Recent questions in Algebra

Equations
Answered

odenut6b
2022-09-27

Logarithms
Answered

Conrad Beltran
2022-09-27

Using the method shown here, I have found the following closed form.

${\int}_{0}^{\phantom{\rule{negativethinmathspace}{0ex}}\frac{\pi}{2}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}{(\frac{1}{\mathrm{log}(\mathrm{tan}x)}+\frac{1}{1-\mathrm{tan}x})}^{2}\phantom{\rule{negativethinmathspace}{0ex}}\mathrm{d}x=3\mathrm{ln}2-\frac{4}{\pi}G-\frac{1}{2},$

where $G$ is Catalan's constant.

I can see that replicating the techniques for the following integral could be rather lenghty.

${\int}_{0}^{\phantom{\rule{negativethinmathspace}{0ex}}\frac{\pi}{2}}\phantom{\rule{negativethinmathspace}{0ex}}\phantom{\rule{negativethinmathspace}{0ex}}{(\frac{1}{\mathrm{log}(\mathrm{tan}x)}+\frac{1}{1-\mathrm{tan}x})}^{3}\phantom{\rule{negativethinmathspace}{0ex}}\mathrm{d}x$

My question: Could someone have, ideally, a different idea to evaluate the latter integral?

Logarithms
Answered

Chelsea Lamb
2022-09-27

For estimates, the inequality $\mathrm{log}(y)\le y-1,$$y>0$ is often helpful. Is there any sort of upper bound for the logarithm function in the complex plane? Specifically, $|\mathrm{log}(z)|\le $ something for all $z\in \mathbb{C}$

Perhaps this would work?: $\mathrm{log}(z)\le \sqrt{{\mathrm{log}}^{2}|z|+\mathrm{arg}(z{)}^{2}}$

Measurement
Answered

traffig75
2022-09-27

Exponential growth and decay
Answered

Lustyku8
2022-09-26

sys = tf([1 0],[1 -0.5])

figure(1);

step(sys);

figure(2);

impulse(sys);

However, both graphs look the same (can't post images of my graphs, I need more rep to do it).

Both graphs have exponential growth, but shouldn't the impulse response look like exponential decay?

Logarithms
Answered

Haiphongum
2022-09-26

I'm studying logarithms and I encountered this equation:

$[{\mathrm{log}}_{9}(k+1){]}^{2}+{\mathrm{log}}_{9}(k+1)+(k+1)>3$

I tried a lot but I still couldn't solve it! I know this may be easy for most of you but please could you help me?

Thanks!

Systems of equations
Answered

Stacy Barr
2022-09-26

Let the length be 𝑥 m and the breadth be 𝑦 m

As we know, Perimeter =2(𝑥+𝑦)=48 $\Rightarrow x+y=24$ 𝑥+𝑦=24 [⋯(1)]

Area=135 m${}^{2}$.

As we know, Area=𝑙𝑏

Therefore, 135 m${}^{2}$ =𝑥𝑦 [⋯(2)]

Sequences
Answered

fion74185296322
2022-09-26

Polynomial division
Answered

zaiskaladu
2022-09-26

Fractions
Answered

kennadiceKesezt
2022-09-26

Let $f(x,y)=xy+\frac{50}{x}+\frac{20}{y}$, Find the global minimum / maximum of the function for $x>0,y>0$

Clearly the function has no global maximum since $f$ is not bounded. I have found that the point $(5,2)$ is a local minimum of $f$. It seems pretty obvious that this point is a global minimum, but I'm struggling with a formal proof.

Equations and inequalities
Answered

Megan Herman
2022-09-26

$\frac{1}{3}$

$3x-6$

1) 3

2) 6

3) 9

4) 12

Forms of linear equations
Answered

koraby2bc
2022-09-26

Fractions
Answered

Joyce Sharp
2022-09-26

Using all numbers 0 to 9 only once, form two fractions whose sum is 1.

I have tried every possible combination but with no luck. I believe the fractions must be xx/xx + xxx/xxx but I am not sure. Any ideas are most welcome. I even tried getting all different ways to select 3 out of 10 digits, then omitting all the primes and trying to make fractions with simple values 1/3, 1/4, 2/5 etc using only different digits but again with no luck! By the way, two years ago I was given a similar one, with three fractions and without the digit 0, for which I found a solution 7/68+9/12+5/34 but now I am stuck!!

Sequences
Answered

wijii4
2022-09-26

Sequences
Answered

Corbin Bradford
2022-09-26

Forms of linear equations
Answered

trkalo84
2022-09-26

Rational functions
Answered

Camila Brandt
2022-09-26

Forms of linear equations
Answered

Addyson Bright
2022-09-26

Even as we are dealing with college subjects like Sociology or Data Science, the use of high school Algebra is inevitable. Some of us may still remember the rules, yet it is only natural have something as a reminder.

Regardless if you have some questions regarding equations or need some urgent help, we already have a list of the most popular answers that will serve as the starting points for your task. Take your time to explore the list of questions and answers to see the scope of high school algebra tasks.