Answer:
50 gallons
Step-by-step explanation:
18*17*38= a total volume of 11628 in^3. Dividing this by 12^3 to find the volume in cubic feet, you get 11628/1728=6.729. Dividing this by 0.134 to find the number of gallons, you get 6.729/0.134 which is about 50 gallons. Hope this helps!
We have the following:
![10x^2-x+9=0](https://tex.z-dn.net/?f=10x%5E2-x%2B9%3D0)
solving:
![\begin{gathered} 10x^2-x+9=0 \\ 10x^2-x+9-9=-9 \\ 10x^2-x=-9 \\ \frac{10}{10}x^2-\frac{x}{10}=-\frac{9}{10} \\ x^2-\frac{x}{10}+(-\frac{1}{20})^2=-\frac{9}{10}+(-\frac{1}{20})^2 \\ (x-\frac{1}{20})^2=-\frac{359}{400}\rightarrow(x-\frac{1}{20})=\sqrt[]{-\frac{359}{400}} \\ x=\frac{1}{20}+i\frac{\sqrt{359}}{20} \\ x=\frac{1}{20}-i\frac{\sqrt{359}}{20} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2010x%5E2-x%2B9%3D0%20%5C%5C%2010x%5E2-x%2B9-9%3D-9%20%5C%5C%2010x%5E2-x%3D-9%20%5C%5C%20%5Cfrac%7B10%7D%7B10%7Dx%5E2-%5Cfrac%7Bx%7D%7B10%7D%3D-%5Cfrac%7B9%7D%7B10%7D%20%5C%5C%20x%5E2-%5Cfrac%7Bx%7D%7B10%7D%2B%28-%5Cfrac%7B1%7D%7B20%7D%29%5E2%3D-%5Cfrac%7B9%7D%7B10%7D%2B%28-%5Cfrac%7B1%7D%7B20%7D%29%5E2%20%5C%5C%20%28x-%5Cfrac%7B1%7D%7B20%7D%29%5E2%3D-%5Cfrac%7B359%7D%7B400%7D%5Crightarrow%28x-%5Cfrac%7B1%7D%7B20%7D%29%3D%5Csqrt%5B%5D%7B-%5Cfrac%7B359%7D%7B400%7D%7D%20%5C%5C%20x%3D%5Cfrac%7B1%7D%7B20%7D%2Bi%5Cfrac%7B%5Csqrt%7B359%7D%7D%7B20%7D%20%5C%5C%20x%3D%5Cfrac%7B1%7D%7B20%7D-i%5Cfrac%7B%5Csqrt%7B359%7D%7D%7B20%7D%20%5Cend%7Bgathered%7D)
The answer is the last option
Hope this helps! I filled it out below.
Answer
Find out the the value of the fourth term in a geometric sequence for which
![a_{1} = 10\ and\ r =0.5](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%2010%5C%20and%5C%20r%20%3D0.5)
To proof
The formula for the general term for each geometric sequence is
![a_{n} = a_{1} r^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7D%20r%5E%7Bn-1%7D)
where
![a_{1} = first\ term,\ r = common\ ratio](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%20first%5C%20term%2C%5C%20r%20%3D%20common%5C%20ratio)
Put n= 4
![a_{4} = 10\times(0.5)^{4-1}](https://tex.z-dn.net/?f=a_%7B4%7D%20%3D%2010%5Ctimes%280.5%29%5E%7B4-1%7D)
![a_{4} = 10\times(0.5)^{3}](https://tex.z-dn.net/?f=a_%7B4%7D%20%3D%2010%5Ctimes%280.5%29%5E%7B3%7D)
![a_{4} = 10\times0.125](https://tex.z-dn.net/?f=a_%7B4%7D%20%3D%2010%5Ctimes0.125)
Solving
![a_{4} = 1.25](https://tex.z-dn.net/?f=a_%7B4%7D%20%3D%201.25)
The value of the fourth term in a geometric sequence is 1.25 .
Hence proved