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Compute $(\frac{5}{3} + 2 i) + (13 + \frac{7 i}{9})$

Spencer Lutz 2022-05-19

Add $\frac{9}{4} + 2 i$ and $18 + \frac{i}{4}$ .

lnwlf1728112xo85f 2022-05-19

Calculate $(\frac{4}{7} + \frac{17 i}{4}) + (7 + 18 i)$ .

Alissa Hutchinson 2022-05-19

Calculate $(18 + \frac{9 i}{2}) + (\frac{9}{8} + 2 i)$ .

quorums15lep 2022-05-19

Compute $(\frac{3}{8} + 4 i) + (9 + \frac{7 i}{3})$ .

vaganzahi 2022-05-19

Calculate this limit
$lim_{x \to + \infty} \frac{x - \ln (x + 1)}{x \ln (x + 1)}$
I need help with this one .I couldn't figure out anything that could solve it .

Antoine Hill 2022-05-19

Are there other cases similar to Herglotz's integral $\int_{0}^{1} \frac{\ln (1 + t^{4 + \sqrt{15}})}{1 + t} d t$ ?
This post of Boris Bukh mentions amazing Gustav Herglotz's integral
$\int_{0}^{1} \frac{\ln (1 + t^{4 + \sqrt{15}})}{1 + t} d t = - \frac{π^{2}}{12} (\sqrt{15} - 2) + \ln 2 \cdot \ln (\sqrt{3} + \sqrt{5}) + \ln \frac{1 + \sqrt{5}}{2} \cdot \ln (2 + \sqrt{3}) .$
I wonder if there are other irrational real algebraic exponents α such that the integral
$\int_{0}^{1} \frac{\ln (1 + t^{α})}{1 + t} d t$
has a closed-form representation? Is there a general formula giving results for such cases?
Are there such algebraic $α$ of degree $> 2$ ?

Shamar Reese 2022-05-19

The matter of explicitly finding the order of a rational function on an elliptic curve in the projective plane at infinity (i.e. at the point (0,1,0)) still seems unclear.
For example, Silverman (in The Arithmetic of Elliptic Curves) states that the order of the rational function $y$ on the elliptic curve
$y^{2} = (x - e_{1}) (x - e_{2}) (x - e_{3}),$
where $e_{1}$ , $e_{2}$ , and $e_{3}$ are distinct, is −3. That is, the function $y$ has a pole of order 3 at (0,1,0). I have no doubt that this is true; I'd like to know a simple way to see it, based on projective coordinates and independent of the fact that the sum of the orders of the zeros of $y$ is 3 (which I understand).

write a third degree polynomial with integral coefficients if zeros are "-1," "-4," and 5

solve y=f(x) for x. then find the input(s) when the output is 9.

y= ${(x - 2)}^{2}$ -1

If $p = \lg 5$ , express the following in terms of $p$
Express $\log_{5} 2$ in terms of $p$ .
$\log_{5} 2$
$\frac{\log_{10} 2}{\log_{10} 5}$
$\frac{\log_{10} 2}{p}$
Then how to simplify it? My book's answer: $\frac{1}{p} - 1$

Aditya Erickson 2022-05-18

Logarithms melting my brain
So I've got an inequality: $\ln (2 x - 5) > \ln (7 - 2 x)$ and I attempt to solve by doing the following:
$\frac{\ln (2 x)}{\ln (5)} > \frac{\ln (7)}{\ln (2 x)}$
$\Rightarrow \ln (2 x) \cdot \ln (2 x) > \ln (7) \cdot \ln (5)$
$\Rightarrow \ln^{2} (2 x) < \ln (7) \cdot \ln (5)$
$\Rightarrow 2 x < \ln (7) \cdot \ln (5) \cdot e^{2}$
I thought I could multiply by $e^{2}$ to get rid of $\ln^{2}$ but I guess not...I thought they were inverses??? So anyways, my solution seems WAY off as the solution to the problem is: $3 < x < \frac{7}{2}$

madridomot 2022-05-18

How prove this $H_{2 n} - H_{n} + \frac{1}{4 n} > \ln 2$
Show that, for every positive integer $n$ ,
$\frac{1}{n + 1} + \frac{1}{n + 2} + \dots + \frac{1}{2 n} + \frac{1}{4 n} > \ln 2$
I know this
$lim_{n \to \infty} \frac{1}{n + 1} + \frac{1}{n + 2} + \dots + \frac{1}{2 n} = \ln 2$
and use this
$\ln (1 + \frac{1}{n}) < \frac{1}{n}$
is not useful
But for this inequality I can't. Thank you

Charles claimed the function f(x)=(3/2)^X represents exponential decay. Explain the error Charles made.

kromo8hdcd 2022-05-18

Calculate the value of n such that 18-14n=-8.

adocidasiaqxm 2022-05-18

Solve the equation -6x-18=-8x.

agrejas0hxpx 2022-05-18

Find the value of x such that 22x-8=-12.

poklanima5lqp3 2022-05-18

Find the value of x such that 14x-10=8-2x.

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Algebra II