Answer:
C
Step-by-step explanation:
Okay so what we are going to do here is look at our terms first and see what gets us there.
So lets consider the first term or the first sum, when k=1.
So if k=1 then the expression should give us a positive 5. So lets check each one for a +5.
So lets start with (5k-5) if we let k equal one this first term would be 0. So this doesnt work already.
The rest however do work so we need to keep checking.
Lets let k=2
We know that when k=2 we need the value of the term to equal -5.
So lets look at (-5k+10) if we let k be -5 then this second term would be 0 and 0 is not equal to -5 so this is now out.
Now lets look at (15k-10) if we let k=2 then this is (30-10) = 20 and 20 doesnt equal 5 so that not gonna work.
So our answer here must be (-10k+15). If we let k=2 then thats (-20+15) = -5
Now just to be 100% sure lets check some other terms. Lets check the last term which would be -755. This term would be the the 77th term so lets let k=77.
(-10(77) + 15) = -770 + 15 = -755. So that also works.
Hence our answer is the series/answer choice c.
Answer:
- increasing: (π/2, 3π/2)
- decreasing: [0, π/2) ∪ (3π/2, 2π]
- minimum: -16 at x=π/2
- maximum: 16 at x=3π/2
Step-by-step explanation:
If all you want are answers to the questions, a graphing calculator can provide them quickly and easily. (see attached)
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If you need an algebraic solution, you need to find the zeros of the derivative.
f'(x) = -16cos(x)sin(x) -16cos(x) = -16cos(x)(sin(x) +1)
The product is zero where the factors are zero, at x=π/2 and x=3π/2.
These are the turning points, where the function changes from decreasing to increasing and vice versa.
(sin(x)+1) is non-negative everywhere, so the sign of the derivative is the opposite of the sign of the cosine function. This tells us the function f(x) is increasing on the interval (π/2, 3π/2), and decreasing elsewhere (except where the derivative is zero).
The function local extrema will be where the derivative is zero, so at f(π/2) (minimum) and f(3π/2) (maximum). We already know that cos(x) is zero there, so the extremes match those of -16sin(x).
it’s not an exponential function because it is a quadratic function
an exponential function is y=2^x
Answer:
the awnser is 19,500
Step-by-step explanation:
you multiply 325 × 2=650 then you multiply 30×650=19,500