Answer:
Explanation:
{\displaystyle {}^{n}x}{}^{n}x, for n = 2, 3, 4, …, showing convergence to the infinitely iterated exponential between the two dots
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. It is the next hyperoperation after exponentiation, but before pentation. The word was coined by Reuben Louis Goodstein from tetra- (four) and iteration.
Under the definition as repeated exponentiation, the notation {\displaystyle {^{n}a}}{\displaystyle {^{n}a}} means {\displaystyle {a^{a^{\cdot ^{\cdot ^{a}}}}}}{\displaystyle {a^{a^{\cdot ^{\cdot ^{a}}}}}}, where n copies of a are iterated via exponentiation, right-to-left, I.e. the application of exponentiation {\displaystyle n-1}n-1 times. n is called the "height" of the function, while a is called the "base," analogous to exponentiation. It would be read as "the nth tetration of a".
Tetration is also defined recursively as
{\displaystyle {^{n}a}:={\begin{cases}1&{\text{if }}n=0\\a^{\left(^{(n-1)}a\right)}&{\text{if }}n>0\end{cases}}}{\displaystyle {^{n}a}:={\begin{cases}1&{\text{if }}n=0\\a^{\left(^{(n-1)}a\right)}&{\text{if }}n>0\end{cases}}},
allowing for attempts to extend tetration to non-natural numbers suc
T he Richter scale is used to rate the magnitude of an earthquake -- the amount of energy it released. This is calculated using information gathered by a seismograph. The Richter scale is logarithmic, meaning that whole-number jumps indicate a tenfold increase. In this case, the increase is in wave amplitude.
Answer:
Ocean currents act much like a conveyor belt, transporting warm water and precipitation from the equator toward the poles and cold water from the poles back to the tropics. Thus, ocean currents regulate global climate, helping to counteract the uneven distribution of solar radiation reaching Earth's surface.
Explanation:
Answer:
Acetone and water is immiscible
Acetone and hexane is miscible
Explanation:
Acetone with the chemical formula (CH3)2CO, is a nonpolar organic liquid that will mix easily. Hexane, an aliphatic hydrocarbon with 6 carbon atoms represented as C6H14 is also nonpolar. Thus, acetone and hexane would mixed completely to form a clear solution in the test tube.
On the other hand, acetone and water is immiscible (do not mix) since water, H2O, is a polar compound. And polar compounds do not react or dissolve nonpolar compounds (acetone). Usually, a mixture of acetone and water will be seen to form two distinct layers in the test tube.
