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pochemuha
3 years ago
8

A plane decides to travel along AB towards the North with a velocity of V.

Mathematics
1 answer:
Maru [420]3 years ago
8 0

Step-by-step explanation:

The wind has a speed of w and a direction α with the vertical.  The x component of that speed is w sin α.  The y component is -w cos α.

In order to stay on the north trajectory AB, the plane must have a horizontal speed of -w sin α.  The plane's speed is v, so using Pythagorean theorem, the y component of the plane's speed is:

v² = (-w sin α)² + vᵧ²

v² = w² sin²α + vᵧ²

vᵧ = √(v² − w² sin²α)

The total vertical speed is therefore √(v² − w² sin²α) − w cos α.

If a is the length of AB, then the time is:

t = a / [√(v² − w² sin²α) − w cos α]

To rationalize the denominator, we multiply by the conjugate.

t = a / [√(v² − w² sin²α) − w cos α] × [√(v² − w² sin²α) + w cos α] / [√(v² − w² sin²α) + w cos α]

t = a [√(v² − w² sin²α) + w cos α] / (v² − w² sin²α − w² cos²α)

t = a [√(v² − w² sin²α) + w cos α] / (v² − w²)

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3(c-4)=4(c-6)<br> i don't know how to solve it, either
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4 0
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Last questions, plz help
Goryan [66]

Answer:

9. a_n=7+6n

10. a_n=a_{n-1}+7

Step-by-step explanation:

9. Given the sequence

13, 19, 25, ...

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a_1=13\\ \\a_2=19\\ \\a_3=25\\ \\...

Note that

a_2-a_1=19-13=6\\ \\a_3-a_2=25-19=6,

then the common difference in this sequence is d=6

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a_n=a_1+(n-1)d\\ \\a_n=13+(n-1)\cdot 6\\ \\a_n=13+6n-6\\ \\a_n=7+6n

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-10,-3, 4, 11, ...

In this sequence,

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Note that

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then the common difference in this sequence is d=7

You have

a_1=-10\\ \\d=7,

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a_n=a_{n-1}+d\\ \\a_n=a_{n-1}+7

5 0
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