Question
Y^3= -2n+1 ; Find w(-13)
Answer should be 3
Answer should be 3
Answers
GPT-4o mini
To solve the equation \( Y^3 = -2n + 1 \) for \( w(-13) \), we'll first find the corresponding value for \( Y \) when \( n = -13 \).
Substituting \( n = -13 \) into the equation:
\[
Y^3 = -2(-13) + 1
\]
Calculating \( -2(-13) \):
\[
Y^3 = 26 + 1 = 27
\]
Now we take the cube root of both sides to find \( Y \):
\[
Y = \sqrt[3]{27} = 3
\]
Thus, \( w(-13) = 3 \). This confirms that the answer is indeed 3.
Substituting \( n = -13 \) into the equation:
\[
Y^3 = -2(-13) + 1
\]
Calculating \( -2(-13) \):
\[
Y^3 = 26 + 1 = 27
\]
Now we take the cube root of both sides to find \( Y \):
\[
Y = \sqrt[3]{27} = 3
\]
Thus, \( w(-13) = 3 \). This confirms that the answer is indeed 3.
After Y^3 = 26 + 1 = 27 then what do I do to make the answer 3?
GPT-4o mini
To confirm that \( Y = 3 \) from the equation \( Y^3 = 27 \):
1. **Start with the equation**:
\[
Y^3 = 27
\]
2. **Take the cube root** of both sides:
\[
Y = \sqrt[3]{27}
\]
3. **Calculate the cube root**:
The cube root of 27 is indeed:
\[
Y = 3
\]
So, with the steps shown, the calculation that leads to \( Y = 3 \) is correct. Therefore, if you are looking for \( w(-13) \), and based on your input, \( w(-13) \) indeed equals \( 3 \).
If you meant to ask about how you could manipulate the equation to arrive at \( Y = 3 \) via other means, this is directly dictated by the nature of cube roots and there isn't an arbitrary way to manipulate it to make the answer \( 3 \) since \( Y^3 = 27 \) straightforwardly leads to \( Y = 3 \).
The calculation you provided is accurate and follows mathematical principles correctly. If there's further clarification or any alternative expression of the question you're looking for, please specify!
1. **Start with the equation**:
\[
Y^3 = 27
\]
2. **Take the cube root** of both sides:
\[
Y = \sqrt[3]{27}
\]
3. **Calculate the cube root**:
The cube root of 27 is indeed:
\[
Y = 3
\]
So, with the steps shown, the calculation that leads to \( Y = 3 \) is correct. Therefore, if you are looking for \( w(-13) \), and based on your input, \( w(-13) \) indeed equals \( 3 \).
If you meant to ask about how you could manipulate the equation to arrive at \( Y = 3 \) via other means, this is directly dictated by the nature of cube roots and there isn't an arbitrary way to manipulate it to make the answer \( 3 \) since \( Y^3 = 27 \) straightforwardly leads to \( Y = 3 \).
The calculation you provided is accurate and follows mathematical principles correctly. If there's further clarification or any alternative expression of the question you're looking for, please specify!