Answer:
Step-by-step explanation:
Given
Fireplace is in the form of semi-ellipse with height of 3 ft from center
Length of base=8 ft
if the arch is in the form of ellipse then it can be considered as horizontal ellipse with 2 a and 2 b be length of major and minor axis
2 a =8
a=4 ft
If contractor cover the whole base
then total length of string=2a =8 ft
(b)String should be nailed at focus
focus of ellipse is a e
where e=eccentricity
![e=\sqrt{1-(\frac{b}{a})^2}](https://tex.z-dn.net/?f=e%3D%5Csqrt%7B1-%28%5Cfrac%7Bb%7D%7Ba%7D%29%5E2%7D)
![e=\sqrt{1-(\frac{3}{4})^2}=\frac{\sqrt{7}}{4}](https://tex.z-dn.net/?f=e%3D%5Csqrt%7B1-%28%5Cfrac%7B3%7D%7B4%7D%29%5E2%7D%3D%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B4%7D)
Focus ![=ae =\sqrt{7}](https://tex.z-dn.net/?f=%3Dae%20%3D%5Csqrt%7B7%7D)
Thus string should be nailed at 2.64 m from center
The sequence can be represented by
, where
is a whole number(
and
is an integer). By this, we should be able to plug in some whole number x and be able to get these values if they are in the sequence. To test this, let's set these numbers equal to
and confirm that there is a whole number x which equals the values selected.
![2 + 4x = 90 \Rightarrow 4x = 88 \Rightarrow x = 22 \, \checkmark](https://tex.z-dn.net/?f=%202%20%2B%204x%20%3D%2090%20%5CRightarrow%204x%20%3D%2088%20%5CRightarrow%20x%20%3D%2022%20%5C%2C%20%5Ccheckmark%20)
![2 + 4x = 150 \Rightarrow 4x = 148 \Rightarrow x = 37 \, \checkmark](https://tex.z-dn.net/?f=%202%20%2B%204x%20%3D%20150%20%5CRightarrow%204x%20%3D%20148%20%5CRightarrow%20x%20%3D%2037%20%5C%2C%20%5Ccheckmark%20)
![2 + 4x = 160 \Rightarrow 4x = 158 \Rightarrow x = 39.5](https://tex.z-dn.net/?f=%202%20%2B%204x%20%3D%20160%20%5CRightarrow%204x%20%3D%20158%20%5CRightarrow%20x%20%3D%2039.5%20)
When trying 160 with our equation, we find that x doesn't equal a whole number, thus our answer is C, or 160. To confirm our answer, we can test 170 and 210 and confirm that they both give us a value for x which is a whole number.
![2 + 4x = 170 \Rightarrow 4x = 168 \Rightarrow x = 42 \, \checkmark](https://tex.z-dn.net/?f=%202%20%2B%204x%20%3D%20170%20%5CRightarrow%204x%20%3D%20168%20%5CRightarrow%20x%20%3D%2042%20%5C%2C%20%5Ccheckmark%20)
![2 + 4x = 210 \Rightarrow 4x = 208 \Rightarrow x = 52 \, \checkmark](https://tex.z-dn.net/?f=%202%20%2B%204x%20%3D%20210%20%5CRightarrow%204x%20%3D%20208%20%5CRightarrow%20x%20%3D%2052%20%5C%2C%20%5Ccheckmark%20)
So lets just assume first that there are a total of 2700 species of snakes all in all. Out of the 2700 snakes, 600 are known to be venomous. So first of all, let's get the number of the non venomous ones. Subtract 2700 and 600 and you will end up with 2100. So there are a total of 2100 non venomous snakes. So the fraction of the non venomous snakes will be 2100/2700. In its simplified form it is 7/9. In its decimal form (just divide it), you will get an answer of 0.7777.......
Ooooooooooooooooop I don’t even know