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Home » 30-Gallon Aquarium Power: Grow Bigger Fish in This Massive Tank! - Carbonext

30-Gallon Aquarium Power: Grow Bigger Fish in This Massive Tank! - Carbonext

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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\( = \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{7056} = 84 \) cm²
#### 84 cm²
A ball is thrown upward with initial velocity 32 m/s from 20 meters hi...
Equation: \( h(t) = -4.9t^2 + 32t + 20 \)
Set \( h(t) = 0 \): \( -4.9t^2 + 32t + 20 = 0 \)
Use quadratic formula: \( t = \frac{-32 \pm \sqrt{32^2 + 4 \times 4.9...
Discriminant: \( 1024 + 392 = 1416 \), \( \sqrt{1416} \approx 37.65 \)
\( t = \frac{-32 + 37.65}{9.8} \approx 0.68 \) (discard negative root)
More precisely: \( t \approx 6.94 \) seconds
#### 6.94 seconds

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n_k = 3 + (k-1)\cdot 7 = 7k - 4.
We require $n_k \leq 100$:
7k - 4 \leq 100 \Rightarrow 7k \leq 104 \Rightarrow k \leq rac{104}{7...
So the largest integer $k$ is $14$.
Thus, there are $14$ such numbers.
Check: $n_{14} = 7(14) - 4 = 98 - 4 = 94 \leq 100$, and $n_{15} = 7(15...
So only $14$ terms.
Therefore, the number is $oxed{14}$.
Question: What is the remainder when the sum $1^3 + 2^3 + 3^3 + \dots...
Solution: Use the formula for the sum of cubes:

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