Answer: Choice B) ![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
Work Shown:
![\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\](https://tex.z-dn.net/?f=%5Csec%5E2%28%5Ctheta%29%20%3D%20%5Ctan%5E2%28%5Ctheta%29%20%2B%201%5C%5C%5C%5C%5Csec%5E2%28%5Ctheta%29%20%3D%20%28%5Ctan%28%5Ctheta%29%29%5E2%20%2B%201%5C%5C%5C%5C%5Csec%5E2%28%5Ctheta%29%20%3D%20%28-1%29%5E2%20%2B%201%5C%5C%5C%5C%5Csec%5E2%28%5Ctheta%29%20%3D%202%5C%5C%5C%5C%5Csec%28%5Ctheta%29%20%3D%20%5Csqrt%7B2%7D%5C%5C%5C%5C)
Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.
Answer:
LMP and NMP
Step-by-step explanation:
Adjacent angles are next to each other and share a side
LMP and NMP share a side and are next to each other
To solve this problem, you will have to first find how many US Dollars are in 1 Euro. Upon looking this up, I see that currently 1 Euro is worth 1.23 US Dollars. Next, you must calculate how many liters are in a gallon. Looking this up shows that 1 liter is equal to 0.264 gallons.
Since 0.264 is not a whole gallon and we are asked to find the price per gallon, we should next calculate how many liters can fit in a gallon. To do this, we will divide 1 by 0.264, which gives us 3.78. This tells us that 3.78 liters will fit into a gallon.
The cost of 1L of gas in euros is 1.50 Euros. Since we need 3.78L to equal 1 gallon, we can calculate the cost of this to be:
3.78 * 1.50 = €5.67
Earlier we determined that 1 euro is worth 1.23 US Dollars. Our final step is to convert our €5.67 per gallon to dollars per gallon. To do this, we simply have to multiply 5.67 by 1.23. This gives us $6.97.
So, our answer is that the cost is $6.97 per gallon.
Hopefully this is correct and makes sense to you. This is how I would approach the question.
Answer:
![1\times 10^4\ times](https://tex.z-dn.net/?f=1%5Ctimes%2010%5E4%5C%20times)
Step-by-step explanation:
Given:
Width of average grain of salt is, ![w=0.0003\ m](https://tex.z-dn.net/?f=w%3D0.0003%5C%20m)
Width of Rhinovirus is, ![W=0.00000003\ m](https://tex.z-dn.net/?f=W%3D0.00000003%5C%20m)
Now, expressing each width in scientific notation form, we get:
![w=0.0003\ m = 3\times 10^{-4}\ m\\\\W=0.00000003\ m = 3\times 10^{-8}\ m](https://tex.z-dn.net/?f=w%3D0.0003%5C%20m%20%3D%203%5Ctimes%2010%5E%7B-4%7D%5C%20m%5C%5C%5C%5CW%3D0.00000003%5C%20m%20%3D%203%5Ctimes%2010%5E%7B-8%7D%5C%20m)
Now, in order to get how many times 'W' is wider than 'w', we divide the two widths. This gives,
![\frac{W}{w}=\frac{3\times 10^{-4}\ m}{3\times 10^{-8}\ m}\\\\\frac{W}{w}=1\times 10^{-4-(-8)}=1\times 10^{-4+8}=1\times 10^4\\\\\therefore W=1\times 10^4\times w](https://tex.z-dn.net/?f=%5Cfrac%7BW%7D%7Bw%7D%3D%5Cfrac%7B3%5Ctimes%2010%5E%7B-4%7D%5C%20m%7D%7B3%5Ctimes%2010%5E%7B-8%7D%5C%20m%7D%5C%5C%5C%5C%5Cfrac%7BW%7D%7Bw%7D%3D1%5Ctimes%2010%5E%7B-4-%28-8%29%7D%3D1%5Ctimes%2010%5E%7B-4%2B8%7D%3D1%5Ctimes%2010%5E4%5C%5C%5C%5C%5Ctherefore%20W%3D1%5Ctimes%2010%5E4%5Ctimes%20w)
Therefore, the grain of salt is
wider than Rhinovirus.