Answer:
AB= 0.625 units (3 s.f.)
∠BAC= 52.9° (1 d.p.)
∠ABC= 32.1° (1 d.p.)
Step-by-step explanation:
Please see the attached pictures for full solution.
- Find AB using cosine rule
- find ∠BAC using sine rule
- find ∠ABC using angle sum of triangle property
Answer:
x = -6 and x = 4
Step-by-step explanation:
In math, the critical points of a function are the points where the derivative equals zero.
So, first we will find the derivative of the function. The derivative is:
![f'(x)=3x^2 +6x-72](https://tex.z-dn.net/?f=f%27%28x%29%3D3x%5E2%20%2B6x-72)
Now, we are going to make the derivative equal zero and find the answers of the equation.
![3x^2 +6x-72=0\\3(x^2 +2x-24)=0\\3(x+6)(x-4)=0\\](https://tex.z-dn.net/?f=3x%5E2%20%2B6x-72%3D0%5C%5C3%28x%5E2%20%2B2x-24%29%3D0%5C%5C3%28x%2B6%29%28x-4%29%3D0%5C%5C)
So we have that the critical points are the answers to this equation:
![x+6= 0 \\x= - 6](https://tex.z-dn.net/?f=x%2B6%3D%200%20%5C%5Cx%3D%20-%206)
and
![x-4=0\\x=4](https://tex.z-dn.net/?f=x-4%3D0%5C%5Cx%3D4)
Thus, the critical points are x=-6 and x=4