Question
Y^3=-2n+1 ; Find W(-13)
Answer should be 3
Answer should be 3
Answers
GPT-4o mini
To find \( W(-13) \) given the equation \( Y^3 = -2n + 1 \), we start by re-arranging the equation to express \( n \) in terms of \( Y \):
\[
Y^3 + 2n - 1 = 0
\]
This can be rewritten as:
\[
2n = 1 - Y^3 \implies n = \frac{1 - Y^3}{2}
\]
Now, if we want to find \( n \) when \( Y = -13 \):
\[
n = \frac{1 - (-13)^3}{2}
\]
Calculating \( (-13)^3 \):
\[
(-13)^3 = -2197
\]
Thus, substituting back into the equation:
\[
n = \frac{1 - (-2197)}{2} = \frac{1 + 2197}{2} = \frac{2198}{2} = 1099
\]
So, we have:
\[
n = 1099
\]
To find \( W(-13) \), we notice we assumed the output should lead to a specified answer of \( 3 \). Hence, let's understand if there is another context or requirement where:
If it's said \( W(-13) = 3 \) directly without connection back to our equation beyond being simply the arithmetic equation's solver, please clarify further what "W" represents if it is not directly derived from substituted results associated with the cubic relationship indicated by letter \( Y \).
If indeed you need \( W \) with output \( 3 \), could you specify if there's additional algebra or framework for its designation as such?
The original equation, based on inputs, leads to \( n \) revealing numerical outputs not directly amounting to the value \( 3 \) from \( -13\). Thus, the framework might underpin further clarity or directive for \( W \).
Please provide that context.
\[
Y^3 + 2n - 1 = 0
\]
This can be rewritten as:
\[
2n = 1 - Y^3 \implies n = \frac{1 - Y^3}{2}
\]
Now, if we want to find \( n \) when \( Y = -13 \):
\[
n = \frac{1 - (-13)^3}{2}
\]
Calculating \( (-13)^3 \):
\[
(-13)^3 = -2197
\]
Thus, substituting back into the equation:
\[
n = \frac{1 - (-2197)}{2} = \frac{1 + 2197}{2} = \frac{2198}{2} = 1099
\]
So, we have:
\[
n = 1099
\]
To find \( W(-13) \), we notice we assumed the output should lead to a specified answer of \( 3 \). Hence, let's understand if there is another context or requirement where:
If it's said \( W(-13) = 3 \) directly without connection back to our equation beyond being simply the arithmetic equation's solver, please clarify further what "W" represents if it is not directly derived from substituted results associated with the cubic relationship indicated by letter \( Y \).
If indeed you need \( W \) with output \( 3 \), could you specify if there's additional algebra or framework for its designation as such?
The original equation, based on inputs, leads to \( n \) revealing numerical outputs not directly amounting to the value \( 3 \) from \( -13\). Thus, the framework might underpin further clarity or directive for \( W \).
Please provide that context.