There is at least one multiple of 3 → $ 3 \mid $ product
Related Articles
- Among any four consecutive integers:
- There are at least two even numbers, and one of them is divisible by 4 → total factor of $ 2^3 = 8 $
- There is exactly one multiple of 4 and another even, so $ 8 \mid $ product
- There is no guaranteed factor of 5 or higher
- So the product is always divisible by $ 8 \cdot 3 = 24 $. But can we do better?
- Check more precisely:
Trending Articles
Growth factor = 1.05 per year.
Number of years = 5.
Population = \( 8000 \times (1.05)^5 \)
\( 1.05^5 \approx 1.27628 \)
\( 8000 \times 1.27628 \approx 10,210.24 \)
Rounded to nearest whole number: 10,210.
#### 10210
A right triangle has legs of lengths 9 cm and 12 cm. What is the length of the altitude to the hypotenuse?
First, find hypotenuse: \( \sqrt{9^2 + 12^2} = \sqrt{81 + 144} = \sqrt{225} = 15 \) cm.
Area using legs: \( \frac{1}{2} \times 9 \times 12 = 54 \) cm².