Answer:
![11\dfrac{13}{25}\pi](https://tex.z-dn.net/?f=11%5Cdfrac%7B13%7D%7B25%7D%5Cpi)
Step-by-step explanation:
r = Radius of semicircle = ![2\dfrac{4}{5}=\dfrac{24}{5}\ \text{units}](https://tex.z-dn.net/?f=2%5Cdfrac%7B4%7D%7B5%7D%3D%5Cdfrac%7B24%7D%7B5%7D%5C%20%5Ctext%7Bunits%7D)
Area of semicircle is given by
![A=\dfrac{\pi r^2}{2}\\\Rightarrow A=\dfrac{\pi \left(\dfrac{24}{5}\right)^2}{2}\\\Rightarrow A=\dfrac{288}{25}\pi=11\dfrac{13}{25}\pi\ \text{sq. units}](https://tex.z-dn.net/?f=A%3D%5Cdfrac%7B%5Cpi%20r%5E2%7D%7B2%7D%5C%5C%5CRightarrow%20A%3D%5Cdfrac%7B%5Cpi%20%5Cleft%28%5Cdfrac%7B24%7D%7B5%7D%5Cright%29%5E2%7D%7B2%7D%5C%5C%5CRightarrow%20A%3D%5Cdfrac%7B288%7D%7B25%7D%5Cpi%3D11%5Cdfrac%7B13%7D%7B25%7D%5Cpi%5C%20%5Ctext%7Bsq.%20units%7D)
The area of the semicircle is
.
Answer:
rational
Step-by-step explanation:
Answer:
58 degrees
Step-by-step explanation:
subtract 122 from 180
Answer:
Of the given geometric sequence, the first term a is 6 and its common ratio r is 2.
Step-by-step explanation:
Recall that the direct formula of a geometric sequence is given by:
![\displaystyle T_ n = ar^{n-1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20T_%20n%20%3D%20ar%5E%7Bn-1%7D)
Where <em>T</em>ₙ<em> </em>is the <em>n</em>th term, <em>a</em> is the initial term, and <em>r</em> is the common ratio.
We are given that the fifth term <em>T</em>₅ = 96 and the eighth term <em>T</em>₈ = 768. In other words:
![\displaystyle T_5 = a r^{(5) - 1} \text{ and } T_8 = ar^{(8)-1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20T_5%20%3D%20a%20r%5E%7B%285%29%20-%201%7D%20%5Ctext%7B%20and%20%7D%20T_8%20%3D%20ar%5E%7B%288%29-1%7D)
Substitute and simplify:
![\displaystyle 96 = ar^4 \text{ and } 768 = ar^7](https://tex.z-dn.net/?f=%5Cdisplaystyle%2096%20%3D%20ar%5E4%20%5Ctext%7B%20and%20%7D%20768%20%3D%20ar%5E7)
We can rewrite the second equation as:
![\displaystyle 768 = (ar^4) \cdot r^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20768%20%3D%20%28ar%5E4%29%20%5Ccdot%20r%5E3)
Substitute:
![\displaystyle 768 = (96) r^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20768%20%3D%20%2896%29%20r%5E3)
Hence:
![\displaystyle r = \sqrt[3]{\frac{768}{96}} = \sqrt[3]{8} = 2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B768%7D%7B96%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B8%7D%20%3D%202)
So, the common ratio <em>r</em> is two.
Using the first equation, we can solve for the initial term:
![\displaystyle \begin{aligned} 96 &= ar^4 \\ ar^4 &= 96 \\ a(2)^4 &= 96 \\ 16a &= 96 \\ a &= 6 \end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%2096%20%26%3D%20ar%5E4%20%5C%5C%20ar%5E4%20%26%3D%2096%20%5C%5C%20a%282%29%5E4%20%26%3D%2096%20%5C%5C%2016a%20%26%3D%2096%20%5C%5C%20a%20%26%3D%206%20%5Cend%7Baligned%7D)
In conclusion, of the given geometric sequence, the first term <em>a</em> is 6 and its common ratio <em>r</em> is 2.