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Algebra

1. The mass of Earth is about 6 x 10^21 metric tons. The mass of the sun is about 1.998 x 10^27 metric tons. About how many times the mass of Earth is the mass of the sun? Express the answer in scientific notation.

2. The perimeter P of a square of side x is given by the polynomial equation: P=4x. A baseball diamond is a square 90 ft on a side. Find the perimeter of a baseball diamond.

3. Hadley Electronics is marketing a new kind of plasma TV. The firm determines that when it sells x TVs, its total revenue R (the total amount of money taken in) will be R = 280x - 0.4x^2 dollars. What is the total revenue from the sale of 75 TVs?

4. The polynomial equation C = 0.041h - 0.018A - 2.69 can be used to estimate the lung capacity C, in liters, of a female of height h, in centimeters, and age A, in years. Find the lung capacity of a 20-year-old woman who is 165 cm tall.

5. A researcher wants to investigate the potential spread of germs by contact. She knows that the number of possible handshakes within a group of x people, assuming each person shakes every other person's hand only once, is given by the following formula.

Use this formula for the following exercises. N = (1/2)(x^2 - x).

a. There are 100 people at a party. How many handshakes are possible?

b. Everyone at a meeting shook hands with each other. There were 300 handshakes in all. How many people were at the meeting?

Solution Preview

Please refer to the attachment for the solutions.

1. Earth vs. Sun. The mass of Earth is about 6 x 1021 metric tons. The mass of the sun is about 1.998 x 1027 metric tons. About how many times the mass of Earth is the mass of the sun? Express the answer in scientific notation.

Solution:

Mass of Sun/ Mass of Earth = 1.998 x 1027 metric tons/6 x 1021 metric tons = 333000
= 3.33 x 105.
So, the mass of the Sun is about 3.33 x 105 times the mass of the Earth.

2. Perimeter of a Baseball Diamond. The ...

Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given algebra problems and provides a clear perspective of the underlying concepts.

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