A garden has a circular border and a fountain in the center. I measured the distance from one side of the garden to the other, g
1 answer:
Answer:
The length of the border is approximately 4 feet.
Step-by-step explanation:
Since the garden has a circular border we can apply the formula for the circle's length, which is shown below:
Where the radius is half the diameter. The diameter is the distance between two points in the circle going through the center, therefore for this garden the diameter is 1.2 feet and the radius is 0.6 feet. Applying this to the formula gives us:
The length of the border is approximately 4 feet.
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If the population is doubling every 10 years, the rate of change is 100%, for the period of 10 years, so, whatever it happens to be at the time, it grows by 100%, namely it doubles.
![\bf \textit{Periodic Exponential Growth}\\\\ A=I(1 + r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &4100\\ r=rate\to 100\%\to \frac{100}{100}\to &1.00\\ t=\textit{elapsed time}\to &8\\ p=period\to &10 \end{cases} \\\\\\ A=4100(1 + 1)^{\frac{8}{10}}\implies A=4100(2)^{\frac{4}{5}}\implies A=4100\sqrt[5]{2^4}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7BPeriodic%20Exponential%20Growth%7D%5C%5C%5C%5C%0AA%3DI%281%20%2B%20r%29%5E%7B%5Cfrac%7Bt%7D%7Bp%7D%7D%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D%5Ctextit%7Baccumulated%20amount%7D%5C%5C%0AI%3D%5Ctextit%7Binitial%20amount%7D%5Cto%20%264100%5C%5C%0Ar%3Drate%5Cto%20100%5C%25%5Cto%20%5Cfrac%7B100%7D%7B100%7D%5Cto%20%261.00%5C%5C%0At%3D%5Ctextit%7Belapsed%20time%7D%5Cto%20%268%5C%5C%0Ap%3Dperiod%5Cto%20%2610%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D4100%281%20%2B%201%29%5E%7B%5Cfrac%7B8%7D%7B10%7D%7D%5Cimplies%20A%3D4100%282%29%5E%7B%5Cfrac%7B4%7D%7B5%7D%7D%5Cimplies%20A%3D4100%5Csqrt%5B5%5D%7B2%5E4%7D)
Answer:
Please check the explanation.
Step-by-step explanation:
Given the expression
as
similarly
Convert element to a decimal form
so
Thus, the expression becomes
Hence,
<em>converting -86999999999.9941 in a scientific notation</em>
In order to make our job easier we will remove the sign "-" from number -86999999999.9941 (we will write "-" at the final solution). So after this step we have:
<em>−86999999999.9941 ⟶ 86999999999.9941</em>
<em></em>
In order to write number 86999999999.9941 in scientific notation, we need to move the decimal point from its current location (black dot) to the new position such as:
<em>8.6999999999.9941</em>
<em />
So, we need to move the decimal point 10 places to the right.
This means that the power of 10 will be positive 10.
Now we have that the
Number part = 8.69999999999941 and
Exponent part = 10
Thus, we conclude that:
−86999999999.9941 = − 8.69999999999941 × 10¹⁰