Michael C.

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Basic Chemistry

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Question:

A combustion reaction produces carbon dioxide and water as its products. What are the products of an acid-base reaction (assuming that all reactants are consumed)?

Michael C.

Answer:

Acid-base reactions yield a salt and water.

Calculus

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Question:

What is the relationship, as it pertains to calculus, of the position, velocity, and acceleration functions found in most physics courses?

Michael C.

Answer:

The if the position function is the parent function, then the velocity is the first derivative of that function, and the acceleration is the second derivative of the parent function. Alternatively, if the acceleration function is the parent function, then the velocity function is the first anti-derivative (or integral), and the position function is the second anti-derivative of the parent function.

Algebra

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Question:

If the water in a reservoir decreases every day by 4%, by how much will the water decrease over a 7-day week?

Michael C.

Answer:

Since the remaining amount of water each day is 96% (100% - 4%) of the day before, this can be written as an exponential decay function 0.96^d, where d is the number of days. Substituting 7 for d, we get 0.96^7 = 0.751. Since this is the remaining amount, we subtract it from the initial to find the amount missing. Since the full reservoir was represented by 1, the answer can be converted to a decimal to properly address the question. Thus, 1 - 0.751 = 0.249 or 24.9%.

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