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
lyudmila [28]
3 years ago
8

Two airplanes are flying in the air at the same height: airplane A is flying east at 250 mi/h and airplane B is flying north at

300 mi/h. If they are both heading to the same airport, located 30 miles east of airplane A and 40 miles north of airplane B, at what rate is the distance between the airplanes changing?
Mathematics
1 answer:
just olya [345]3 years ago
3 0

Answer:

  decreasing at 390 miles per hour

Step-by-step explanation:

Airplane A's distance in miles to the airport can be written as ...

  a = 30 -250t . . . . . where t is in hours

Likewise, airplane B's distance to the airport can be written as ...

  b = 40 -300t

The distance (d) between the airplanes can be found using the Pythagorean theorem:

  d^2 = a^2 + b^2

Differentiating with respect to time, we have ...

  2d·d' = 2a·a' +2b·b'

  d' = (a·a' +b·b')/d

__

To find a numerical value of this, we need to find the values of its variables at t=0.

  a = 30 -250·0 = 30

  a' = -250

  b = 40 -300·0 = 40

  b' = -300

  d = √(a²+b²) = √(900+1600) = 50

Then ...

  d' = (30(-250) +40(-300))/50 = -19500/50 = -390

The distance between the airplanes is decreasing at 390 miles per hour.

You might be interested in
Solve the following equation. Then place the correct number in the box provided. 3x/7-2=15
seraphim [82]
3x/7-2=15

3x/7 = 17

3x = 119

x = 39.67
5 0
3 years ago
Solve the system of equations.<br><br><br> −5x+2y=9<br> y=7x<br> ​
RUDIKE [14]

Answer:

x=1  y=7

Step-by-step explanation:

−5x+2y=9

y=7x

Substitute the second equation into the first

-5x +2(7x) = 9

Distribute

-5x +14x = 9

Combine like terms

9x=9

Divide by 9

9x/9 =9/9

x= 1

Now find y

y = 7(1)

y = 7

5 0
3 years ago
Read 2 more answers
Solve the system of equations by using substitution.<br> x+8y=-2<br> x-3y=20
zysi [14]

Answer:

(14, -2)

Step-by-step explanation:

To solve by using substitution, begin by solving for a variable in the first equation. Let's solve for x:

x+8y=-2\\x=-2-8y

Now we know what <em>x</em> equals. Let's substitute this into the second equation:

x-3y=20\\(-2-8y)-3y=20

We can then simplify:

-2-8y-3y=20 Given equation

-2-11y=20 Combine y terms

-11y=22 Add 2

y=-2 Divide by -11

So, we now know the value of y = -2.

To find the value of X, we can substitute the value of Y into one of the equations. Let's use the first one:

x+8y=-2

x+8(-2)=-2 Substitute for y

x-16=-2 Distribute 8

x=14 Add 16

So, we now know the value of x = 14.

Therefore, we know a solution to the system of equations is (14, -2).

4 0
3 years ago
Why is 4 4/10 greater than 32/10?
Elena-2011 [213]

Answer:

Because

Step-by-step explanation:

4 4/10 = 4.4  and  32/10 = 3.2

4.4 is bigger than 3.2 so that's why 4 4/10 is bigger.

7 0
3 years ago
1. How many variables are involved in the chi-square test?
GarryVolchara [31]

The result of the respective questions are:

  • This chi-square test only takes into consideration one variable.
  • The  type of chi-square test this is is a Goodness of Fit
  • df= 3
  • NO

<h3>How many variables are involved in the chi-square test?</h3>

a)

This chi-square test only takes into consideration one variable.

b)

The  type of chi-square test this is, is a Goodness of Fit

To test the hypothesis, we must determine whether the actual data conform to the assumed distribution.

The "Goodness-of-Fit" test is a statistical hypothesis test that determines how well the data that was seen resembles the data that was predicted.

c)

Parameter

n = 4

Therefore

Degrees of freedom

df= n - 1

df= 4 - 1

df= 3

d)

In conclusion

Parameters

\alpha = 0.05

df = 3

Hence

Critical value = 7.814728

Test statistic = 6.6

Test statistic < Critical value, .

NO, the result of this test is not statistically significant.

Read more about Probability

brainly.com/question/11234923

#SPJ1

3 0
2 years ago
Other questions:
  • Find the 90% confidence interval for the population standard deviation given the following.
    14·1 answer
  • Which input value produces the same output value for the
    12·2 answers
  • The graph shows the function f(x) = 3x.What is the value of x when f(x) = 9?
    14·1 answer
  • 6(-p+8)= -6p + 12<br> Can someone help me please
    13·1 answer
  • What are the rules to solving an equation with variables on one side​
    7·1 answer
  • Solve. 2x+4 3 b. x 1/3 d. x&lt; 1/3
    8·1 answer
  • If you can do your homework at a rate of 5.3 minutes for every problem, how many problems could be done after 9.01 hours? Round
    13·1 answer
  • Answer right to get points
    7·2 answers
  • Please helppppppppppppppppp
    12·1 answer
  • Please please please help me asap! I need to get this done!!!
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!