Let's simplify the expression step by step:
The given expression is:
\[ -15 + \frac{4}{5}(15e^{-10}) - 10e \]
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Start with the multiplication: \[ \frac{4}{5}(15e^{-10}) = 12e^{-10} \]
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Now substitute this back into the expression: \[ -15 + 12e^{-10} - 10e \]
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Since there are no like terms that can be simplified further with respect to \(e^{-10}\) or \(e\), the expression cannot be further simplified.
Thus, the most simplified form is:
\[ -15 + 12e^{-10} - 10e \]
However, none of the answer choices match directly with this expression. Assume we might be looking for a form wherein we factor \(e^{-10}\) out or factor in a meaningful way, but based on the provided responses, it appears these results are related to manipulating the exponent.
If we had \(e^{-10}\) represented in a different exponent, the negative exponent \(e^{-10}\) could be expressed differently.
If we consider \(e^{-10} = \frac{1}{e^{10}}\), we can interpret our response options in terms of powers of \(e\):
- None of the responses seem to fit perfectly.
- Given that all final choices reflect \(e^{23}\) and \(e^{-23}\), it indicates either a misinterpretation or comparison isn't laid right.
From the setup of variables in contrast to clear number results, we pick: \[ \text{Final answer could be interpreted as potentially innovative relative to choices, but no direct match in style.} \]
Ultimately, evaluate against position pattern from your representation alongside \(e\) and constants but anticipation leads to some decode as listing choices reveal:
None accurately match calculated output directly!
Would need cross-check wider context or assess based on additional instruction data!
In given setups, verify precision of comparison since context strings differ based outcome design.
1 answer