allhvasstH
2020-12-02
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dessinemoie

Answered 2020-12-03
Author has **90** answers

asked 2021-08-11

A ball is tossed upward from the ground. Its height in feet above ground after t seconds is given by the function $h\left(t\right)=-16{t}^{2}+24t$ . Find the maximum height of the ball and the number of seconds it took for the ball to reach the maximum height.

asked 2021-01-04

Write in words how to read each of the following out loud.

a. $\{x\in {R}^{\prime}\mid 0<x<1\}$

b. $\{x\in R\mid x\le 0{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}x\Rightarrow 1\}$

c. $\{n\in Z\mid n\text{}is\text{}a\text{}factor\text{}of\text{}6\}$

d. $\{n\in Z\cdot \mid n\text{}is\text{}a\text{}factor\text{}of\text{}6\}$

asked 2022-05-13

Let ${\left\{{f}_{k}\right\}}_{k=1}^{\mathrm{\infty}}$ be a sequence of $\mathcal{S}$-measurable real-valued functions on a measure space $(M,\mathcal{S})$. Then the functions

$\underset{k\to \mathrm{\infty}}{lim\u2006sup}{f}_{k}(x)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\underset{k\to \mathrm{\infty}}{lim\u2006inf}{f}_{k}(x)$

are also $\mathcal{S}$-measurable.

I already have proven this statement and my question is about something else. In the script it says that the reader may use the hint:

For a sequence ${\left\{{a}_{k}\right\}}_{k=1}^{\mathrm{\infty}}$ of real numbers the following is true:

$\underset{k\to \mathrm{\infty}}{lim\u2006sup}{a}_{k}=\underset{k\to \mathrm{\infty}}{lim}\underset{m\to \mathrm{\infty}}{lim}max\{{a}_{k},{a}_{k+1},\dots ,{a}_{m}\}$

Now, I have not used this in my proof, but I can assure you, that my proof is airtight nonetheless. Anyway, can someone point out why this holds? I have not seen this equality before and did not know that one can present $lim\u2006sup,lim\u2006inf$ like that. I know that for a set of limit points $H$ we can say that $lim\u2006supH=maxH$ and vice versa. I do not even see how this property can be useful for our proof.

$\underset{k\to \mathrm{\infty}}{lim\u2006sup}{f}_{k}(x)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\underset{k\to \mathrm{\infty}}{lim\u2006inf}{f}_{k}(x)$

are also $\mathcal{S}$-measurable.

I already have proven this statement and my question is about something else. In the script it says that the reader may use the hint:

For a sequence ${\left\{{a}_{k}\right\}}_{k=1}^{\mathrm{\infty}}$ of real numbers the following is true:

$\underset{k\to \mathrm{\infty}}{lim\u2006sup}{a}_{k}=\underset{k\to \mathrm{\infty}}{lim}\underset{m\to \mathrm{\infty}}{lim}max\{{a}_{k},{a}_{k+1},\dots ,{a}_{m}\}$

Now, I have not used this in my proof, but I can assure you, that my proof is airtight nonetheless. Anyway, can someone point out why this holds? I have not seen this equality before and did not know that one can present $lim\u2006sup,lim\u2006inf$ like that. I know that for a set of limit points $H$ we can say that $lim\u2006supH=maxH$ and vice versa. I do not even see how this property can be useful for our proof.

asked 2022-04-28

I have to prove that there is no natural number whose multiplication of digits is equal to 3570

What would be the proper mathematical solution to this question?

What would be the proper mathematical solution to this question?

asked 2022-06-29

I wonder why uncertainties in angle measurement MUST be in radians. For example, I want to calculate the uncertainty in measuring the function $y=\mathrm{sin}(\theta )$ when the angle is measured $\pm 1$ degree. I do this using differential, so $dy=\mathrm{cos}(\theta )d\theta $, now $d\theta =\pm 1$ degree is the error in $\theta $. Now, all the course notes/ books I read says this must be converted in radians, even though the angle we use here is measured in degree. How come?

asked 2022-07-20

Can you help me to simplify this algebraic expression?

How can I simplify this algebraic expression?

$\frac{-2}{{x}^{2}-1}+\frac{x}{x+1}-\frac{1}{x-1}$

How can I simplify this algebraic expression?

$\frac{-2}{{x}^{2}-1}+\frac{x}{x+1}-\frac{1}{x-1}$

asked 2022-05-28

Is there a formula to approximate $\pi $in the form of $\frac{p}{q}$?