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anzhelika [568]
3 years ago
8

Which geometric series represents 0.4444... as a fraction?

Mathematics
2 answers:
STALIN [3.7K]3 years ago
8 0

Answer: It can be expressed as

\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+........

Step-by-step explanation:

Since we have given that 0.44444.......

We need  geometric series that represents as a fraction.

so, it can be written as

0.4+0.04+0.004+0.0004...............

But as we are required to write it as a fraction , So, it becomes,

\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+\frac{4}{10000}............

and it is a geometric series.

Because it has first term = a = \frac{4}{10}

and common ratio = r = \frac{a_2}{a_1}=\frac{\frac{4}{100}}{\frac{4}{10}}=\frac{1}{10}

Hence, it can be expressed as

\frac{4}{10}+\frac{4}{100}+\frac{4}{1000}+........

aliina [53]3 years ago
7 0
The geometric series that represents 0.4444... as a fraction is: <span>4/6 * [k=0, ∞]∑1/6^k </span>
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The value of x is 4/3

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

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Given data ,

Let the triangles be ΔRST and ΔQRT

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And RS = 2/√3

∠T = 60° in the triangle ΔRST

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sin 60° = opposite / hypotenuse

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Substituting the value of  sin 60° in the equation , we get

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Multiply by RT on both sides , we get

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Now , from the figure

∠R = 90° in the triangle ΔQRT

and ∠T = 45° in the triangle ΔQRT

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tan 45° = opposite / adjacent

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Step-by-step explanation:

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2. Solve:

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Because the exponent 2/3 is raised to the power of 6, you can use the power rule, which basically just means that whenever an exponent is raised to an exponent, multiply them. So, 2/3 * 6 equals 12/3, and 12/3 equals 4, making your answer x^4.

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Answer:

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