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defon
3 years ago
14

What number goes into 104 and 60?

Mathematics
1 answer:
Maslowich3 years ago
5 0

Well I don't know ! 
Let's find out:

The factors of 104 are  1,  2,  4,  8,  13,  26,  52, and  104 .

The factors of 60 are  1,  2,  3,  4,  5,  6,  10,  12,  15,  20,  30, and  60 .

The common factors (the numbers that go into both 104 and 60) are 

           1,  2, and  4 . 

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avanturin [10]

By <em>direct</em> substitution and simplification, the <em>trigonometric</em> function z = cos (2 · x + 3 · y) represents a solution of the <em>partial differential</em> equation  \frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z.

<h3>How to analyze a differential equation</h3>

<em>Differential</em> equations are expressions that involve derivatives. In this question we must prove that a given expression is a solution of a <em>differential</em> equation, that is, substituting the variables and see if the equivalence is conserved.

If we know that z = \cos (2\cdot x + 3\cdot y) and \frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z, then we conclude that:

\frac{\partial t}{\partial x} = -2\cdot \sin (2\cdot x + 3\cdot y)

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\frac{\partial t}{\partial y} = - 3 \cdot \sin (2\cdot x + 3\cdot y)

\frac{\partial^{2} t}{\partial y^{2}} = - 9 \cdot \cos (2\cdot x + 3\cdot y)

- 4\cdot \cos (2\cdot x + 3\cdot y) + 9\cdot \cos (2\cdot x + 3\cdot y) = 5 \cdot \cos (2\cdot x + 3\cdot y) = 5\cdot z

By <em>direct</em> substitution and simplification, the <em>trigonometric</em> function z = cos (2 · x + 3 · y) represents a solution of the <em>partial differential</em> equation  \frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z.

To learn more on differential equations: brainly.com/question/14620493

#SPJ1

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