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3 years ago

What are rational numbers and how do you tell the difference between integers? Please answer what are rational numbers first.

Mathematics

1 answer:

Maslowich3 years ago

6 0

1. A rational number is a number that can be written as a fraction.

For example: 1/3, 5/7, 90/666, etc

Note: Any integer can be written as a fraction.

Look:

5 = 5/1 = rational

-14 = -14/1 = rational

2. There is no difference between a rational and integer.

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The question is missing the figure. So, it is in the atachment.

Answer: MN = x $\sqrt{2}$ LN = $\frac{x}{2}.(\sqrt{2} + \sqrt{6} )$

Step-by-step explanation: The first figure in the attachment is the figure of the question. The second figure is a way to respond this question by tracing the altitude from M to LN as suggested. When an altitude is drawn, it forms a 90° angle with the base, as shown in the drawing. To determine the other angle, you have to remember that all internal angles of a triangle sums up to 180°.

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$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

For MN:

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MN = $\frac{x.sen(45)}{sen(30)}$

MN = x $\sqrt{2}$

For LN:

$\frac{LN}{sen(105)} =\frac{x}{sin(30)}$

LN = $\frac{x.sin(105)}{sin(30)}$

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sin(105) = $\frac{\sqrt{2} }{4} + \frac{\sqrt{6} }{4}$

LN = $\frac{x.sin(105)}{sin(30)}$

LN = $x.(\frac{\sqrt{2} }{4} + \frac{\sqrt{6} }{4} ) .2$

LN = $\frac{x}{2}.(\sqrt{2} + \sqrt{6} )$

The expressions for:

MN = x $\sqrt{2}$

LN = $\frac{x}{2}.(\sqrt{2} + \sqrt{6} )$

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