mishaps

Solution: Write the ratio $15:20$ and simplify by dividing by 5:

Question: A mammalogist tracks two species of Arctic birds with 9 males and 15 females. What is the ratio of males to females in simplest terms?

Solution: Express the ratio as $9:15$ and simplify by dividing by 3:

Solution: The particle comes to rest when its velocity is zero, i.e., when $ h(t) = 0 $.

So the particle is at rest at $ t = 1 $ and $ t = 3 $. The final answer is:

Question: A sequence of five real numbers forms an arithmetic progression, and the sum of the first and fifth terms is 20. If the third term is 6, find the common difference.

Solution: Let the sequence be $ a - 2d, a - d, a, a + d, a + 2d $, where $ a $ is the third term and $ d $ is the common difference.

But were also told the third term is 6, so:

This contradicts $ a = 10 $, unless we re-express the sequence differently. Let the sequence be $ a, a + d, a + 2d, a + 3d, a + 4d $.

And the third term is $ a + 2d = 6 $.

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