1 fl oz. is equivalent to 29.6 ml.
0.5 * 4 * 29.6 = 59.2 ml
Answer:
x = 7.5
Step-by-step explanation:
Proportions:
5 x
_ = _
6 9
Hi there!
![\sqrt{\frac{1-cosA}{1+cosA}} =](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B1-cosA%7D%7B1%2BcosA%7D%7D%20%3D)
We can begin by multiplying by its conjugate:
![\sqrt{\frac{1-cosA}{1+cosA}} * \sqrt{\frac{1+cosA}{1+cosA}} = \\\\\sqrt{\frac{(1-cosA)(1 + cosA)}{(1+cosA)(1 + cosA)}} =](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B1-cosA%7D%7B1%2BcosA%7D%7D%20%2A%20%5Csqrt%7B%5Cfrac%7B1%2BcosA%7D%7B1%2BcosA%7D%7D%20%20%3D%20%5C%5C%5C%5C%5Csqrt%7B%5Cfrac%7B%281-cosA%29%281%20%2B%20cosA%29%7D%7B%281%2BcosA%29%281%20%2B%20cosA%29%7D%7D%20%3D)
Simplify using the identity:
![1 - cos^2A = sin^2A](https://tex.z-dn.net/?f=1%20-%20cos%5E2A%20%3D%20sin%5E2A)
![\sqrt{\frac{(1-cos^2A)}{(1+cosA)^2}} =\\\\\sqrt{\frac{(sin^2A)}{(1+cosA)^2}} =](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B%281-cos%5E2A%29%7D%7B%281%2BcosA%29%5E2%7D%7D%20%3D%5C%5C%5C%5C%5Csqrt%7B%5Cfrac%7B%28sin%5E2A%29%7D%7B%281%2BcosA%29%5E2%7D%7D%20%3D)
Take the square root of the expression:
![{\frac{sinA}{1+cosA} =](https://tex.z-dn.net/?f=%7B%5Cfrac%7BsinA%7D%7B1%2BcosA%7D%20%3D)
Multiply again by the conjugate to get a SINGLE term in the denominator:
![{\frac{sinA}{1+cosA} * {\frac{1-cosA}{1-cosA} =\\](https://tex.z-dn.net/?f=%7B%5Cfrac%7BsinA%7D%7B1%2BcosA%7D%20%2A%20%7B%5Cfrac%7B1-cosA%7D%7B1-cosA%7D%20%3D%5C%5C)
Simplify:
![{\frac{sinA(1-cosA)}{1-cos^2A} =](https://tex.z-dn.net/?f=%7B%5Cfrac%7BsinA%281-cosA%29%7D%7B1-cos%5E2A%7D%20%3D)
Use the above trig identity one more:
![{\frac{sinA(1-cosA)}{sin^2A} =](https://tex.z-dn.net/?f=%7B%5Cfrac%7BsinA%281-cosA%29%7D%7Bsin%5E2A%7D%20%3D)
Cancel out sinA:
![{\frac{(1-cosA)}{sinA} =](https://tex.z-dn.net/?f=%7B%5Cfrac%7B%281-cosA%29%7D%7BsinA%7D%20%20%3D)
Split the fraction into two:
![{\frac{1}{sinA} - \frac{cosA}{sinA} =](https://tex.z-dn.net/?f=%7B%5Cfrac%7B1%7D%7BsinA%7D%20%20%20-%20%5Cfrac%7BcosA%7D%7BsinA%7D%20%3D)
Recall:
![1/sinA = cscA\\\\cosA/sinA = cotA](https://tex.z-dn.net/?f=1%2FsinA%20%3D%20cscA%5C%5C%5C%5CcosA%2FsinA%20%3D%20cotA)
Simplify:
![\frac{1}{sinA} + \frac{cosA}{sinA} = \boxed{cscA - cotA}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BsinA%7D%20%2B%20%5Cfrac%7BcosA%7D%7BsinA%7D%20%3D%20%5Cboxed%7BcscA%20-%20cotA%7D)
Use the proportion equation. Cross multiply. Answer is 10.4%
The answer is B because -3 -8 = -11.