# High school math questions and answers

Recent questions in Secondary
Zhyar Hoshyar Wali 2022-05-25
Mackenzie Rios 2022-05-24 Answered

### Is there a method for polynomial regression in $2D$ dimensions (fitting a function $f\left(x,y\right)$ to a set of data $X,Y$, and $Z$)? And is there a way to apply a condition to the regression in $2D$ that requires all functions fitted to go through the axis line $x=0$?

VARSANI R 2022-05-24

### 3.1 (10 points) Calculate the density of the atmosphere at the surface of Mars, where the pressure is 650 Pa and the temperature is typically 253 K, with a CO2 (44×10-3 kg/mol) atmosphere., and. (b) Compare each of these densities with that of the earth’s atmosphere, which is 1.20 kg/m3 . 3.2 (5 points) Venus (with an average temperature of 730 K and pressure of 92 atm, with a CO2 atmosphere 3.3 (5 points) Saturn’s moon Titan, where -178 oC the pressure is 1.5 atm and the temperature is with a N2 (28×10-3 kg/mol)atmosphere

VARSANI R 2022-05-24
VARSANI R 2022-05-24

### Examine the uniform convergence of $\sum _{n=1}^{\mathrm{\infty }}\frac{x}{\left(1+nx\right)\left(1+\left(n+1\right)x\right)}$

Anthony Kramer 2022-05-24 Answered

### In $\mathrm{\Delta }ABC$,such $3{\mathrm{sin}}^{2}B+7{\mathrm{sin}}^{2}C=2{\mathrm{sin}}^{2}A+2\mathrm{sin}A\mathrm{sin}B\mathrm{sin}C$, and such $a=|BC|=1$, show that$\mathrm{sin}A=\frac{\sqrt{5}}{5}$I think this problem$3{b}^{2}+7{c}^{2}=2{a}^{2}+2\mathrm{sin}Abc=2+\mathrm{sin}A\cdot bc$where $|AC|=b,|AB|=c$

Briana Petty 2022-05-24 Answered

### Given: $△AKM,KD\perp AM$,$△AKM,KD\perp AM$ Find: $KD$

Brice Colon 2022-05-24 Answered

### Find the water pumped to flowers using fractions.A certain tank has water filled to $\frac{1}{5}$ of it's capacity. A persons opens a tap and allows the tank to fill upto to $\frac{3}{4}$ of it's capacity. Then he uses the water in the tank and finally $\frac{1}{3}$ water remains in the tank.What I have found :Water that was added to the tank after opening the tap : $\frac{11}{20}$Fraction of water he used was : $\frac{5}{12}$Total capacity of water in the tank : 1800 litresProblem:Find the amount water he used up in litresHow many more litres remained in the tank in the end when compared to the beginning

Charity Daniels 2022-05-24 Answered

### Let $\left({X}_{n}{\right)}_{n\ge 0}$ be a sequence of random variables and $\tau ,t$ stopping times with respect to the sequence $\left({X}_{n}{\right)}_{n\ge 0}$$\begin{array}{rl}\left\{\tau +t=n\right\}=\left\{\tau +t=n\right\}\cap \left\{t\le n\right\}& =\bigcup _{k=0}^{n}\left\{\tau +t=n\right\}\cap \left\{t=k\right\}\\ & =\bigcup _{k=0}^{n}\left\{\tau =n-k\right\}\cap \left\{t=k\right\}.\end{array}$As $\left\{\tau =n-k\right\}\in {\mathcal{F}}_{n-k}\subseteq {\mathcal{F}}_{n}$ and $\left\{t=k\right\}\in {\mathcal{F}}_{k}\subseteq {\mathcal{F}}_{n}$ for any $k\le n$, this implies that $\left\{\tau +t=n\right\}\in {\mathcal{F}}_{n}$, and so $\tau +t$ is a stopping time.Now, my question is, let assume that I am considering $\tau -t$ I know that in general, $\tau -t$ is not a stopping time. However, if I were to consider my birthday this year (a stopping time), which is a deterministic stopping time. At any time, I know exactly when my birthday occurs. Also, I know two days before my birthday i.e, $\tau -2$. What kind of a formulated counterexample will show that $\tau -2$ is indeed a stopping time in this setting.

Ryan Reynolds 2022-05-24 Answered

### How to sum up these fractions?Found this question in a competitive math test for elementary students. The long way is to add all the decimal values but is there a pattern/trick to solve this question (or these types)? I don't know how to solve this except by the long method of adding all the decimal equivalents.The Answer is 1Compute:$\frac{1}{7}+\frac{1}{8}+\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}+\frac{1}{14}+\frac{1}{15}+\frac{1}{18}+\frac{1}{22}+\frac{1}{24}+\frac{1}{28}+\frac{1}{33}=?$

Monserrat Sawyer 2022-05-24 Answered

### Negative IndicesI am not exactly good at evaluating negative indices--can someone please show me how to work out this expression:$\frac{{m}^{-3}{n}^{-2}}{{m}^{-5}{n}^{6}}$Both m's and the top n have negative indices.Thanks!

Thomas Hubbard 2022-05-24 Answered

### How do you find the average value of $f\left(x\right)=-{x}^{5}+4{x}^{3}-5x-3$ as x varies between [-2, 0]?

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