I assume you need to solve for g?
12g + 6 = 78
- 6
12g = 72
÷ 12
g = 6
I hope this helps! Let me know if you want me to explain anything :)
So, we know that a^2 + b^2 = c^2. Right? That is called the Pythagorean Theorem.
In this case. We can say that 39 is a, 40 is b, and x is c.
NOTE: It doesn't really matter whether 39 is a or b. a & b are just the two legs of the right triangle.
So, if we say that 39 is a, 40 is b, and x is c. We can plug it into the Pythagorean Theorem.
39^2 + 40^2 = x^2
I'll let you take it from there.
The slope of the line is -2/1.
Answer:
![f(x_1)=2\sqrt{118}\\f(x_2)=-2\sqrt{118}](https://tex.z-dn.net/?f=f%28x_1%29%3D2%5Csqrt%7B118%7D%5C%5Cf%28x_2%29%3D-2%5Csqrt%7B118%7D)
Step-by-step explanation:
![f(x)=13x^3-x^2-3x+10](https://tex.z-dn.net/?f=f%28x%29%3D13x%5E3-x%5E2-3x%2B10)
Differentiate with respect to ![x](https://tex.z-dn.net/?f=x)
![f'(x)=39x^2-2x-3](https://tex.z-dn.net/?f=f%27%28x%29%3D39x%5E2-2x-3)
For equation of the form
, solutions are given by ![x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
To find: critical points
![39x^2-2x-3=0](https://tex.z-dn.net/?f=39x%5E2-2x-3%3D0)
![x=\frac{2\pm \sqrt{4+468}}{78}\\=\frac{2\pm \sqrt{472}}{78}\\=\frac{2\pm 2\sqrt{118}}{78}\\=\frac{1\pm \sqrt{118}}{39}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B4%2B468%7D%7D%7B78%7D%5C%5C%3D%5Cfrac%7B2%5Cpm%20%5Csqrt%7B472%7D%7D%7B78%7D%5C%5C%3D%5Cfrac%7B2%5Cpm%202%5Csqrt%7B118%7D%7D%7B78%7D%5C%5C%3D%5Cfrac%7B1%5Cpm%20%5Csqrt%7B118%7D%7D%7B39%7D)
Let ![x_1=\frac{1+\sqrt{118}}{39}\,,\,x_2=\frac{1- \sqrt{118}}{39}](https://tex.z-dn.net/?f=x_1%3D%5Cfrac%7B1%2B%5Csqrt%7B118%7D%7D%7B39%7D%5C%2C%2C%5C%2Cx_2%3D%5Cfrac%7B1-%20%5Csqrt%7B118%7D%7D%7B39%7D)
Differentiate
again with respect to ![x](https://tex.z-dn.net/?f=x)
![f''(x)=78x-2](https://tex.z-dn.net/?f=f%27%27%28x%29%3D78x-2)
![f(x_1)=f\left (\frac{1+\sqrt{118}}{39} \right )\\=78\left ( \frac{1+\sqrt{118}}{39} \right )-2\\=2\left ( 1+\sqrt{118} \right )-2\\=2\sqrt{118}\\f(x_2)=f\left (\frac{1-\sqrt{118}}{39} \right )\\=78\left ( \frac{1-\sqrt{118}}{39} \right )-2\\=2\left ( 1-\sqrt{118} \right )-2\\=-2\sqrt{118}](https://tex.z-dn.net/?f=f%28x_1%29%3Df%5Cleft%20%28%5Cfrac%7B1%2B%5Csqrt%7B118%7D%7D%7B39%7D%20%20%5Cright%20%29%5C%5C%3D78%5Cleft%20%28%20%5Cfrac%7B1%2B%5Csqrt%7B118%7D%7D%7B39%7D%20%5Cright%20%29-2%5C%5C%3D2%5Cleft%20%28%201%2B%5Csqrt%7B118%7D%20%5Cright%20%29-2%5C%5C%3D2%5Csqrt%7B118%7D%5C%5Cf%28x_2%29%3Df%5Cleft%20%28%5Cfrac%7B1-%5Csqrt%7B118%7D%7D%7B39%7D%20%20%5Cright%20%29%5C%5C%3D78%5Cleft%20%28%20%5Cfrac%7B1-%5Csqrt%7B118%7D%7D%7B39%7D%20%5Cright%20%29-2%5C%5C%3D2%5Cleft%20%28%201-%5Csqrt%7B118%7D%20%5Cright%20%29-2%5C%5C%3D-2%5Csqrt%7B118%7D)