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dangina [55]
2 years ago
11

Find the value of x 2x-1 /3x-7​

Mathematics
1 answer:
fiasKO [112]2 years ago
6 0

Answer:

x=-6

Step-by-step explanation:

2x-1=3x-7

2x-3x=-7+1

x=-6

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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
PLEASE HELP TIMED TEST!!!! I WILL REPORT YOU IF YOU GIVE ME A LINK!!
Elenna [48]

Answer:

x=40

Step-by-step explanation:

you have to get a answer of 60

(40)+20=60

and 2(40)-20=60

5 0
2 years ago
Please help I need help with this question
denpristay [2]

Answer:

2.5% and 2.5 · 10^-3, 0.25, 2/5, √5

Step-by-step explanation:

0.25, 2/5, 2.5 · 10^-3, 2.5%, √5

Now let's list them all in the same form, why not decimals.

0.25 = 0.25

2/5 = 4/10 = 40/100 = 0.4

2.5 · 10^-3 = 2.5 · 0.01 = 0.025

2.5% = 0.025

√5 ≅ 2.236

5 0
2 years ago
How would i etimate the first digit of the quotient
Sergio039 [100]
first you have to look to the right of that number .check if it is more than 5. if it is ,than add one to the first digit in the quotient. all the other numbers will turn to zeroes.
6 0
3 years ago
Need ko na po this now<br><br>please answer this question<br><br>thank you po​
Umnica [9.8K]

Answer:

B.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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