As you progress in math, it will become increasingly important that you know how to express exponentiation properly.
y = 2x3 – x2 – 4x + 5 should be written <span>y = 2^x3 – x^2 – 4^x + 5. The
" ^ " symbol denotes exponentiation.
I see you're apparently in middle school. Is that so? If so, are you taking calculus already? If so, nice!
Case 1: You do not yet know calculus and have not differentiated or found critical values. Sketch the function </span>y = 2x^3 – x^2 – 4^x + 5, including the y-intercept at (0,5). Can you identify the intervals on which the graph appears to be increasing and those on which it appears to be decreasing?
Case 2: You do know differentiation, critical values and the first derivative test. Differentiate y = 2x^3 – x^2 – 4^x + 5 and set the derivative = to 0:
dy/dx = 6x^2 - 2x - 4 = 0. Reduce this by dividing all terms by 2:
dy/dx = 3x^2 - x - 2 = 0 I used synthetic div. to determine that one root is x = 2/3. Try it yourself. This leaves the coefficients of the other factor, (3x+3); this other factor is x = 3/(-3) = -1. Again, you should check this.
Now we have 2 roots: -1 and 2/3
Draw a number line. Locate the origin (0,0). Plot the points (-1, 0) and (2/3, 0). This subdivides the number line into 3 subintervals:
(-infinity, -1), (-1, 2/3) and (2/3, infinity).
Choose a test number from each interval and subst. it for x in the derivative formula above. If the derivative comes out +, the function is increasing on that interval; if -, the function is decreasing.
Ask all the questions you want, if this explanation is not sufficiently clear.
The first place and 15th place are already decided, so we have to find the number of
different ways that the <em>other</em> 13 students can line up, in the places from #2 to #14.
2nd place can be any one of 13 people. For each of those . . .
3rd place can be any one of 12 people. For each of those . . .
4th place can be any one of 11 people. For each of those . . .
.
.
.
13th place can be any one of 2 people. For each of those . . .
14th place has to be the one student who is left.
Total number of ways that 13 students can line up in places #2 through #14 is
(13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
That number is called "thirteen factorial". The number is <u>6,227,020,800</u> .
When you write it in math, you write it like this: 13!
<span>22.35200 m / s so the answer is going to be a or c
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I'd say angle A = angle B
arc tangent (angle B) = 150 / 555
<span><span><span>arc tangent (angle B) = 0.2702702703
</span>
angle B = 15.124 degrees
By the way 555 feet is the height of the Washington Monument.
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