In first question x=8, I’m too lazy to solve the rest
Answer:
56.3 cm
Step-by-step explanation:
![\dfrac{\sin 28^\circ}{27} = \dfrac{\sin 102^\circ}{c}](https://tex.z-dn.net/?f=%20%5Cdfrac%7B%5Csin%2028%5E%5Ccirc%7D%7B27%7D%20%3D%20%5Cdfrac%7B%5Csin%20102%5E%5Ccirc%7D%7Bc%7D%20)
![c\sin 28^\circ = 27 \sin 102^\circ](https://tex.z-dn.net/?f=%20c%5Csin%2028%5E%5Ccirc%20%3D%2027%20%5Csin%20102%5E%5Ccirc%20)
![c = \dfrac{27 \sin 102^\circ}{\sin 28^\circ}](https://tex.z-dn.net/?f=%20c%20%3D%20%5Cdfrac%7B27%20%5Csin%20102%5E%5Ccirc%7D%7B%5Csin%2028%5E%5Ccirc%7D%20)
![c = 56.3](https://tex.z-dn.net/?f=%20c%20%3D%2056.3%20)
Answer: 56.3 cm
Answer:
(6, -4)
Step-by-step explanation:
Answer:
Step-by-step explanation:
My approach was to draw out the probabilities, since we have 3 children, and we are looking for 2 boys and 1 girl, the probabilities can be Boy-Boy-Girl, Boy-Girl-Boy, and Girl-Boy-Boy. So a 2/3 chance if you think about it, your answer 2/3 can't be correct. If we assume that boys and girls are born with equal probability, then the probability to have two girls (and one boy) should be the same as the probability to have two boys and one girl. So you would have two cases with probability 2/3, giving an impossible 4/3 probability for both cases. Also, your list "Boy-Boy-Girl, Boy-Girl-Boy, and Girl-Boy-Boy" seems strange. All of those are 2 boys and 1 girl, so based on that list, you should get a 100 percent chance. But what about Boy-Girl-Girl, or Girl-Girl-Girl? You get 2/3 if you assume that adjacencies in the (ordered) list are important, i.e., "2 boys and a girl" means that the girl was not born between the boys.
The function is
![f(x)= x^{5} -9x ^{3}](https://tex.z-dn.net/?f=f%28x%29%3D%20x%5E%7B5%7D%20-9x%20%5E%7B3%7D%20)
1. let's factorize the expression
![x^{5} -9x ^{3}](https://tex.z-dn.net/?f=x%5E%7B5%7D%20-9x%20%5E%7B3%7D%20)
:
![f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)](https://tex.z-dn.net/?f=f%28x%29%3D%20x%5E%7B5%7D%20-9x%20%5E%7B3%7D%3D%20x%5E%7B3%7D%20%28%20x%5E%7B2%7D%20-9%29%3Dx%5E%7B3%7D%28x-3%29%28x%2B3%29)
the zeros of f(x) are the values of x which make f(x) = 0.
from the factorized form of the function, we see that the roots are:
-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3
(the multiplicity of the roots is the power of each factor of f(x) )
2.
The end behavior of f(x), whose term of largest degree is
![x^{5}](https://tex.z-dn.net/?f=%20x%5E%7B5%7D%20)
, is the same as the end behavior of
![x^{3}](https://tex.z-dn.net/?f=%20x%5E%7B3%7D%20)
, which has a well known graph. Check the picture attached.
(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of
![x^{2}](https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20)
)
so, like the graph of
![x^{3}](https://tex.z-dn.net/?f=%20x%5E%7B3%7D%20)
, the graph of
![f(x)= x^{5} -9x ^{3}](https://tex.z-dn.net/?f=f%28x%29%3D%20x%5E%7B5%7D%20-9x%20%5E%7B3%7D%20)
:
"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "