Answer:
![x_1=\frac{3(2+i\sqrt{6})}{10}](https://tex.z-dn.net/?f=x_1%3D%5Cfrac%7B3%282%2Bi%5Csqrt%7B6%7D%29%7D%7B10%7D)
![x_2=\frac{3(2-i\sqrt{6})}{10}](https://tex.z-dn.net/?f=x_2%3D%5Cfrac%7B3%282-i%5Csqrt%7B6%7D%29%7D%7B10%7D)
Step-by-step explanation:
Use the Quadratic formula:
![x=\frac{-b\±\sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5C%C2%B1%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
You can identify that, in this case:
![a=-10\\b=12\\c=-9](https://tex.z-dn.net/?f=a%3D-10%5C%5Cb%3D12%5C%5Cc%3D-9)
Now you need to substitute these values into the formula:
![x=\frac{-12\±\sqrt{12^2-4(-10)(-9)}}{2(-10)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-12%5C%C2%B1%5Csqrt%7B12%5E2-4%28-10%29%28-9%29%7D%7D%7B2%28-10%29%7D)
![x=\frac{-12\±\sqrt{-216}}{-20}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-12%5C%C2%B1%5Csqrt%7B-216%7D%7D%7B-20%7D)
Remember that:
![i=\sqrt{-1}](https://tex.z-dn.net/?f=i%3D%5Csqrt%7B-1%7D)
Therefore,rewriting and simplifying, you get:
![x=\frac{-12\±6i\sqrt{6}}{-20}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-12%5C%C2%B16i%5Csqrt%7B6%7D%7D%7B-20%7D)
![x=\frac{-6(2\±i\sqrt{6})}{-2(10)}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-6%282%5C%C2%B1i%5Csqrt%7B6%7D%29%7D%7B-2%2810%29%7D)
![x=\frac{3(2\±i\sqrt{6})}{10}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%282%5C%C2%B1i%5Csqrt%7B6%7D%29%7D%7B10%7D)
Then, you get the following roots:
![x_1=\frac{3(2+i\sqrt{6})}{10}](https://tex.z-dn.net/?f=x_1%3D%5Cfrac%7B3%282%2Bi%5Csqrt%7B6%7D%29%7D%7B10%7D)
![x_2=\frac{3(2-i\sqrt{6})}{10}](https://tex.z-dn.net/?f=x_2%3D%5Cfrac%7B3%282-i%5Csqrt%7B6%7D%29%7D%7B10%7D)
Q. 1 is y=1 passes through that point
Q.2 is x= 1
This is an arithmetic sequence question
The formula for the nth term of a sequence is 1+(n-1)d where a is the first term(63360), n is the 55th term, d is the common difference between consecutive terms(63368-63360)=8
Altitude on 55th step= 63360+(55-1)8
=63360+(54x8)
=63360+432
=63792 inches
I assume that there is an operato ^ missing in each function and that the right functions are:
f(m) = (m+40)^2 + 10 and
g(m) = (m+12)^2 - 50
C(m) = f(m) + g(m)
To perform that sum you need to expand the two square parentheses, this way:
f(m) = (m+40)^2 + 10 = m^2 + 80m + 1600 + 10 = m^2 + 80m + 1610
g(m) = (m+12)^2 - 50 = m^2 + 24m + 144 - 50 = m^2 +24m + 94
Now you can add f(m) + g(m) = 2m^2 + 104m + 1704
Answer: c(m) = 2m^2 + 104m + 1704