Answer:
a) If a=20 the system has no solutions.
b) If a≠20 the system has exactly one solution.
Step-by-step explanation:
The augmented matrix of the system is
.
Using rows operations we obtain the echelon form of the matrix, ie,
![\left[\begin{array}{cccc}1&2&-3&4\\0&-7&-4&-10\\0&0&a-20&a+4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%262%26-3%264%5C%5C0%26-7%26-4%26-10%5C%5C0%260%26a-20%26a%2B4%5Cend%7Barray%7D%5Cright%5D)
Since the echelon form of the matrix does not have free variables then the problem has exactly one solution or has no solutions.
a) If a=20 the system has no solutions because in the last equation solving for x3 it has that 0=24. Then the system is inconsistent.
b) If a≠20, the the system has exactly one solution that is obtained solving the system of the echelon form matrix.
An unknown quantity is called a variable.
We typically use letters (ie: x) to represent these unknown values.
Answer:
166.28
Step-by-step explanation:
I'm going to use n instead of t
rⁿ=6.25rⁿ+2
minus rⁿ both sides
0=5.25rⁿ+2
minus 2 both sides
-2=5.25rⁿ
divide both sides by 5.25
-2/5.25=rⁿ
take the nth root of both sides
![\sqrt[n]{\frac{-2}{5.25}}= \sqrt[n]{r^n}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7B%5Cfrac%7B-2%7D%7B5.25%7D%7D%3D%20%5Csqrt%5Bn%5D%7Br%5En%7D)