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Marianna [84]
3 years ago
7

Convert 0.9 into a fraction using 100 for denominator

Mathematics
2 answers:
Arisa [49]3 years ago
7 0
<em>Remove the decimal sign and divide by 100 to get the answer</em>

<em>In this case: 0.9 = 90 / 100</em>
Nuetrik [128]3 years ago
6 0
0.9 =  \frac{90}{100} =  \boxed{ \frac{9}{10} \ Answer}
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Let f be defined by the function f(x) = 1/(x^2+9)
riadik2000 [5.3K]

(a)

\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}

Substitute <em>x</em> = 3 tan(<em>t</em> ) and d<em>x</em> = 3 sec²(<em>t </em>) d<em>t</em> :

\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt

=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}

(b) The series

\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}

converges by comparison to the convergent <em>p</em>-series,

\displaystyle\sum_{n=3}^\infty\frac1{n^2}

(c) The series

\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}

converges absolutely, since

\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}

That is, ∑ (-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ converges absolutely because ∑ |(-1)ⁿ (<em>n</em> ² + 9)/<em>e</em>ⁿ| = ∑ (<em>n</em> ² + 9)/<em>e</em>ⁿ in turn converges by comparison to a geometric series.

5 0
3 years ago
Can someone help me with question 3 i really dont understand this.
makvit [3.9K]

Answer:28 hours

Step-by-step explanation:

2x7x2

5 0
3 years ago
Read 2 more answers
There are two twins. One twin wants to explore the planet near Proxima Centauri and leaves on a spaceship traveling at 90% of th
miskamm [114]

Answer:

<em>4.7 years</em>

Step-by-step explanation:

Distance of planet from Earth = 1.3 parsec

We know that 1 parsec = 3.26 light years

And a light year is the distance traveled by light in time period of 1 year.

So, Distance of planet from Earth = 1.3 \times 3.26 = 4.24 light years

Given that, the person travels at a speed equal to 90% of the light speed.

To travel to the planet from Earth, Light takes 4.24 years.

To travel the distance D, at a speed s light takes time of 4.24 years.

To travel the distance D, at a speed 0.90s, the person takes time:

\dfrac{4.24}{0.90} = \bold{4.7\ years}

So, the twin on Earth ages by <em>4.7 years.</em>

7 0
3 years ago
50b 50=11b 95 what is b?
ohaa [14]
<span>50b 50=11b 95 collect the like terms 
50b-11b=95-50
39b=45 divide both sides by 39
b=1.2</span>
7 0
3 years ago
Please help!! it’s overdue
Gnesinka [82]

9 I think, soo sorry if i'm wrong...

6 0
2 years ago
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