Two planes are 1380 miles apart and traveling toward each other. One plane is traveling

Mathematics

1 answer:

vaieri [72.5K]3 years ago

8 0

Answer: plane 1: 420 mph; plane 2: 500 mph

Step-by-step explanation:

This is a physics exercise, but in order to solve this problem, you need to identify both planes first:

Let's call the plane 1 speed X

V1 = X

And V2 would be:

V2 = V1 + 80 = X + 80

If we combine both speeds:

V = V1 + V2 = X + X + 80 = 2X + 80

Now that we have an expression for the combined speed, let's see the rest of the data:

Distance: d = 1380 mile

Time: t = 1.5 h

We also know that the formula to get speed is:

V = d/t

We have the combined speed, so, let replace it in the above formula to solve for X:

2X + 80 = 1380/1.5

2X + 80 = 920

2X = 920 - 80

2X = 840

X = 840/2

X = V1 = 420 mph

We have V1, so to get V2:

V2 = 420 + 80 = 500 mph

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Which of the following is NOT a variation of a Pythagorean identity?

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The expression that is not a variation of the Pythagorean identity is the third option.

<h3>What is the Pythagorean identity?</h3>

The Pythagorean identity can be written as:

$sin^2(x) + cos^2(x) = 1$

For example, if we subtract cos^2(x) on both sides we get the second option:

$sin^2(x) = 1 - cos^2(x)$

Which is a variation.

Now, let's divide both sides by cos^2(x).

$sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x) = 1/cos^2(x)\\\\tan^2(x) + 1 = sec^2(x)\\\\tan^2(x) - sec^2(x) = -1$

Notice that the third expression in the options looks like this one, but the one on the right side is positive. The above expression is in did a variation of the Pythagorean identity, then the one written in the options (with the 1 instead of the -1) is incorrect, meaning that it is not a variation of the Pythagorean identity.

Concluding, the correct option is the third one.

If you want to learn more about the Pythagorean identity, you can read:

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3 years ago

A survey among freshman at a certain university revealed that the number of hours spent studying before final exams was normally

patriot [66]

Answer: 0.0775

Step-by-step explanation:

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