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Virty [35]
2 years ago
12

A hiker on the Appalachian Trail planned to increase the distance covered by 10% each day. After 7 days, the total distance trav

eled is 56.923 miles. Part A: How many miles did the hiker travel on the first day
Mathematics
1 answer:
Anastaziya [24]2 years ago
5 0

Answer:

  6.0 miles

Step-by-step explanation:

The sequence of distances is a geometric sequence with first term a1 and common ratio (1 +10%) = 1.10. The sum of 7 terms of the sequence is ...

  S7 = a1·(r^7 -1)/(r -1)

  56.923 = a1·(1.1^7 -1)/(1.1 -1)

  5.6923 = a1·0.9487171

Dividing by the coefficient of a1 gives its value:

  5.6923/0.9487171 ≈ 5.999997 ≈ 6.000

The hiker traveled 6.0 miles on the first day.

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Answer:

52

Step-by-step explanation:

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3 years ago
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Can someone please help with this math question:)
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<u>Solution</u><u>:</u>

The rationalisation factor for \frac{1}{ a -  \sqrt{b}  } is a + \sqrt{b}

So, let us apply it here.

\frac{1}{5 -  \sqrt{2} }

The rationalising factor for 5 - √2 is 5 + √2.

Therefore, multiplying and dividing by 5 + √2, we have

=  \frac{1}{5 -  \sqrt{2} }  \times  \frac{5 +  \sqrt{2} }{5 +  \sqrt{2} }  \\  =  \frac{5 +  \sqrt{2} }{(5 -  \sqrt{2})(5 +  \sqrt{2} ) }  \\  =  \frac{5 +  \sqrt{2} }{ {(5)}^{2} - ( \sqrt{2})^{2}   }  \\  =  \frac{5 +  \sqrt{2} }{25 -  2}  \\  =  \frac{5 +  \sqrt{2} }{23}

<u>Answer:</u>

<u>\frac{5 +  \sqrt{2} }{23}</u>

Hope you could understand.

If you have any query, feel free to ask.

5 0
2 years ago
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Jean works as a secretary for a local business. She is paid $10.50 per hour. She
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Answer:

$472.5

Step-by-step explanation:

10.5x

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Increase £2193.67 by 8.5%
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Answer:

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Step-by-step explanation:

The increase will be 8.5% of £2193.76 added to £2193.76

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8.5% of £2193.76

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Increase = £2193.76 + £186.47

= £2380.23

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3 years ago
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