Can anyone make an algebraic formula out of the boxed expression? i’m trying to make a formula that gives you the correct answer if you input ‘a’ into it. i’ve used tetration, super square roots, and super logarithms but cant find a solution.

i am giving out 100 points and the brainliest to the person that can solve this.

answer:

step-by-step 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

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d