# High school math questions and answers

Recent questions in Secondary
Camille Flynn 2022-05-24 Answered

### How do you tell whether the given value $r=8$ is a solution to $r-3\le 9$ ?

prensistath 2022-05-24 Answered

### How do you grap $-y\le 3x-5$ ?

Nylah Burnett 2022-05-24 Answered

### Suppose ${Y}_{1},{Y}_{2},\dots$ is any sequence of iid real valued random variables with $E\left({Y}_{1}\right)=\mathrm{\infty }$ . Show that, almost surely, $\underset{n}{lim sup}\left(|{Y}_{n}|/n\right)=\mathrm{\infty }$ and $\underset{n}{lim sup}\left(|{Y}_{1}+...+{Y}_{n}|/n\right)=\mathrm{\infty }$.I have solved the first part by considering non-negative integer iid r.vs ${X}_{n}=\text{floor}\left(|{Y}_{n}|\right)$ and using $E\left(X\right)=\sum _{0}^{\mathrm{\infty }}P\left(X\ge n\right)$ then doing some clever tricks so I can apply the (2nd) Borel-Cantelli lemma, but I'm not really sure how I can use the same approach to solve the second part seeing as it is tempting to set ${S}_{n}=\text{floor}\left(|{Y}_{1}+...+{Y}_{n}|\right)$ but then the ${S}_{i}$ are not iid. I'm pretty sure its gonna be Borel-Cantelli again (since limsup) so I need to come up with the right events. Please can someone nudge me in the right direction.Hints only pleaseEDIT: Suppose $\underset{n}{lim sup}|{a}_{1}+...+{a}_{n}|/n<\mathrm{\infty }$. Then set ${S}_{n}=\sum _{1}^{n}{a}_{k}$$\frac{|{a}_{n}|}{n}=\frac{|{S}_{n}-{S}_{n-1}|}{n}\phantom{\rule{0ex}{0ex}}\le \frac{|{S}_{n}|}{n}+\frac{|{S}_{n-1}|}{n-1}$bounded

Jazmine Bruce 2022-05-24 Answered

### How to simplify a diabolical expression involving radicalsA friend and I have been working on this problem for hours - how can the following expression be simplified analytically?It equals $\frac{1}{2},$, and we have tried the following to no avail:1. Substitution of $x=\sqrt{5}$2. Substitution of $x=2\sqrt{5}$3. Substitution of $x=5+\sqrt{5}$4. Substitution of $x=\sqrt{5+\sqrt{5}}$5. Manipulations by substituting the golden ratioHere goes:$\frac{\frac{\sqrt{5+2\sqrt{5}}}{2}+\frac{\sqrt{5\left(5+2\sqrt{5}\right)}}{4}-\frac{\sqrt{10+2\sqrt{5}}}{8}}{\frac{\sqrt{5\left(5+2\sqrt{5}\right)}}{4}+5\cdot \frac{\sqrt{5+2\sqrt{5}}}{4}}$Thanks in advance for any help.

istupilo8k 2022-05-24 Answered

### The standard form of a linear firs-order DE is$\frac{dy}{dx}+P\left(x\right)y=Q\left(x\right)$I think the equation is separable if and only if $P\left(x\right)$ and $Q\left(x\right)$ are constants, but I'm not sure. (Haven't found any counterexamples but also can't seem to prove it.) Can anyone confirm or deny that this is correct?

Thomas Hubbard 2022-05-24 Answered

### Vance wants to have pictures framed. Each frame and mat costs $32 and he has at most$150 to spend. How do you write and solve an inequality to determine the number of pictures he can have framed?

Jaidyn Bush 2022-05-24 Answered

### Extract from a proof in a measure theory script:For each set $A\subset {\mathbb{R}}^{n}$ and each $r>0$, we set.${A}_{r}:=\left\{x\in A:B\left(x,r\right)\subseteq A\right\}$Let $\mathrm{\Sigma }$ be an algebra in ${\mathbb{R}}^{n}$ containing all open subsets of ${\mathbb{R}}^{n}$, then for any set $A\in \mathrm{\Sigma }$ and any $r>0$, we have ${A}_{r}\in \mathrm{\Sigma }$.

Eliaszowyr1 2022-05-24 Answered

### Q is a rational function with . If $Q\left(1\right)=1$. what is Q(2017)?I tried substituting values in for Q(x) but there is no way to have both Q(1) and Q(2017) in the same equation, perhaps im missing a property of a rational function since i haven't used it yet.

Waylon Ruiz 2022-05-24 Answered

### I met an excercise in the book by Rabi Bhattacharya and Edward C. Waymire. Suppose that $\mu ,\nu$ are probbaility measures on ${\mathbb{R}}^{d}$, with $\nu$ absolutely continuous with pdf $f$, i.e., $d\nu =f\left(x\right)dx$. How to show that the convolution, $\mu \ast \nu$, is also absolutely continuous? Thanks!

Carlie Fernandez 2022-05-24 Answered

### There are 10 bicyclists entered in a race. In how many different orders could these 10 bicyclist finish?

Antoine Hill 2022-05-24 Answered

### If I have two algebraic numbers $\alpha$ and $\beta$ and a rational function $w$ with rational coefficients (a function that's the ratio of two rational polynomials) that relates the two $\alpha =w\left(\beta \right)$ if I were to substitute $\beta$ with one of it's algebraic cojugates ${\beta }^{{}^{\prime }}$ in the rational function will I get a conjugate of $\alpha$ or rather is $w\left({\beta }^{{}^{\prime }}\right)$ an algebraic conjugate of alpha? I feel like there is a very obvious counter example but I've been struggling to find one.

Brooke Kramer 2022-05-24 Answered

### In book i read now, the author defines a field just like this:A field is a non-empty class of subsets of $\mathrm{\Omega }$ closed under finite union,finite intersection and complements.In the following, he says like this:A minimal set of postulates for to be a field is (i)$\mathrm{\Omega }\in A.$(ii)$T\in A$ implies $\overline{T}\in A.$(iii)$S,T\in A$ implies $S\cup T\in A$Though I know why it exactly defines a field, the author says nothing about why they are minimal. He even uses the word minimal without an exact definition. Can anyone help me with this problem?

Ryker Stein 2022-05-24 Answered

### How do you find the average value of $f\left(x\right)=\mathrm{cos}x$ as x varies between [1,5]?

Pitrellais 2022-05-24 Answered

### How to find an irrational number in $\mathbb{Q}\cap \left[0,1\right]$?

Despiniosnt 2022-05-24 Answered

### $EXP=\left\{\begin{array}{ll}{n}^{3}\left(\frac{⌊\frac{n+1}{3}⌋+24}{50}\right)& n\le 15\\ {n}^{3}\left(\frac{n+14}{50}\right)& 15\le n\le 36\\ {n}^{3}\left(\frac{⌊\frac{n}{2}⌋+32}{50}\right)& 36\le n\le 100\end{array}$In this equation there are 3 systems of equations, but there are inequalities next to them. Does this mean that for example we use the top equation when$n\le 15\phantom{\rule{0ex}{0ex}}$and so on?

Monserrat Sawyer 2022-05-24 Answered

### I need to evaluate a series of a function that switches sign in the following way:$\begin{array}{r}\sum _{k=-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{\text{sgn}\left(n-k\right)}{\left(\left(2n+1\right)+B\text{sgn}\left(n-k\right)\right)-\left(2k+1\right)}\end{array}$where $B\in \mathbb{R}$ and $n\in \mathbb{Z}$

Isaiah Owens 2022-05-24 Answered

### I have some observed values with measurement errors . I know the error distribution is gaussian with zeros mean and variance ${\sigma }^{2}$. What are the ways to compensate for this error?Any help is appreciated.

Kash Brennan 2022-05-24 Answered

### I curious practical solution.(Step by step)$\left(1+\mathrm{tan}{5}^{\circ }\right)\left(1+\mathrm{tan}{10}^{\circ }\right)\left(1+\mathrm{tan}{15}^{\circ }\right)\cdots \left(1+\mathrm{tan}{40}^{\circ }\right)$

Bailee Landry 2022-05-24 Answered

### Prove that if ${a}_{n}\to L$ then the sequence ${b}_{n}=1/{n}^{2}\cdot \left({a}_{1}+2{a}_{2}+3{a}_{3}+...+n{a}_{n}\right)$ converges to 0.5L

Erick Clay 2022-05-24 Answered

### Solve for:$2{\mathrm{log}}_{3}\left({x}^{2}-4\right)+3\sqrt{{\mathrm{log}}_{3}{\left(x+2\right)}^{2}}-{\mathrm{log}}_{3}{\left(x-2\right)}^{2}\le 4$My try:$2{\mathrm{log}}_{3}\left({x}^{2}-4\right)+3\sqrt{{\mathrm{log}}_{3}{\left(x+2\right)}^{2}}-{\mathrm{log}}_{3}{\left(x-2\right)}^{2}\le 4\phantom{\rule{0ex}{0ex}}⇔{\mathrm{log}}_{3}{\left({x}^{2}-4\right)}^{2}+3\sqrt{{\mathrm{log}}_{3}{\left(x+2\right)}^{2}}-{\mathrm{log}}_{3}{\left(x-2\right)}^{2}\le 4\phantom{\rule{0ex}{0ex}}⇔{\mathrm{log}}_{3}\left[{\left(x-2\right)}^{2}×{\left(x+2\right)}^{2}\right]+3\sqrt{{\mathrm{log}}_{3}{\left(x+2\right)}^{2}}-{\mathrm{log}}_{3}{\left(x-2\right)}^{2}\le 4\phantom{\rule{0ex}{0ex}}⇔{\mathrm{log}}_{3}{\left(x-2\right)}^{2}+{\mathrm{log}}_{3}{\left(x+2\right)}^{2}+3\sqrt{{\mathrm{log}}_{3}{\left(x+2\right)}^{2}}-{\mathrm{log}}_{3}{\left(x-2\right)}^{2}\le 4\phantom{\rule{0ex}{0ex}}⇔{\mathrm{log}}_{3}{\left(x+2\right)}^{2}+3\sqrt{{\mathrm{log}}_{3}{\left(x+2\right)}^{2}}-4\le 0\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\left(\ast \right)$Put: $t=\sqrt{{\mathrm{log}}_{3}{\left(x+2\right)}^{2}}⇒\left(\ast \right)⇔{t}^{2}+3t-4\le 0$But I don't know Conditions defined for this math? Could help me?

Turning back to high school math can be essential to understand engineering tasks that you may encounter later. The high school math problems have all the basics that have good equations and answers, which will let you see things clearly. The list of high school math questions below will help you identify your weaknesses and find various solutions. Taking a look at high school math equations, you will see certain parts that can be applied to Physics. In either case, the best way is to learn by example, which is why high school math problems with answers will be essential.