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lakkis [162]
3 years ago
7

What number divided by 8 equals 9

Mathematics
2 answers:
disa [49]3 years ago
8 0
9 x 8 = 72
72 ÷ 8 = 9
I hope I helped :)
lora16 [44]3 years ago
7 0

9 x 8= 72, so the answer would be:


72

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icang [17]

Answer: B

Step-by-step explanation:

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2 years ago
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interv
sleet_krkn [62]

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

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|x−8| < 8

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0 < x < 16

Now we check the endpoints.  If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

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3 years ago
If Josie runs a 25-mile race in 5 hours and Greta runs a 18-mile race in 4 hours. Who runs at a FASTER pace?
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Answer:

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Step-by-step explanation:

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Answer:

3 \sqrt{3}

Step-by-step explanation:

See the attachment for better understanding..

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