4. How many ways can you shuffle 7 songs in a playlist?
2 answers:
Answer:
5040
Step-by-step explanation:
There are 7 options for the 1st song, 6 options for the 2nd song, 5 options for the 3rd song, 4 options for the 4th song, 3 options for the 5th song, 2 options for the 6th song, and 1 option for the 7th song. We get:
(<em>Note: when you have a number n, where it is multiplied by every number until one (ex. 7. 7*6*5*4*3*2*1), then the number in the result is n! (n factorial). So we get that 7*6*5*4*3*2*1 is 7! is 7 factorial. So 5040 is 7! </em>)
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9514 1404 393
Answer:
maximum difference is 38 at x = -3
Step-by-step explanation:
This is nicely solved by a graphing calculator, which can plot the difference between the functions. The attached shows the maximum difference on the given interval is 38 at x = -3.
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Ordinarily, the distance between curves is measured vertically. Here that means you're interested in finding the stationary points of the difference between the functions, along with that difference at the ends of the interval. The maximum difference magnitude is what you're interested in.
h(x) = g(x) -f(x) = (2x³ +5x² -15x) -(x³ +3x² -2) = x³ +2x² -15x +2
Then the derivative is ...
h'(x) = 3x² +4x -15 = (x +3)(3x -5)
This has zeros (stationary points) at x = -3 and x = 5/3. The values of h(x) of concern are those at x=-5, -3, 5/3, 3. These are shown in the attached table.
The maximum difference between f(x) and g(x) is 38 at x = -3.
