For a positive integer n,if 10^{n-2} 91n,th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) We test values for $n$ to check the inequality $10^{n-2} > 91n$: For $n=1$: $10^{-1} = 0.1$,$91(1) = 91$. $0.1 > 91$ is false. For $n=2$: $10^{0}

Vedclass · Accepted Answer

$\left\{ 5, 6, 7, 8, \dots \right\}$

Vedclass · Answer

(C) We test values for $n$ to check the inequality $10^{n-2} > 91n$: For $n=1$: $10^{-1} = 0.1$,$91(1) = 91$. $0.1 > 91$ is false. For $n=2$: $10^{0} = 1$,$91(2) = 182$. $1 > 182$ is false. For $n=3$: $10^{1} = 10$,$91(3) = 273$. $10 > 273$ is false. For $n=4$: $10^{2} = 100$,$91(4) = 364$. $100 > 364$ is false. For $n=5$: $10^{3} = 1000$,$91(5) = 455$. $1000 > 455$ is true. For $n=6$: $10^{4} = 10000$,$91(6) = 546$. $10000 > 546$ is true. Since the exponential function $10^{n-2}$ grows much faster than the linear function $91n$,the inequality will hold for all $n \ge 5$. Thus,the set of values is $\left\{ 5, 6, 7, 8, \dots \right\}$.

For a positive integer $n$,if $10^{n-2} > 91n$,then the complete set of values of $n$ is:

Similar Questions

Solve $\frac{1 - |x|}{2 - |x|} \ge 0$.

Solve the following inequality: $|x-1|+|x-2|+|x-3| \geq 6$

If $x \in R$ and $1 \leq \frac{3x^2-7x+8}{x^2+1} \leq 2$,then the minimum and maximum values of $x$ are respectively.

How many litres of water will have to be added to $1125$ litres of the $45 \%$ solution of acid so that the resulting mixture will contain more than $25 \%$ but less than $30 \%$ acid content?

Find all pairs of consecutive even positive integers,both of which are larger than $5$,such that their sum is less than $23$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module