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julsineya [31]
2 years ago
11

Kenneth has entered a check payment of $350.25 in his checkbook. If the old balance was $545.95, what is his latest balance?

Mathematics
2 answers:
Dennis_Churaev [7]2 years ago
8 0

Answer:

The latest balance is $896.2

Step-by-step explanation:

It is important to know that balance refers to the amount of money that is available in a bank account.

The problem says that the old balance of Kenneth was $545.95, that is the money available before entering the check payment. When Kenneth entered the check payment of $350.25 the available money increased. So, the current balance would be the sum of the two values.

balance_{latest}=\$545.95+\$350.25=\$896.2

Thus, the latest balance is $896.2

Rama09 [41]2 years ago
5 0
Just add the new paycheck to the old balance:
350.25 + 545.95 = $896.2
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Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to
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Answer:

Part 1)

See Below.

Part 2)

\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)

Step-by-step explanation:

Part 1)

The linear approximation <em>L</em> for a function <em>f</em> at the point <em>x</em> = <em>a</em> is given by:

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Then the slope of the linear approximation at <em>x</em> = 0 will be:

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Part B)

We want to determine the values of <em>x</em> for which the linear approximation <em>L</em> is accurate to within 0.1.

In other words:

\displaystyle \left| f(x) - L(x) \right | \leq 0.1

By definition:

\displaystyle -0.1\leq f(x) - L(x) \leq 0.1

Therefore:

\displaystyle -0.1 \leq \left(\frac{1}{(1+9x)^4} \right) - (1-36x) \leq 0.1

We can solve this by using a graphing calculator. Please refer to the graph shown below.

We can see that the inequality is true (i.e. the graph is between <em>y</em> = 0.1 and <em>y</em> = -0.1) for <em>x</em> values between -0.179 and -0.178 as well as -0.010 and 0.012.

In interval notation:

\displaystyle (-0.179, -0.178) \cup (-0.010, 0.012)

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