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Home » Storm Superhero Unleashed: Can This Weather Hero Save the Day? - Tacotoon

Storm Superhero Unleashed: Can This Weather Hero Save the Day? - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Subtract 10: \( 6w = 44 \).
Divide by 6: \( w = \frac{44}{6} = \frac{22}{3} \approx 7.33 \) meters...
Then \( l = 2(\frac{22}{3}) + 5 = \frac{44}{3} + 5 = \frac{59}{3} \app...
#### Width: 7.33 meters, Length: 19.67 meters
A company’s profit in thousands of dollars is modeled by \( P(x) = -2x...
This is a quadratic function in vertex form. The vertex occurs at \( x...
So maximum profit occurs when \( x = 5 \), i.e., 500 units.
Plug into \( P(x) \): \( P(5) = -2(25) + 20(5) - 30 = -50 + 100 - 30 =...
Thus, maximum profit is $20,000.
#### Maximum profit: $20,000 at 500 units

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So we are looking for the smallest three-digit number $x$ such that $x...
Let $x = 60k$. Then we solve $60k \equiv 1 \pmod{7}$. Since $60 \equiv...
4k \equiv 1 \pmod{7}
Multiplying both sides by the modular inverse of 4 modulo 7, which is...
k \equiv 2 \pmod{7}
So $k = 7m + 2$. Then $x = 60k = 60(7m + 2) = 420m + 120$. We seek the...
x = 420m + 120 \geq 100 \Rightarrow m \geq 0
Try $m = 0$: $x = 120$ (valid, three-digit). Check $120 \mod 7 = 1$?
\div 7 = 17 \text{ remainder } 1 \Rightarrow \text{Yes}
Thus, the smallest such number is $\boxed{120}$.

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