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AlekseyPX
3 years ago
8

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example tha

t disproves the statement.
The equation y' = 3y - 2x + 6xy - 1 is separable.
Mathematics
1 answer:
ioda3 years ago
3 0
True.

You're allowed to move stuff around. Dogs of the AMS.

y' = 3y - 2x + 6xy - 1 \\
y' = 3y + 6xy - 2x - 1 \\
dy/dx= 3y(1 + 2x) - (2x + 1) \\
dy/dx = 3y(1 + 2x) - (1 + 2x) \\
\frac{dy}{dx} = (3y - 1)(1 + 2x) \ \Rightarrow\ \dfrac{dy}{3y-1} = (1 + 2x) dx

We wrote it in the form dy/dx = g(x) f(y) so this is separable.
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The sets of numbers 3, 4, 5 and 8, 15, 17 are Pythagorean triples. Use what you know about the Pythagorean Theorem and explain o
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Answer:

When we have 3 numbers, like:

a, b and c.

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a < b < c.

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This is equivalent to the Pythagorean Theorem, where the sum of the squares of the cathetus is equal to the hypotenuse squared.

Now that we know this, we can check if the given sets are Pythagorean triples.

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solving the left side we get:

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2) 8, 15, 17

We must have that:

8^2 + 15^2 = 17^2

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And in the right side we have:

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Answer:

c and d are correct

Step-by-step explanation:

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