Answer: he will be able to play 32.6 games at the arcade
Step-by-step explanation:
He made an error is step 2
3x + 18 = 2x +8
subtract 2x from each side
x + 18 = 8
Answer:
Part 1)
See Below.
Part 2)

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:

We want to verify that the expression:

Is the linear approximation for the function:

At <em>x</em> = 0.
So, find f'(x). We can use the chain rule:

Simplify. Hence:

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

And the value of the function at <em>x</em> = 0 is:

Thus, the linear approximation will be:

Hence verified.
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:

By definition:

Therefore:

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:

Answer:
A
Step-by-step explanation:
15*18=270.
270-46.50=223.5
223.5-129.95=93.55.
A. $93.55
Answer:
42
Step-by-step explanation:
The permutation formula is P(n, r) = n! / (n - r)!. We know that n = 7 and r = 2 so we can write:
7! / (7 - 2)!
= 7! / 5!
= 7 * 6 * 5 * 4 * 3 * 2 * 1 / 5 * 4 * 3 * 2 * 1
= 7 * 6 (5 * 4 * 3 * 2 * 1 cancels out)
= 42