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3 years ago

7

An airplane travels 4374 kilometers against the wind in 6 hours and 5514 kilometers with the wind in the same amount of time. Wh

at is the rate of the plane in
still air and what is the rate of the wind?

1 answer:

Rudik [331]3 years ago

6 0

Answer:

air = 95 mph

plane = 824 MPH

Step-by-step explanation:

6(x-y) = 4374

6(x+y)= 5514

6x - 6y = 4375

6x + 6y = 5514

12x = 9889

x = 824 mph

y = 95 mph

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Suppose cos(x)= -1/3, where π/2 ≤ x ≤ π. What is the value of tan(2x). EDGE

AVprozaik [17]

Answer:

D

Step-by-step explanation:

We are given that:

$\displaystyle \cos x = -\frac{1}{3}\text{ where } \pi /2 \leq x \leq \pi$

And we want to find the value of tan(2<em>x</em>).

Note that since <em>x</em> is between π/2 and π, it is in QII.

In QII, cosine and tangent are negative and only sine is positive.

We can rewrite our expression as:

$\displaystyle \tan(2x)=\frac{\sin(2x)}{\cos(2x)}$

Using double angle identities:

$\displaystyle \tan(2x)=\frac{2\sin x\cos x}{\cos^2 x-\sin^2 x}$

Since cosine relates the ratio of the adjacent side to the hypotenuse and we are given that cos(<em>x</em>) = -1/3, this means that our adjacent side is one and our hypotenuse is three (we can ignore the negative). Using this information, find the opposite side:

$\displaystyle o=\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}$

So, our adjacent side is 1, our opposite side is 2√2, and our hypotenuse is 3.

From the above information, substitute in appropriate values. And since <em>x</em> is in QII, cosine and tangent will be negative while sine will be positive. Hence:

<h2> $\displaystyle \tan(2x)=\frac{2(2\sqrt{2}/3)(-1/3)}{(-1/3)^2-(2\sqrt{2}/3)^2}$ </h2>

Simplify:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{(1/9)-(8/9)}$

Evaluate:

$\displaystyle \tan(2x)=\frac{-4\sqrt{2}/9}{-7/9} = \frac{4\sqrt{2}}{7}$

The final answer is positive, so we can eliminate A and B.

We can simplify D to:

$\displaystyle \frac{2\sqrt{8}}{7}=\frac{2(2\sqrt{2}}{7}=\frac{4\sqrt{2}}{7}$

So, our answer is D.

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3 years ago

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Answer:

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Step-by-step explanation:

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A set of numbers satisfies Benford’s Law if the probability of a number starting with digit d is P(d) = log(d + 1) – log(d).

irakobra [83]

Interpreting the graph and the situation, it is found that the values of d that can be included in the solution set are 1 and 4.

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A number can start with 10 possible digits, ranging from 1 to 9, which are all integer digits.

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A similar problem is given at brainly.com/question/16764162

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3 years ago

A train covers 168 miles at a speed of 42 mph. How much time dod it take?

Sergio039 [100]

Answer:

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Step-by-step explanation:

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