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m_a_m_a [10]
3 years ago
14

If the geometric mean of a and 34 is 6 sqrt(17) find the value of a

Mathematics
1 answer:
Alborosie3 years ago
3 0

Using the geometric mean concept, it is found that the value of a is 18.

----------------------

The geometric mean, of a data-set of n elements, (n_1, n_2, ..., n_n), is given by:

G = \sqrt[n]{n_1 \times n_2 \times ... \times n_n}

That is, the nth root of the multiplication of all elements.

----------------------

In this question:

  • Two elements(n = 2), a and 34.
  • G = 6\sqrt{17}

Thus:

\sqrt{34a} = 6\sqrt{17}

We find the square of each side, so:

(\sqrt{34a})^2 = (6\sqrt{17})^2

34a = 36\times17

Simplifying both sides by 17:

2a = 36

a = \frac{36}{2}

a = 18

The value of a is 18.

A similar example is given at brainly.com/question/15010240

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7 0
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Madison received a share of $4230 for a fishing competition. She deposited it in the bank and left it for 3 years accumulating s
Elis [28]

Answer:

$4785.68

Step-by-step explanation:

Original amount: <u>$</u><u>4</u><u>2</u><u>3</u><u>0</u>

Interest for 1 year: <u>4</u><u>.</u><u>2</u><u>%</u>

<em>First year;</em>

4230 + (4230 \times  \frac{4.2}{100})  \\  = 4230 + 177.66 \\  = 4407.66

<em>S</em><em>e</em><em>c</em><em>o</em><em>n</em><em>d</em><em> </em><em>y</em><em>e</em><em>a</em><em>r</em><em>;</em>

4407.66 + (4407.66 \times  \frac{4.2}{100} ) \\  = 4407.66 + 185.12172 \\  = 4592.78172

<em>T</em><em>h</em><em>i</em><em>r</em><em>d</em><em> </em><em>y</em><em>e</em><em>a</em><em>r</em><em> </em><em>(</em><em>t</em><em>o</em><em>t</em><em>a</em><em>l</em><em> </em><em>b</em><em>a</em><em>l</em><em>a</em><em>n</em><em>c</em><em>e</em><em> </em><em>a</em><em>f</em><em>t</em><em>e</em><em>r</em><em> </em><em>3</em><em> </em><em>y</em><em>e</em><em>a</em><em>r</em><em>s</em><em>)</em><em>;</em>

4592.78172 + (4592.78172 \times  \frac{4.2}{100} ) \\  = 4592.78172 + 192.89683224 \\  =4785.67855224

Round the number;

<em><u>$4785.68</u></em>

YOUR ANSWER hope this helps :))

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