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dsp73
2 years ago
9

An air traffic controller is tracking two planes. To start, Plane A was at an altitude of890 meters, and Plane B was at an altit

ude of1322 meters. Plane A is losing altitude at 16 meters per second, and Plane B is losing altitude at25 meters per second.
Mathematics
1 answer:
kari74 [83]2 years ago
4 0

An air traffic controller is tracking two planes. To start, Plane A was at an altitude of890 meters, and Plane B was at an altitude of1322 meters. Plane A is losing altitude at 16 meters per second, and Plane B is losing altitude at25 meters per second. Expression which shows altitude of plane after x seconds.

Equation to show when they'll both be at the same altitude

Answer:

890 - 16x ; 1322 - 25x ; 9x = 432 = x = 48

Step-by-step explanation:

Plane A:

Altitude = 890 m

Altitude loss = 16 m per second

Plane A:

Altitude = 1322 m

Altitude loss = 25 m per second

Equation :

Altitude - (altitude loss * time)

Plane A:

890 - 16x

Plane B:

1322 - 25x

Plane A = Plane B

890 - 16x = 1322 - 25x

-16x + 25x = 1322 - 890

9x = 432

x = 432 / 9

x = 48 seconds

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Nothing further can be done with this topic (when trying to find the quotient)  but, you might be looking for these Answer(s)

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2 years ago
Read 2 more answers
The height of a volleyball, h, in feet, is given by h = −16t2 + 11t + 5.5, where t is the number of seconds after it has been hi
slavikrds [6]

Answer:

It will travel high enough

Step-by-step explanation:

Find the vertex of the parabola:

x=-b/2a

x=-11/2(-16)

x=-11/-32

x=11/32

Plug x=11/32 into quadratic to get the y-coordinate:

h=-16(11/32)^2+11(11/32)+5.5

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Since 7.391>7.3, the volleyball will travel high enough (aka. yes)

3 0
3 years ago
How do you do this question?
ElenaW [278]

x*y' + y = 8x

y' + y/x = 8 .... divide everything by x

dy/dx + y/x = 8

dy/dx + (1/x)*y = 8

We have something in the form

y' + P(x)*y = Q(x)

which is a first order ODE

The integrating factor is u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x

Multiply both sides by the integrating factor (x) and we get the following:

dy/dx + (1/x)*y = 8

x*dy/dx + x*(1/x)*y = x*8

x*dy/dx + y = 8x

y + x*dy/dx = 8x

Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).

Since (xy)' turns into y + x*dy/dx, and vice versa, this means

y + x*dy/dx = 8x turns into (xy)' = 8x

Integrating both sides with respect to x leads to

xy = 4x^2 + C

y = (4x^2 + C)/x

y = (4x^2)/x + C/x

y = 4x + Cx^(-1)

where C is a constant. In this case, C = -5 leads to a solution

y = 4x - 5x^(-1)

you can check this answer by deriving both sides with respect to x

dy/dx = 4 + 5x^(-2)

Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.

6 0
3 years ago
Someone help me solve this and could you explain why too?
yulyashka [42]

Answer:

3.5

Step-by-step explanation:

Well its easiest to just plug in the answers and see like 2 times 3.5 is 7.

Another way is saying 7 divided by 2 is 3.5

then u check to make sure its the same for all the numbers.

Which it is because 21 divided by 6 is also 3.5 :)

5 0
3 years ago
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