Answer:
a) 1/2; reduction
b) 5/4; enlargement
Step-by-step explanation:
In each case, the scale factor is CP'/CP. When it is more than 1, the dilation is an enlargement.
Even before you run the numbers, you can tell if it is an enlargement or not. If the dilated figure is larger, P is closer to C than is P'. If P' is closer to C, then it is a reduction.
a) CP'/CP = (4-2)/4 = 2/4 = 1/2 . . . . a reduction
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b) CP'/CP = 25/20 = 5/4 . . . . an enlargement
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.
Answer:
-1/8
Step-by-step explanation:
(-1/2) ^3
(-1/2)(-1/2)(-1/2)
-1/8
Answer:
Step-by-step explanation:
and 
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