Determine whether the given set S is a subspace of the Vector space V.

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ntabb1
2022-03-31

Determine whether the given set S is a subspace of the Vector space V.

(there are multiple)

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asked 2022-05-08

${\int}_{1}^{3}\frac{8x}{(2x+4)*3}dx$

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In a jet engine a diffuser decreases the kinetic energy of the air entering the engine. The air enters a the diffuser at 132 kPa and 25°C with a velocity of 502 m/s and leaves at 229 kPa and 64°C. The heat lost from the diffuser is estimated to be 6 kJ/kg. Determine the exit velocity in m/s to 1 decimal place. Take the specific heat at constant pressure of air to be 1.009 kJ/(kgK).

asked 2022-04-29

Prove that $n\mid \varphi ({a}^{n}-1)$ in "Topics in Algebra 2nd Edition" by I. N. Herstein. Any natural solution that uses $Aut\left(G\right)$

asked 2022-04-25

Simple Linear Regression - Difference between predicting and estimating?

Here is what my notes say about estimation and prediction:

Estimating the conditional mean

"We need to estimate the conditional mean $\beta}_{0}+{\beta}_{1}{x}_{0$ at a value $x}_{0$, so we use $\hat{{Y}_{0}}=\hat{{\beta}_{0}}+\hat{{\beta}_{1}}{x}_{0}$ as a natural estimator." here we get

$\hat{{Y}_{0}}~N({\beta}_{0}+{\beta}_{1}{x}_{0},{\sigma}^{2}{h}_{00})\text{}\text{where}{h}_{00}=\frac{1}{n}+\frac{{({x}_{0}-\stackrel{\u2015}{x})}^{2}}{(n-1){s}_{x}^{2}}$

with a confidence interval for $E\left({Y}_{0}\right)={\beta}_{0}+{\beta}_{1}{x}_{0}$ is

$(\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}-cs\sqrt{{h}_{00}},\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}+cs\sqrt{{h}_{00}})$

where $c={t}_{n-2,1-\frac{\alpha}{2}}$ Where these results are found by looking at the shape of the distribution and at $E\left(\hat{{Y}_{0}}\right)$ and $var\left(\hat{{Y}_{0}}\right)$

Predicting observations

"We want to predict the observation $Y}_{0}={\beta}_{0}+{\beta}_{1}{x}_{0}+{\u03f5}_{0$ at a value $x}_{0$"

$E(\hat{{Y}_{0}}-{Y}_{0})=0\text{}\text{and}var(\hat{{Y}_{0}}-{Y}_{0})={\sigma}^{2}(1+{h}_{00})$

Hence a prediction interval is of the form

$(\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}-cs\sqrt{{h}_{00}+1},\hat{{b}_{0}}+\hat{{b}_{1}}{x}_{0}+cs\sqrt{{h}_{00}+1})$

asked 2022-03-19

I want to know how to find the vertices of the conic equation

20x^2 +4y^2-800=0

asked 2022-05-03

200.54 |

asked 2022-04-28

Prove if $F\left(\sqrt[n]{a}\right)$ is unramified or totally ramified in certain conditions