Which is the same function as -2x

Find all possible values of each expression. Suppose 3

Tomtit [17]

The inequality that describes the possible values of the expression is:

$0 < \frac{b}{3a} - \frac{a}{3b} < \frac{9}{60}$

<h3>What is the lower bound of values of the expression?</h3>

The expression is given by:

$\frac{b}{3a} - \frac{a}{3b}$

To find the lower bound, we try to see when the expression is negative, hence:

$\frac{b}{3a} - \frac{a}{3b} < 0$

$\frac{b}{3a} < \frac{a}{3b}$

Applying cross multiplication and simplifying the 3's, we have that:

$b^2 < a^2$

From the bounds given, this expression will never be true, at most they can be equal, when:

a = b = 4.

Hence the lower bound of values of the expression is of 0.

<h3>What is the upper bound of values of the expression?</h3>

The expression is a subtraction, hence we want to maximize the first term and minimize the second.

Considering that the first term is direct proportional to b and inverse to a, and the second vice versa, we want to:

Maximize b, hence b = 5.

Minimize a, hence a = 4.

Then:

$\frac{b}{3a} - \frac{a}{3b} = \frac{5}{12} - \frac{4}{15} = \frac{25 - 16}{60} = \frac{9}{60}$

Hence the bounds are:

$0 < \frac{b}{3a} - \frac{a}{3b} < \frac{9}{60}$

More can be learned about values of expressions at brainly.com/question/625174

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4 0

2 years ago

Lucas spends $83.42 in additional interest and charges on monthly payments as the result of a prior bankruptcy. if lucas been ab

coldgirl [10]

The total amount Lusac have in his savings after 3 more years with 1.8% saving interest is $1055.10.

<h3>What is simple interest?</h3>

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

The formula for the simple interest can be given as,

$I=\dfrac{Prt}{100}$

Here, (I) is the interest amount earned on the principal amount of (P) with the rate of (r) in the time period of (t).

Lucas spends $83.42 in additional interest and charges on monthly payments as the result of a prior bankruptcy. The amount save in a year (12 months) is,

$P=83.42\times12\\P=1001.04$