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lianna [129]
3 years ago
12

A rational number can be written as the ratio of one blank to another and can be represented by a repeating or blank decimal

Mathematics
2 answers:
DaniilM [7]3 years ago
6 0
<span>A rational number can be written in the form:

</span>\frac{p}{q}; \  called \ the \ ratio \\ \\ where \ p \ and \ q \ are \ whole \ numbers<span>

The number $q$ isn't equal to zero because the division by zero is not defined. So we can represent rational numbers by a repeating or terminating decimal, for instance in the following four exercises we have:

</span>\frac{2}{3}=0.6666...=0.\stackrel{\frown}{6} \\ \\ \frac{5}{8}=0.625000...=0.625\stackrel{\frown}{0} \\ \\ \frac{3}{1}=3.000...=3.\stackrel{\frown}{0} \\ \\ \frac{3446}{2475}=1.392323...=1.39\stackrel{\frown}{23}<span>
</span>
Nesterboy [21]3 years ago
6 0

we know that

A rational number is the quotient of two integers with a denominator that is not zero , and can be represented by a repeating or terminating decimal.

Repeating Decimal is a decimal number that has digits that go on forever

Terminating decimal is a decimal number that has digits that do not go on forever.

examples

\frac{1}{3} = 0.333... (the 3 repeats forever)----> Is a Repeating Decimal

0.25 (it has two decimal digits)----> Is a Terminating Decimal

therefore

the answer is

A rational number can be written as the ratio of one integer to another and can be represented by a repeating or terminating decimal

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Use separation of variables to solve dy dx − tan x = y2 tan x with y(0) = √3. Find the value of c in radians, not degrees
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y(x)=tan(-log(cos(x))+\frac{\pi }{3} )

Step-by-step explanation:

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Factor:

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\int\ \frac{dy}{1+y^{2} } = \int\ tan(x)  dx

Evaluate the integrals:

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Evaluating the initial condition:

y(0)=\sqrt{3} =tan(-log(cos(0))+C_1)=tan(-log(1)+C_1)=tan(0+C_1)

\sqrt{3} =tan(C_1)\\arctan(\sqrt{3} )=C_1\\60=C_1

Converting 60 degrees to radians:

60degrees*\frac{\pi }{180degrees} =\frac{\pi }{3}

Replacing C_1 in the diferential equation solution:

y(x)=tan(-log(cos(x))+\frac{\pi }{3} )

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