Answer:
![\frac{1}{1 + \cos(x) }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B1%20%2B%20%20%5Ccos%28x%29%20%7D%20)
Step-by-step explanation:
![y = \frac{ \sin(x) }{1 + \cos(x) }](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B%20%5Csin%28x%29%20%7D%7B1%20%2B%20%20%5Ccos%28x%29%20%7D%20)
<u>differentiating numerator wrt x :-</u>
(sinx)' = cos x
<u>differentiating denominator wrt x :- </u>
(1 + cos x)' = (cosx)' = - sinx
- Let's say the denominator was "v" and the numerator was "u"
![(\frac{u}{v} )' = \frac{v. \: (u)' - u.(v)' }{ {v}^{2} }](https://tex.z-dn.net/?f=%20%28%5Cfrac%7Bu%7D%7Bv%7D%20%20%29%27%20%20%3D%20%20%5Cfrac%7Bv.%20%5C%3A%20%28u%29%27%20%20-%20u.%28v%29%27%20%7D%7B%20%7Bv%7D%5E%7B2%7D%20%7D%20)
here,
- since u is the numerator u= sinx and u = cos x
- v(denominator) = 1 + cos x; v' = - sinx
![= \frac{((1 + \cos \: x) \cos \: x )- (\sin \: x. ( - \sin \: x) ) }{( {1 + \cos(x)) }^{2} }](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B%28%281%20%2B%20%20%5Ccos%20%5C%3A%20x%29%20%5Ccos%20%5C%3A%20x%20%29-%20%28%5Csin%20%5C%3A%20x.%20%28%20-%20%20%5Csin%20%5C%3A%20x%29%20%20%29%20%7D%7B%28%20%7B1%20%2B%20%20%5Ccos%28x%29%29%20%7D%5E%7B2%7D%20%7D%20)
![= \frac{ \cos(x) + \cos {}^{2} (x) + \sin {}^{2} (x) }{(1 + \cos \: x) {}^{2} }](https://tex.z-dn.net/?f=%20%20%3D%20%20%5Cfrac%7B%20%5Ccos%28x%29%20%20%2B%20%20%5Ccos%20%7B%7D%5E%7B2%7D%20%28x%29%20%20%2B%20%20%20%5Csin%20%7B%7D%5E%7B2%7D%20%28x%29%20%7D%7B%281%20%2B%20%20%5Ccos%20%5C%3A%20x%29%20%7B%7D%5E%7B2%7D%20%20%7D%20)
since cos²x + sin²x = 1
![= \frac{ \cos \: x + 1}{(1 + \cos \: x) {}^{2} }](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B%20%5Ccos%20%5C%3A%20x%20%2B%201%7D%7B%281%20%2B%20%20%5Ccos%20%5C%3A%20x%29%20%7B%7D%5E%7B2%7D%20%20%7D%20%20)
diving numerator and denominator by 1 + cos x
![= \frac{1}{1 + \cos(x) }](https://tex.z-dn.net/?f=%20%3D%20%20%5Cfrac%7B1%7D%7B1%20%2B%20%20%5Ccos%28x%29%20%7D%20)
Answer:
The answer is 900
Step-by-step explanation:
Hope this helps : )
Answer:
B
Step-by-step explanation:
Note:
1 gal = 4 quarts
1 pint = 0.5 quart
Re-writing all the choices in dollars and quarts and calculating how much each quart costs
A) $1 per 1 quart
B) $2 per gallon = $2 per 4 quarts = $2 ÷ 4 quarts = $0.50 per quart
C) $1.50 per 2 quarts = $1.50 ÷ 2 quarts = $0.75 per quart
D) $0.50 per 1 pint = $0.50 per 0.5 quart = $0.50 ÷ 0.5 quart = $1 per quart
If you compare all of the above, it is clear that answer B ($0.50 per quart) is the cheapest rate and hence the best deal.
Answer: The greatest depth of the Southern Ocean is 7.24
Step-by-step explanation:
So, if you add all the greatest depths up, you get 33.23
(33.23 + x)/5 = 8.094
Multiply each side by 5
33.23 + x = 40.47
Subtract 33.23 from each side
x = 7.24
You can check this by adding all the numbers up and dividing them by 5
40.47/5 = 8.094