 answer
  • Find the acute angle θ <br><br> cosθ = 0.5 (to the nearest degree)
    9·1 answer
  • For the data in the table, tell whether y varies directly with x. If it does, write an equation for the direct variation.
    9·1 answer
  • (5x-6) squared <br>please answer​
    10·2 answers
  • Write the number for eight million sixty thousand
    7·1 answer
  • Give the quotient in simplest form: 5/9 divided by 1/3
    5·2 answers
  • 3. A rectangular floor of dimensions
    9·2 answers
  • Which function has a domain of all real numbers?
    10·1 answer
  • ASAP PLS I NEED IT AND TY
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!