Answer:
2 real solutions
Step-by-step explanation:
x^2+18x+c-25-c=0
x^2+18x-25
D=18^2 - 4 x 1 x (-25)
D=424
D> 0 --> 2 real solutions
Answer:
![y' = \frac{4x}{3(x^{2} - 2)}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B4x%7D%7B3%28x%5E%7B2%7D%20-%202%29%7D)
Step-by-step explanation:
The derivative of
is
. The derivative of
is
, for example.
We also have that the derivative of
![y = \ln{f(x)}](https://tex.z-dn.net/?f=y%20%3D%20%5Cln%7Bf%28x%29%7D)
Is
![y' = \frac{f'(x)}{f(x)}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7Bf%27%28x%29%7D%7Bf%28x%29%7D)
In this problem, we have that:
![y = \ln{(x^{2}-2)^{\frac{2}{3}}}](https://tex.z-dn.net/?f=y%20%3D%20%5Cln%7B%28x%5E%7B2%7D-2%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D)
So
![f(x) = (x^{2} - 2)^{\frac{2}{3}}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%28x%5E%7B2%7D%20-%202%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D)
![f'(x) = \frac{2*2x}{3}*(x^{2} - 2)^{-\frac{1}{3}}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20%5Cfrac%7B2%2A2x%7D%7B3%7D%2A%28x%5E%7B2%7D%20-%202%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D)
The derivative of the function is:
![y' = \frac{f'(x)}{f(x)}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7Bf%27%28x%29%7D%7Bf%28x%29%7D)
![y' = \frac{\frac{2*2x}{3}*(x^{2} - 2)^{-\frac{1}{3}}}{(x^{2}-2)^{\frac{2}{3}}}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B%5Cfrac%7B2%2A2x%7D%7B3%7D%2A%28x%5E%7B2%7D%20-%202%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%7D%7B%28x%5E%7B2%7D-2%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%7D)
![y' = \frac{4x}{3(x^{2} - 2)}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B4x%7D%7B3%28x%5E%7B2%7D%20-%202%29%7D)
Answer:
I believe that the answer is C
Option D:
The measure of angle x is 71 degree.
Solution:
m(ar AB) =92° and m(ar CD) = 50°
<em>The measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.</em>
![$\Rightarrow \angle x^\circ =\frac{1}{2} (m (ar AB) + m (ar CD))](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5Cangle%20x%5E%5Ccirc%20%3D%5Cfrac%7B1%7D%7B2%7D%20%28m%20%28ar%20AB%29%20%2B%20m%20%28ar%20CD%29%29)
![$\Rightarrow \angle x^\circ =\frac{1}{2} (92^\circ+50^\circ)](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5Cangle%20x%5E%5Ccirc%20%3D%5Cfrac%7B1%7D%7B2%7D%20%2892%5E%5Ccirc%2B50%5E%5Ccirc%29)
![$\Rightarrow \angle x^\circ =\frac{1}{2} \ (142^\circ)](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5Cangle%20x%5E%5Ccirc%20%3D%5Cfrac%7B1%7D%7B2%7D%20%20%5C%20%28142%5E%5Ccirc%29)
![$\Rightarrow \angle x^\circ =71^\circ](https://tex.z-dn.net/?f=%24%5CRightarrow%20%5Cangle%20x%5E%5Ccirc%20%3D71%5E%5Ccirc)
The measure of angle x is 71 degree.
Option D is the correct answer.
26 people got goldfish and 11 got catfish. For goldfish all you need to do is count by 5's and for catfish count by 12's hope this helps.