It rained on 15% of those days
Answer:
just by using similarity of triangles we can deduce that (2x-6) is half of 16
OR you can get it by applying Mid point theorem also.
so 2x-6= 16/2
so x=7
Given the function,
![t(v) = \sqrt{ {v}^{2} + 2v - 8 }](https://tex.z-dn.net/?f=t%28v%29%20%3D%20%20%5Csqrt%7B%20%7Bv%7D%5E%7B2%7D%20%2B%202v%20-%208%20%7D%20)
We are aware that square root function is defined for only non negative values.
So,
![\to {v}^{2} + 2v - 8 \geqslant 0](https://tex.z-dn.net/?f=%5Cto%20%7Bv%7D%5E%7B2%7D%20%20%2B%202v%20-%208%20%5Cgeqslant%200)
![\to{v}^{2} + 4v - 2v- 8 \geqslant 0](https://tex.z-dn.net/?f=%20%5Cto%7Bv%7D%5E%7B2%7D%20%20%2B%204v%20%20-%202v-%208%20%5Cgeqslant%200)
![\to {v}(v + 4) - 2(v + 4) \geqslant 0](https://tex.z-dn.net/?f=%5Cto%20%7Bv%7D%28v%20%20%2B%204%29%20-%202%28v%20%2B%204%29%20%5Cgeqslant%200)
![\to(v + 4)(v - 2) \geqslant 0](https://tex.z-dn.net/?f=%5Cto%28v%20%20%2B%204%29%28v%20%20-%202%29%20%5Cgeqslant%200)
Therefore,
![\boxed{\red{v\in (-\infty, -4] \cup [2,\infty})}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cred%7Bv%5Cin%20%28-%5Cinfty%2C%20-4%5D%20%5Ccup%20%5B2%2C%5Cinfty%7D%29%7D%20)
Since this is the possible input values of v for which the given function is defined, it is the domain of the function.