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2 years ago

What is the geometric mean of 5 and 7?

Mathematics

1 answer:

Harman [31]2 years ago

5 0

<h3>Geometric mean of 5 and 7 is 5.9161</h3>

<em><u>Solution:</u></em>

Given that,

We have to find the geometric mean of 5 and 7

The geometric mean of two numbers a and b is the square root of product of a and b

Which means,

$Geometric\ mean = \sqrt{ab}$

<h3><u>Geometric mean of 5 and 7</u></h3>

$Geometric\ mean = \sqrt{5 \times 7}\\\\Geometric\ mean = \sqrt{35}\\\\Geometric\ mean = 5.9161$

Thus geometric mean of 5 and 7 is 5.9161

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Answer / Step-by-step explanation:

(1) Given t = 0.0588s ¹.¹²⁵

where s is the distance and t is the time to run that distance.

The second portion asks us to find the derivative of the equation when our s value is equal to 20 and interpret.

(2) First, we try to convert the unit from miles to meters

Therefore, 1 mile = 1609 meters

Then,

t = 0.0588 ( 1609 ) ¹.¹²⁵

=238 . 09

This gives us the instantaneous rate of change of seconds between every 20 meters ran.

The last portion asks us to compare this estimate to current world records. And have they been surpassed?

As of today, the fastest official record for a standard mile is held by a man from Morocco named Hichan El Guerrouj. The time was recorded at 3.43 minutes in Rome, Italy on July 7th, 1999.

Now, keep in mind that this is almost a full minute slower than the estimated time. However, how do these projections hold up against Usain Bolt, the man that is considered the fastest man in the world ?

Although, Usain Bolt does run long distances, he holds records in nearly every sprinting event that he has ever competed in.

Hence, Kennelly's estimate for the fastest mile is 238.09

(3) Now, noting that since dt / ds = 0.0588 ( 1.25 ) s ⁰.¹²⁵

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