We can calculate using cosinus method in triangle
c² = a² + b² - 2ab cos c
Plug in the number to the formula
c² = a² + b² - 2ab cos c
c² = 10² + 8² - 2(10)(8) cos 105°
c² = 100 + 64 - 160 cos 105°
c² = 164 - 160 (-0.26)
c² = 164 + 41.6
c² = 205.6
c = √205.6
c =14.34
C is 14.34 unit length
For this case we have the following polynomial:
![x ^ 4 + 8x ^ 2 - 9](https://tex.z-dn.net/?f=%20x%20%5E%204%20%2B%208x%20%5E%202%20-%209%20%20)
We make the following change of variables:
![u = x ^ 2](https://tex.z-dn.net/?f=%20u%20%3D%20x%20%5E%202%20%20)
Rewriting we have
![u ^ 2 + 8u - 9](https://tex.z-dn.net/?f=%20u%20%5E%202%20%2B%208u%20-%209%20%20)
Factoring the second order polynomial we have:
![(u + 9) (u-1)](https://tex.z-dn.net/?f=%20%28u%20%2B%209%29%20%28u-1%29%20%20)
Then, returning the change we have:
![(x ^ 2 + 9) (x ^ 2-1)](https://tex.z-dn.net/?f=%20%28x%20%5E%202%20%2B%209%29%20%28x%20%5E%202-1%29%20%20)
Finally, we factor the expression in the parentheses of the second term:
![(x ^ 2 + 9) (x + 1) (x-1)](https://tex.z-dn.net/?f=%20%28x%20%5E%202%20%2B%209%29%20%28x%20%2B%201%29%20%28x-1%29%20%20)
Answer:
the completely factored form is:
![(x ^ 2 + 9) (x + 1) (x-1)](https://tex.z-dn.net/?f=%20%28x%20%5E%202%20%2B%209%29%20%28x%20%2B%201%29%20%28x-1%29%20)
Step-by-step explanation:
She made a sign error when multiplying and should have had 256 as a final answer.
<u><em>Answer:</em></u>
y^2 = 28x
<em><u>Step-by-step explanation:</u></em>
Since the directrix is horizontal, use the equation of a parabola that opens left or right.
(y−k)^2 = 4p(x−h)
Find the vertex.
(0,0)
Find the distance from the focus to the vertex.
p = 7
Substitute in the known values for the variables into the equation
(y−k)^2 = 4p(x−h).
(y−0)^2 = 4(7)(x−0)
Simplify.
<em>y^2 = 28x</em>