High school math questions and answers

Recent questions in Secondary
Databasex3 2022-08-12

I am trying to compute this integral ${\int }_{0}^{\mathrm{\infty }}\frac{x}{1+{x}^{6}}dx$ using the residue theorem. To do so, I am integrating $f\left(z\right)=\frac{z}{1+{z}^{6}}$ in the frontier of this sector of a circle: $\left\{z:|z|.I kwo how to deal with the integrals over the horizontal segment of the sector and over the arc of the circle. My problem is the "diagonal segment". When I parametrize it, I do not get something easy to integrate. How could I approach this?(The path of integration was suggested in my book, so I do not think that is the problem).

garkochenvz 2022-08-12

You can feel almost nothing by touching the battery pole of your flashlight with your fingers. When an electric call is connected to the battery, electric punctures are felt with the fingers. Why?

Flambergru 2022-08-12

MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document Find the sum of a probability of dice roll that is prime.Consider rolling n fair dice. Let p(n) be the probability that the product of the faces is prime when you roll n dice. For example, when = $\frac{1}{2}$When When $\frac{1}{24}$. Find the infinite sum of p(n) (when n starts at 0) (Hint: Consider differentiating both sides of the infinite geometric series: infinite sum of when )I can differentiate the two sides of the geometric series but I'm lost regarding what to do after that. I don't fully understand the question.

garkochenvz 2022-08-12

What is the distance between (8,0,6) and (1,-4,5)?

targetepd 2022-08-12

Finding unknown in log equationI was given a log equation:$D=10\mathrm{log}\left(I/{I}_{0}\right)$$I$ is the unknown in this case, ${I}_{0}={10}^{-12}$ and $D=89.3$I did the following steps:I'm not quite sure how to isolate I after step 3, and I'm also unsure if dividing $89.3/10$ is correct as well. So how can I find the unknown ($I$)?

rivasguss9 2022-08-12

Illustrate with examples, what is "mutual exclusive event" and what is "independent event".

Mark Elliott 2022-08-12

What is the range of 2,1,7,3,5,2,9,7,10,4,2,10?

Katelyn Reyes 2022-08-12

Express the given decimal as a percentage and a reduced fraction. 0.75What is the percentage form of 0.75?

garkochenvz 2022-08-12

We know that a soft iron bar placed inside a solenoid turns into an electromagnet when current passes through the solenoid. Now my question is how is electricity produced? Is the iron core moved by the turbine inside a solenoid?

Taliyah Reyes 2022-08-12

I will be so grateful if someone can explain me in a simple language what is difference between vector magnitude namely$r=|{\stackrel{\to }{r}}_{1}-{\stackrel{\to }{r}}_{2}|$and distance vector namely${\stackrel{\to }{r}}_{12}={\stackrel{\to }{r}}_{1}-{\stackrel{\to }{r}}_{2}$

Passafaromx 2022-08-12

Finding the volume of a solid of revolution about the x-axisLet R be the area laying beneath the curve $f\left(x\right)=8-{x}^{2}$ and above the line $y=7$. Find the volume of the solid of revolution which is created when R is revolved around the x-axis.I graphed the functions and found out I have to integrate from -1 to 1. I want to use the disc method, but I don't know how to only get the discs with radii higher than $y=7$ and lower than f(x). I thought it would be logical if the radii of the discs would be $8-{x}^{2}-7=1-{x}^{2}$, but this approach gives me the wrong answer when i plug it into the formula.

Garrett Sheppard 2022-08-12

For what t will the following vector be an orthogonal basis?$\begin{array}{rl}{u}_{1}& =\left(1,t,t\right)\\ {u}_{2}& =\left(2t,t+1,2t-1\right)\\ {u}_{3}& =\left(2-2t,t-1,1\right)\end{array}$Till now I have tried using the Gram-Schmidt process but did not really reach anywhere. Can you please provide a hint or some theory that may help me get the solution for this question?

Max Macias 2022-08-12

Polynomial $P\in \mathbb{R}\left[x\right]$ with $\overline{P\left(\overline{x}\right)}=P\left(x\right),\mathrm{\forall }x\in \mathbb{C}$

betterthennewzv 2022-08-12

Suppose you have two alnico bar magnets, one with a mass of 100 g and one with a mass of a kg. At a distance of a meter from the center of either one, how would the magnetic field differ? Why?

Matonya 2022-08-12

Volume between under parabaloidSuppose I want to find the volume between $z=2{x}^{2}+3{y}^{2}$ and $z=4$. Is there a way finding that with a double integral? I tried to use $4-2{x}^{2}-3{y}^{2}$ inside the integral and then convert it to polar coordinates...

pominjaneh6 2022-08-12

set $S$ of coordinates $\left(x,y\right)$, and am estimating $f\left(x\right)=ax+b$ where $a>0$. I also happen to know that $\mathrm{\forall }x,y\left(\left(x,y\right)\in S\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}y.The question is how I can utilize this knowledge of the upper bound on values to improve the regression result?My intuition is to run a "normal" linear regression on all coordinates in $S$ giving $g\left(x\right)$ and then construct ${g}^{\prime }\left(x\right)=g\left(x\right)+c$, with $c$ being the lowest number such that $\mathrm{\forall }x,y\left(\left(x,y\right)\in S\phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}y\le {g}^{\prime }\left(x\right)\right)$, e.g. such that ${g}^{\prime }\left(x\right)$ lies as high as it can whilst still touching at least point in $S$. I do, however, have absolutely no idea if this is the best way to do it, nor how to devise an algorithm that does this efficiently.

schnelltcr 2022-08-12