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alekssr [168]
2 years ago
13

Write the number 63 in four different ways

Mathematics
2 answers:
barxatty [35]2 years ago
7 0
60+3+ sixty-three 63 and 6.3
RoseWind [281]2 years ago
4 0
60+3
sixty three
(10+6)+3
I can't think of another but I hope I helped you with 3
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Test for convergence
Elan Coil [88]
You've established that

\displaystyle\sum_{n\ge1}\frac1{2^n}\le\int_1^\infty\frac{\mathrm dx}{2^x}

so all you need to do is compute the integral. Rewrite the integrand as

\dfrac1{2^x}=2^{-x}=e^{\ln2^{-x}}=e^{-x\ln2}

and replace y=-x\ln2, so that \mathrm dy=-\ln2\,\mathrm dx. Then

\displaystyle\int_{x=1}^{x\to\infty}\frac{\mathrm dx}{2^x}=\int_{y=-\ln2}^{y\to-\infty}e^y\,\frac{\mathrm dy}{-\ln 2}=\frac1{\ln2}\int_{-\infty}^{-\ln2}e^y\,\mathrm dy

By the fundamental theorem of calculus, this evaluates to

\dfrac1{\ln2}e^y\bigg|_{y\to-\infty}^{y=-\ln2}=\dfrac1{\ln2}\left(e^{-\ln2}-\lim_{y\to-\infty}e^y\right)=\dfrac{e^{-\ln2}}{\ln2}=\dfrac{\frac12}{\ln2}=-\dfrac1{2\ln2}=\dfrac1{\ln4}

and so the series converges.

You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.
4 0
3 years ago
Is - 5¼ or greater than -5⅓
Dmitry [639]

Answer:

-51/4 is greater

Step-by-step explanation:

3 0
3 years ago
15,000 blue trout were released into the Meherrin River for a scientific study. The function, f(x) = 15,000 (9/8)^x represents t
Ainat [17]
I'm guessing you mean f(x)=15,000(9/8)^x. If this is what you mean, the population would increase by about 12,000 (12030.4870605 to be exact).
Step-by-step explanation:
Starting equation: f(x)=15,000(9/8)^x
You can clean up the 9/8 to be 1.125
Now what you want to do is find the answer to (9/8)^5 which is 1.8020324707
Next multiply 1.8020324707 by 15,000 and you get 27030.4870605
Finally 27,030.4870605 - 15,000 gives you 12030.4870605. Which means that the population increased by about 12,000.

Please mark me brainiest cuz I need one more to level up!! Thank you
5 0
3 years ago
Factor n(2n+3)+4(2n-3)
zavuch27 [327]
The answer would be 2n^2+3n+ 8n-1
3 0
2 years ago
There are 48 different animals pictured in Jorge's book. If 1/3 of them are herbivores how many herbivores?
Stolb23 [73]
16. 48 divided by 3 is 16
8 0
2 years ago
Read 2 more answers
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