More Algebra 2 problems.

*January 2018*
*17. The function below models the average price of gas in a small town computations.
since January 1st.
G(t) = -0.0049t ^{4} + 0.0923t^{3} - 0.56t^{2} + 1.166t + 3.23,
where 0 ≤ t ≤ 10.
*

*If G(t) is the average price of gas in dollars and t represents the number of months since January 1st, the absolute maximum G(t) reaches over the given domain is about
(1) $1.60
(2) $3.92
(3) $4.01
(4) $7.73
*

**Answer: (3) $4.01**

Graph the function and use "maximum" to find the highest value, which you should see is just above $4.00.

See the graph below:

At approximately t = 1.6, G(t) = 4.01, approximately.

*18. Written in simplest form, (c ^{2} - d^{2}) / (d^{2} + cd - 2c^{2}), where c =/= d, is equivalent to
*

(1) (c + d) / (d + 2c)

(2) (c - d) / (d + 2c)

(3) (-c - d) / (d + 2c)

(4) (-c + d) / (d + 2c)

**Answer: (3) (-c - d) / (d + 2c)**

The numerator, *(c ^{2} - d^{2})*, is the difference of two perfect squares, and factors into the conjugates,

*(c + d)(c - d)*.

Note that all four choices have

*(d + 2c)*as the denominator, which makes factoring

*(d*that much easier into

^{2}+ cd - 2c^{2})*(d + 2c)(d - c)*.

(c - d) / (d - c) = -1, which reduces the fraction to (-1)(c + d) / (d + 2c).

Distribute the -1, and you get choice (3).

Comments and questions welcome.

More Algebra 2 problems.

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