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masha68 [24]
2 years ago
12

Examine the following table of points, which are all on a certain line.

Mathematics
1 answer:
Lapatulllka [165]2 years ago
4 0

\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} {-2}~~\ast&{4}~~\ast\\ 0&2\\ 1&1\\ {3}~~\ast&{-1}~~\ast\\ \cline{1-2} \end{array}~\hspace{10em} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-4}{3-(-2)}\implies \cfrac{-5}{3+2}\implies \cfrac{-5}{5}\implies -1

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How do you do this question?
IRINA_888 [86]

Answer:

∑ (-1)ⁿ⁺³ 1 / (n^½)

∑ (-1)³ⁿ 1 / (8 + n)

Step-by-step explanation:

If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.

Option A: (-1)²ⁿ is always +1.  So an =│an│and both series converge (absolutely convergent).

Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).

Option C: an = 1 / n³ isn't an alternating series.  So an =│an│and both series converge (p series with p > 1).  This is absolutely convergent.

Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series.  Since lim(n→∞) bn = 0, and bn is decreasing, then an converges.  So this is conditionally convergent.

Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series.  bn = 1 / (8 + n), which diverges.  Since lim(n→∞) bn = 0, and bn is decreasing, then an converges.  So this is conditionally convergent.

5 0
3 years ago
What is a rational number
dsp73
Anything except pi is a rational number. So 9 and 7/10 is one or it could be a whole number
7 0
3 years ago
Mark is planning to swim the 200-yard freestyle event at the next
bazaltina [42]
Mark will swim 182.88 meters
7 0
1 year ago
The length of a rectangle is five times its width.
Vera_Pavlovna [14]

Answer:

72

Step-by-step explanation:

l = 5w

A = l*w

180 = 5w *w

180 = 5w^2

Divide each side by 5

180/5 = 5w^2 /5

36 = w^2

Taking the square root of each side

sqrt(36) = sqrt(w)^2

6 =w

l = 5w = 5*6 = 30

The perimeter is

P = 2(l+w)

P = 2(6+30) = 2(36) = 72

4 0
3 years ago
B=ym+y for m   m=   help me solve thank u
Sveta_85 [38]
B = ym + y

B - y = ym

(B - y) / y = m
or
B/y - 1 = m


7 0
3 years ago
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