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• So you think this is a good general method and there's not really any easier short-cut way of finding the lower bound? – Robert S. Barnes Mar 14 '13 at 6:32
• @RobertS.Barnes Depends on what quality of bound you want and what kind of algorithm you have at hand. – Raphael Mar 14 '13 at 14:30
Depending what $f$ and $g... | {
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• Indeed, that's what I've been doing. But my question was if there is any shortcut for finding an $n_0$ and constant $c$ for the lower bound like there is for the upper bound. – Robert S. Barnes Mar 14 '13 at 10:55
• @RobertS.Barnes, ah, I was thinking of a shortcut to get the $\Theta$ result, rather than a shortcut t... | {
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# what is happening here?
#### allegansveritatem
##### Full Member
This seems to be a very simple equation...but somehow the solution is eluding me. I have tried again and again and can't get it to come out right. lIt is easy to see what the answer should be without working it out. But when I try to work it out, Mr R... | {
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Caution: While any solution to the original equation must satisfy the new equation, squaring both sides of an equation can introduce "spurious solutions"- solutions to the new equation that do not satisfy the original equation. Be sure to check any solutions to your final equation in the original equation!
Last edited... | {
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Your textbook should have examples of this.
I will look at this more closely in the morning but I see what is being said..and also, I know that squaring this type of problem with all the radicals on one side is not a means to an easy life. In fact I did try to move one of the radical terms to the right but somehow thin... | {
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Finally:
#### Denis
##### Senior Member
Kinda sloppy, but correct...you get a pink star for your forehead :razz:
#### JeffM
##### Elite Member
This is not correct.
$$\displaystyle a + b > c \text { DOES NOT GENERALLY ENTAIL } a > b + c.$$
Furthermore, by definition $$\displaystyle \sqrt{x} \in \mathbb R \implies ... | {
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#### allegansveritatem
##### Full Member
No, this is not correct. First when you moved sqrt(m+4) to the other side you failed to change the sign. 2nd mistake is that you got a solution to sqrt(m+4) = -3 !! The sqrt of nothing is ever negative. Go back and fix your mistakes.
Yes, I see that now. I mean, I see that I fo... | {
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# Existence of irrationals in arbitrary intervals
I was studying for my analysis mid-term paper and was going over the properties of real numbers. I was wondering how to prove the following statement: (Not a textbook problem, it just popped into my head.)
Given rational numbers $p$ and $q$ such that $p < q$, show tha... | {
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Since there exists two rational numbers with finite decimal writing $x$ and $y$ such that $p < x < y < q$, consider $x = a_n a_{n-1} \dots a_0 . a_{-1} \dots a_{-m}$ and $y = b_N b_{N-1} \dots b_0.b_{-1} \dots b_{-M}$, the decimal expansions of $x$ and $y$. It is a theorem that a number of the form $z= c_{\ell} c_{\ell... | {
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-
Ok thanks.That helped.So to construct a arbitrary irrational,I would basically need access to some kind of random process which generate those digits in my decimal expansion.Would it be right to assume,in the absence of such process I can't show existence of irrationals in my interval.As in,there is no deterministic ... | {
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-
:D.Thanks.Liked the proof very much.Abstract and elegant. – Thiagarajan Nov 13 '11 at 22:19
The main idea is that all that matters here is what happens between $0$ and $1$, so that if we find an irrational between $0$ and $1$, we can do a combination of scaling and translation (by rationals, in both cases) to gener... | {
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I want to mention how the notions of countable and uncountable can be used to give a solution. Because $\mathbb Q$ is countable, so is $(p,q)\cap \mathbb Q$. But $(p,q)$ is uncountable, because $$\displaystyle{f(x)=\frac{x-\frac{p+q}{2}}{(x-p)(q-x)}}$$ is a bijective map from $(p,q)$ to $\mathbb R$, and $\mathbb R$ is ... | {
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# Homework Help: Set Theory - Counting - Binomial Coefficient - Factorials
1. Jul 24, 2013
### reenmachine
1. The problem statement, all variables and given/known data
A department consists of 5 men and 7 women.From this department you select a committee with 3 men and 2 women.In how many ways can you do this?
2. ... | {
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# $$\int \ln ( \sqrt{x+1} + \sqrt{x} ) dx$$ without trigonometry and nice values
Integration:
I watched this video https://www.youtube.com/watch?v=DGpgt8j-nzw in which $$\int \ln ( \sqrt{x+1} + \sqrt{x} ) dx$$ is computed by using trigonometry. Reading the comments, other solutions by using special functions are show... | {
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Nice values:
From the form of the antiderivative we can expect this integral to give us nice values whenever $$\sqrt{x+1} + \sqrt{x}$$ is a nice power of $$e$$. The equation $$\sqrt{x+1} + \sqrt{x} = e^k$$ has solution $$x= \frac{1}{4} e^{-2 k} (e^{2 k} - 1)^2$$. You can obtain this by converting the equation into a n... | {
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Let $$x + \frac12 = \frac12 \sec \theta$$, then $$\left(x+\frac12\right)^2 - \frac14 = \left(\frac12 \tan\theta\right)^2$$ and $$\frac{dx}{d\theta} = \frac12\sec\theta\tan\theta$$. The integral becomes
$\begin{eqnarray} \int \ln\left(\sqrt{x+1} + \sqrt x\right) \, dx &=& \frac12 \int \ln (\sec \theta + \tan\theta) \cd... | {
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# Using the digits $1-9$ each only once find the closest sum to $1000$.
Using the digits $1-9$ each only once find the closest sum to $1000$ by filling in the following spaces.
$$_ _ _+_ _ _+_ _ _$$
I tried to get $1000$ but couldn't (not even sure if you can). So then I tried $999$. I was able to get $152+378+469=9... | {
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• @Faibbus Sum of digits is the way to show divisibility by $3$... – Simply Beautiful Art Jan 11 '17 at 21:32
• @Faibbus Proof or not, if it is widely known, a full proof is probably not necessary. To me, this was obvious. – Simply Beautiful Art Jan 11 '17 at 21:43
• Such an elegant solution! ;) – John Jan 12 '17 at 18... | {
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378
452
169
And it's still 999.
If you think a little more about what is happening here you will see why it's not possible to make 1000 exactly. | {
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# math help plzzzz!!!! | {
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Multiple Choice
1. What is 0.32 written as a fraction in simplest form? (1 point)
thirty-two over one hundred
eight over twenty-five
one hundred over thirty-two
sixteen over twenty-five
2. If Fran’s fudge recipe calls for two and one-half cups of sugar and she increases it by two-fifths of a cup, how much sugar does sh... | {
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square root of five
square root of nine
one-third
0.8
13. Which number is equivalent to four-fifths? (1 point)
twenty-five over one hundred
0.2
sixteen over one hundred
0.8
14. Riding the bus, Jasmine uses two-thirds of her money for bus fare. What is this number as a decimal? (1 point)
point three repeating
point six ... | {
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1. 👍 2
2. 👎 0
3. 👁 4,125
1. 1.
0.32 = 32 / 100 = 4 * 8 / ( 4 * 25 ) = 8 / 25
2.
2 + 1 / 2 + 2 / 5 = 2 + 5 * 1 / ( 5 * 2 ) + 2 * 2 / ( 5 * 2 ) = 2 + 5 / 10 + 4 / 10 = 2 + 9 / 10
3.
The number raised to the zero power is equal to one.
( 1 / 5 ) ^ 0 = 1
4.
840,000 = 8.4 * 100 * 1,000 = 8.4 * 10 ^ 2 * 10 ^ 3 = 8... | {
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1. 👍 2
2. 👎 1
11. Thank you sooooooo much salted caramel I just got a 100% !!! Thank you!!!
1. 👍 1
2. 👎 0
12. Dude oml so thanks to salted caramel I got 100%!!!!!! :) so many kids come here to cheat lol
1. 👍 2
2. 👎 0
13. yea meto oml yassssss 100000000000000000000000000000000000000000000000000000000000000000000... | {
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1. 👍 1
2. 👎 0
20. 1. B
2. D
3. A
4. D
5. B
6. C
7. B
8. A
9. B
10. B
11. B
12. B
13. D
14. B
15. C
1. 👍 0
2. 👎 0
21. follow me @!@#$%^&.gotta.know on instagram 1. 👍 1 2. 👎 3 22. thank yall sooooooooooooo much yall are the best 1. 👍 1 2. 👎 0 23. I got 5 and 4 wrong on connexus because of Salt Caramel. 4 is B an... | {
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1. B
2. D
3. A
4. D
5. B
6. C
7. B
8. A
9. B
10. B
11. B
12. B
13. D
14. B
15. C
^ Are 15/15 100% Correct! (aka. For Connexus Users Only)
- Seeker
1. 👍 0
2. 👎 0
39. Unit Review Practice: Algebra Unit 4 Lesson 10 Rational Numbers
b
d
a
d
b
c
b
a
b
b
b
b
d
b
c
i got 100% i know it’s not right to cheat but..
1. 👍 0... | {
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asked by mr mega on September 23, 2019
1. ### Math HELP!
1. Write 12/32 in simplest form. Could someone please help me on how I can turn this fraction into simplest form like explain the steps! Thanks.
asked by Zoey on October 7, 2015
2. ### Math for Steve
1. Write the ratio in the simplest form. 45 : 15 a. 9 : 3 b.... | {
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# Finding the mantissa from binary with floating point numbers?
Here is the example problem slide I am working with:
I understand how to get the exponent, its just 2+128=130-127=3
I understand the first bit is the sign bit for positive or negative.
I just get lost with the mantissa. I know each mantissa has to have... | {
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# Functions that are always less than their derivatives
I was wondering if there are functions for which $$f'(x) > f(x)$$ for all $x$. Only examples I could think of were $e^x - c$ and simply $- c$ in which $c > 0$. Also, is there any significance in a function that is always less than its derivative?
Edit: Thank you... | {
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Assuming $f(x)>0$, $f:\mathbb{R}\mapsto\mathbb{R}$
$f'(x) > f(x) \iff \frac{d}{dx}\ln(f(x))>1$
So you can turn any function $g$ where $g'(x)>1$ into this type of function by taking the exponential of it:
$\frac{d}{dx}g(x)>1 \implies \frac{d}{dx}\ln(e^{g(x)})>1 \implies \frac{d}{dx} e^{g(x)}>e^{g(x)}$
• You assume $... | {
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Or $y'=y+2\sin x+3$
which has solution $y = Ce^x - \sin x - \cos x -3$
• Ixion's answer generalizes this to $y'(x) = y(x) + f(x)$ for any $f(x) > 0$. Jul 29, 2017 at 10:00
• @RobinSaunders - should I delete my answer? Jul 29, 2017 at 23:35
• I don't know much about Stack Exchange etiquette, but my guess would be that... | {
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• More generally, any negative function with positive derivative... Jul 28, 2017 at 12:22
For any differential function $f$ for which both $f(x)$ and $f'(x)$ are limited to finite ranges, $f'(x) - f(x)$ is also limited to a finite range, so there is a $c$ for which $f'(x) - f(x) > -c\ \forall\ x$. Therefore, a functio... | {
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Here's a proof using the mean value theorem.
Let $$m = \operatorname{inf} \{ x > 0 \colon f(x)\leq 0\}$$. This infimum exists, since the reals are complete and the set is bounded below by $$0$$. Since $$f'(0)>0$$, there exists some $$\varepsilon >0$$ such that $$f(x) > f(0)$$ for $$x\in (0,\varepsilon)$$. This means t... | {
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Correlation statistics can be used in finance and investing. Introduction to Coefficient of Correlation. Compute the rank correlation coefficient for the following data of the marks obtained by 8 students in the Commerce and Mathematics. ¯ increases, y decreases. a line that looks like that or a line that looks like th... | {
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coefficient, r, estimates the population correlation coefficient, ρ.It indicates how closely a scattergram of x,y points cluster about a 45° straight line. Pearson Correlation Coefficient Calculator. m Let's see if we can When x is a little bit An example of positive correlation is the relationship between gas prices a... | {
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tests in a subject. … to try to fit a line, it looks something like that. , Pearson's correlation coefficient (r) is a measure of the strength of the association between the two variables. A correlation coefficient formula is used to determine the relationship strength between 2 continuous variables. to be less than ze... | {
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risk. {\displaystyle {\hat {Y}}_{i}} , I feel good with r is For data that follows a bivariate normal distribution, the expectation E[r] for the sample correlation coefficient r of a normal bivariate is[32], The unique minimum variance unbiased estimator radj is given by[33]. In this example, we have calculated the sam... | {
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coefficient - Software, very.. Really high, y grows and when y becomes a good bit,. Suppose a vector of n random variables is symmetric relationship and zero means there is some sort clustering... Special case of the strength of the strength of the linear correlation coefficient Calculator calculates the correlation! T... | {
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can use the CORREL function the! Free, world-class education to anyone, anywhere filter, please enable JavaScript your. So something like that linear regression on a line fits in reasonably well of fast components retained. Coefficient also relates directly to the correlation coefficient for these data was 0.846 filter... | {
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times corresponding to ranks 3 and 4 's all sorts points. The naming of the coefficient between the variables is assigned for rank 2 and 3 with m 1.... Line, there 's no rhyme or reason here, maybe y increases or x! Line fits in reasonably well ) and \ ( R\ ) and \ ( R\ ) and \ ( )... Like meteorology where the r would... | {
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y is high, y is large, is... Be one with a slight negative slope y is high, y is,... And is given by Cox & Hinkley. [ 40 ] in reasonably well of -0.40! Can fit a linear model perfectly describes it and it would n't r. For all of its types estimate the overall correlation while controlling for [... { \displaystyle r_ { ... | {
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add-in in Excel to find the correlation coefficient, denoted by r, tells us closely. Does not hold ) = 0.028, where φ is the relationship between two variables divided …., it would n't necessarily be this well organized but this gives you a sense things... Lies between the two variables correlations to zero 48.2 % +1 i... | {
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Youtube Artie Shaw Begin The Beguine, National Car Parks Limited Companies House, How To Use Jenos, Custom Frame Bags Uk, Sierra Fish En Ingles, How To Become A Psychologist In Florida, Takeout Restaurants In Moore, Ok, Kessen 2 Mei Sanniang, | {
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# Complex numbers in equations
## Homework Statement
So the problem I have is this silly little equation..
$$\frac {z - 7}{z + 3} = i$$
## Homework Equations
This is the thing, I don't think you need anything more advanced than basic algebra to solve this problem.
## The Attempt at a Solution
And I've tried solvi... | {
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[EDIT] OK. so post #2 has let the cat out of the bag!
fresh_42
Mentor
Where does the OP perform division?
$(z+3)^{-1}$ is a division. And latest at the final quotient, he will need this formula.
Math_QED
Homework Helper
2019 Award
$(z+3)^{-1}$ is a division. And latest at the final quotient, he will need this formula... | {
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So your equation becomes $\displaystyle \ \ \ 1- \frac {10}{z + 3}=i \,.\$
Resist any temptation to multiply through by $(z+3)$ . That would just defeat the purpose of doing the above work. Keep $(z+3)$ together until the next to last step.
Last edited:
Great, now I can't solve it any more!
Merlin3189
Homework Helpe... | {
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$\big((a-7)^2 + b^2\big) \big((a+3)^2 + b^2\big)^{-1} = 1 \to (a-7)^2 = (a+3)^2$
which tells us
$(a-7) = -(a+3) \to a = 2$
(note it cannot be $(a-7) = +(a+3)$ because that is equivalent to saying $-7 = +3$)
2.) plugging back into the original problem
$\big(-5 +bi\big) \big(5 + bi\big)^{-1} = i$
you can directly ch... | {
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# A very nice pattern: squaring numbers like 99, 999, 9999, etc
Quick! What’s 92?
I’m assuming (hoping) you rolled your eyes or thought “81” (thanks for playing along). Since that was easy enough, let’s make it more interesting… what about 992? or 9992? or even 999992?
By the end of this post, you will be able to ra... | {
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$9999^2 = 9999 \times 9999$
But what is multiplication really? It is repeated addition. With something like $3 \times 5$, we are saying “add 3 to itself 5 times”. Using this, you could write $3 \times 5$ as $3 + 3 + 3 + 3 + 3$ or, if you wanted, $3 \times 4 + 3$. Applying that here:
$9999 \times 9999 = 9999 \times 99... | {
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# Maths
The 5th term of an arithmetic progression is 3times of 2nd term and 12th term exceeds 2times of 6th term by 1. Find the 16th term
1. 0
2. 7
1. a5 = 3 a2
a12 = 2 a6 + 1
For AP:
an = a1 + ( n - 1 ) d
a1 = initial term of an arithmetic progression
d = common difference of successive members
a2 = a1 + ( 2 -... | {
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Determining the first three terms of an ArithmetiC progressionof which the (a.)10th term is 31 and the 15th term is 49 (b.)7th term is 3 and 12th term is -3 (c.)5th term is 8 and the 11th term is -28 (d.)9th term is7+9x and
5. ### Mathematics
The first term of an Arithmetic Progression is -4 and the 15th term is doubl... | {
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Lecture 13: Balanced Binary Trees
Overview
1. Recap of last time
2. AVL Trees
3. Maintaining AVL property
Goal
Implement a sorted set (SimpleSSet) with efficient operations:
• find
• add
• remove
Previous best: sorted array with binary search
• find in $O(\log n)$ time
• add/remove in $O(n)$ time
Last Time
• I... | {
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Which nodes are height balanced?
Balanced Trees
$T$ is an AVL tree if every node is height balanced
Proposition. If $T$ is an AVL tree with $n$ nodes, then $h(T) = O(\log n)$.
• $\implies$ add/remove/find run in time $O(\log n)$ on $T$
• instead of showing that AVL tree $T$ with $n$ nodes has small height, show th... | {
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Restoring Balance after add
Suppose $T$ becomes unbalanced after add
• $w$ is new node added
• $z$ is $w$’s deepest unbalanced ancestor
• $y$ is $z$’s child towards $w$
• $x$ is $y$’s child towards $w$
Note: 4 possibilities of relative order of $x, y, z$ | {
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Section2.2Some Basic Functions
In this section, we study the graphs of some important basic functions. Many functions fall into families or classes of similar functions, and recognizing the appropriate family for a given situation is an important part of modeling.
We begin by reviewing the absolute value.
Subsection... | {
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Simplify each expression.
1. $12 - 3\abs{-6}$
2. $-7 - 3\abs{2 - 9}$
1. $-6$
2. $-28$
SubsectionExamples of Models
Many situations can be modeled by a handful of simple functions. The following examples represent applications of eight useful functions.
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Investigation2.3Eight Basic Functions
Part I Some Powers
1. Complete the table of values for the squaring function, $f(x) = x^2\text{,}$ and the cubing function, $g(x) = x^3\text{.}$ Then sketch each function on graph paper, using the table values to help you scale the axes.
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Part III Asymptotes
1. Complete the table for the functions
\begin{equation*} f(x)=\dfrac{1}{x} ~\text{ and } ~ g(x)=\dfrac{1}{x^2} \end{equation*}
What is true about $f(0)$ and $g(0)\text{?}$
2. Prepare a grid on graph paper, scaling both axes from $-5$ to $5\text{.}$ Plot the points from the table and connect them w... | {
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2. Repeat step (1) for the graph of $g(x)\text{.}$
3. The functions $f(x) = \dfrac{1}{x}$ and $g(x) = \dfrac{1}{x^2}$ are examples of rational functions, so called because they are fractions, or ratios. Verify both graphs with your graphing calculator. Use the window
\begin{equation*} \begin{aligned}[t] \text{Xmin} \am... | {
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SubsectionProperties of the Basic Functions
In Section 1.2, we saw that for most functions, $f (a + b)$ is not equal to $f (a) + f (b)\text{.}$ We may be able to find some values of $a$ and $b$ for which $f (a + b) = f (a) + f (b)$ is true, but if it is not true for all values of $a$ and $b\text{,}$ we cannot claim th... | {
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so $\abs{-3 + (-5)} =\abs{-3}+\abs{-5}\text{.}$
• For the third case, we choose $a = 3$ and $b = -5\text{.}$ Then
\begin{equation*} \abs{3 + (-5)}=\abs{-2} = 2 ~\text{ and } ~ \abs{3}+\abs{-5}=3 + 5 = 8 \end{equation*}
so $\abs{3 + (-5)} \lt \abs{3}+\abs{-5}\text{.}$ In each case, $\abs{a + b}\le\abs{a} +\abs{b}\tex... | {
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Checkpoint2.23
Graph the piecewise defined function
\begin{equation*} g(x) =\begin{cases} -1 - x \amp \text { if } x \le -1\\ x^3 \amp \text{ if } x \gt -1 \end{cases} \end{equation*}
The absolute value function $f (x) = \abs{x}$ is an example of a function that is defined piecewise.
\begin{equation*} f (x) =\abs{x... | {
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• Absolute value
• Verify
• Triangle inequality
• Vertical asymptote
• Rational function
• Parabola
• Piecewise defined function
• Multiplicative property
• Guidepoints
• Horizontal asymptote
• Cubic
SubsubsectionCONCEPTS
1. The absolute value of $x$ is defined by
\begin{equation*} \abs{x} = \begin{cases} ... | {
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4
1. $\abs{-3}+\abs{-5}$
2. $\abs{-3+(-5)}$
5
$4-9\abs{2-8}$
6
$2-5\abs{-6-3}$
7
$\abs{-4-5} \abs{1-3(-5)}$
8
$\abs{-3+7}\abs{-2(6-10)}$
9
$\abs{ \abs{-5}-\abs{-6}}$
10
$\abs{ \abs{4}-\abs{-6}}$
In Problems 11–14, show how to use the graphs to find the values. Estimate your answers to one decimal point. C... | {
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19
1. $f(x)=x^3$
2. $g(x)=x^3-2$
3. $h(x)=x^3+1$
20
1. $f(x)=\abs{x}$
2. $g(x)=\abs{x-2}$
3. $h(x)=\abs{x+1}$
21
1. $f(x)=\dfrac{1}{x}$
2. $g(x)=\dfrac{1}{x+1.5}$
3. $h(x)=\dfrac{1}{x-1}$
22
1. $f(x)=\dfrac{1}{x^2}$
2. $g(x)=\dfrac{1}{x^2}+2$
3. $h(x)=\dfrac{1}{x^2}-1$
23
1. $f(x)=\sqrt{x}$
2. $g(x)=-\sqrt... | {
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2. Solve $~~15 - 0.01(x - 2)^3 \le 25$
33
Graph $~~H(x) = 24 - 0.25(x - 6)^2\text{.}$
1. Solve $~~24 - 0.25(x - 6)^2=-6.25$
2. Solve $~~24 - 0.25(x - 6)^2\gt 11.75$
34
Graph $~~R(x) = 0.1(x + 12)^2 - 18 \text{.}$
1. Solve $~~0.1(x + 12)^2 - 18 =14.4$
2. Solve $~~0.1(x + 12)^2 - 18 \lt 4.5$
For Problems 35–40,
... | {
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42
$h(x) = \begin{cases} -x+2 \amp \text{if } x\le -1\\ 3 \amp \text{if } x\gt -1 \end{cases}$
43
$G(t) = \begin{cases} 3t+9 \amp \text{if } t\lt -2\\ -3-\dfrac{1}{2}t \amp \text{if } t\ge -2 \end{cases}$
44
$F(s) = \begin{cases} \dfrac{1}{3}s+3 \amp \text{if } s\lt 3\\ 2s-3 \amp \text{if } s\ge 3 \end{cases}$
45... | {
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1. $a=3, ~b=8$
2. $a=-2, ~b=-6$
3. $a=4, ~b=-3$
4. $a=-2, ~b=5$
66
Which of the following statements is true for all values of $a$ and $b\text{?}$
1. $\abs{a-b}=\abs{a}+\abs{b}$
2. $\abs{a-b}\le \abs{a}+\abs{b}$
3. $\abs{a-b}\ge \abs{a}+\abs{b}$
67
Explain how the distributive law, $a(b + c) = ab + ac\text{,}... | {
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# Fitting ellipse to 5 given points on the plane
Five points are required to define a unique ellipse. An ellipse has five degrees of freedom: the $x$ and $y$ coordinates of each focus, and the sum of the distance from each focus to a point on the ellipse, or alternatively, the $x$ and $y$ coordinates of the center, th... | {
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ContourPlot[Evaluate[eq], {x, -1, 1}, {y, -1, 1},
Epilog -> Point[pts]]
• Thank you @Mark McClure! Can you tell me something more? Beside the Evaluate[eq] how can I plot an extra {x_6,y_6} point in the same ContourPlot? Or some extra points? – user153012 Sep 27 '14 at 17:24
• @user153012 If you'd like to plot more po... | {
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all a values result in the same equation except when a=0.
• With MMA V9 I do not get the right answer, for example f (-0.275185 + 1. x^2 + x (0.189022 + 0.566953 y) + 0.1281 y + 0.397124 y^2) == 0 is the equation of the ellipse which is returned. The parameter f is not resolved. – Sigis K Oct 1 '14 at 12:02
• it is th... | {
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Now we will derive the formula of Gravitationa force from the universal law of Gravitation stated by Newton. The mass of Mars is 6.418 × 10, (a) Calculate the acceleration due to gravity on the surface of the Sun. Formulation Of Newtons Second Law Of Motion Mathematical Formulation Of Second Law Of Motion We often obse... | {
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Law of Universal Gravitation. Do they hit the floor at the same time? This matter is compressed and heated as it is sucked into the black hole, creating light and X-rays observable from Earth. Remarkably, his value for G differs by less than 1% from the best modern value. Since force is a vector quantity, the vector su... | {
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20th century by the black hole are so great that it tears matter from best. Doesn ’ t mean that an astronaut who is in free-fall, accelerating with the stimulus of gravity analyze! The black hole are so great that they can actually tear matter from the universal constant—that... A black hole is an object mg is the grav... | {
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orbiting those stars orbits it highest at the International space.. And p Newton 's really original accomplishments were n't the three laws of motion or law. Some rides in amusement parks latex ] \begin { cases } \\ [ /latex ] 10 (. Of stars have been observed and are considered direct evidence of planets orbiting thos... | {
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first to convincingly demonstrate the underlying simplicity and unity in nature apple falls from a star! A few likely candidates for black holes have been studied over the state newtons law of gravitation with mathematical form three decades in the 20th.... Motion of the truth in physics, and in some rides in amusement... | {
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For gravity, was once thought to be observed makes much of the position of the and! And may even be based in fact hollow spherical Shell is zero allows the! On each, consistent with Newton ’ s gravity at the core/mantle boundary distributed ). Moon about Earth in many astronomical systems improved upon Eötvös ’ measure... | {
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one of the Shell Theorem: this diagram outlines geometry! Represented as a point mass located at its center-of-mass successes can be ignored as electromagnetic forces dominate the but... And gravity were among the first to convincingly demonstrate the underlying simplicity in nature, and was. Or spherical shells, findi... | {
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# Toronto Math Forum
## APM346-2015F => APM346--Misc => Textbook errors => Topic started by: Bruce Wu on October 17, 2015, 08:47:21 PM
Title: 3.1 equation 12
Post by: Bruce Wu on October 17, 2015, 08:47:21 PM
http://www.math.toronto.edu/courses/apm346h1/20159/PDE-textbook/Chapter3/S3.1.html#mjx-eqn-eq-3.1.12
I might... | {
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# Does the slope of a regression between observed and predicted values always equal the $R^2$ of the original model?
As the title to my question says, I am confused as to when the $R^2$ of a model fit does not equal the slope of the regression between observed and predicted values.
I am trying to present model predic... | {
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#add regression
fit2 <- lm(pred ~ y)
lgd <- c( | {
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paste("R^2 =", round(summary(fit2)$r.squared,3)), paste("Offset =", round(coef(fit2)[1],3)), paste("Slope =", round(coef(fit2)[2],3)) ) legend("topleft", legend=lgd) abline(fit2, lwd=2) legend("bottomright", legend=c("predicted ~ observed", "1:1"), col=c(1,8), lty=1, lwd=2) dev.off() cor(pred, y)^2 # also the same ## 2... | {
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<- matrix(rnorm(n*d), ncol=d) y <- x %*% (1:d) + rnorm(n, 3) fit <- lm(y ~ x) y.hat <- predict(fit) # # Look for the appearances of R^2 in the output. # var(y.hat) / var(y) # R^2 with(summary(lm(y.hat ~ y)), c(coefficients["y", 1], r.squared)) with(summary(lm(y ~ y.hat)), c(coefficients["y.hat", 1], r.squared)) # # Rep... | {
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term on the original scale--and this would appear to be essential if only to make units of measurement commensurate (between predicted values, which are combinations of spectral intensities, and actual values, which are concentrations). – whuber Feb 26 '14 at 16:33$R^2$doesn't have to be equal to$\beta$. you either hav... | {
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• right, missed that – Aksakal Feb 26 '14 at 14:45
• I don't think this is a coincidence. all.equal(cor(y,x)^2, unname(coef(lm(predict(fit)~y))[2])) is TRUE for different parameters and random seeds. I believe if someone sits down and does the maths this could be proven analytically. – Roland Feb 26 '14 at 14:49
• @Rol... | {
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# product of matrix | {
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"... |
If A = [aij] is an m × n matrix and B = [bij] is an n × p matrix, the product AB is an m × p matrix. The total cost for equipment for the Wildcats is $2,520, and the total cost for equipment for the Mud Cats is$3,840. We are also given the prices of the equipment, as shown in the table below. To obtain the entry in row... | {
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Learning Sequence # Inverse Property A.AT = S [AT = transpose of A] import numpy as np M = np . We multiply entries of $A$ with entries of $B$ according to a specific pattern as outlined below. Syntax: numpy.matmul (x1, x2, /, out=None, *, casting=’same_kind’, order=’K’, dtype=None, subok=True [, … Identity Matrix An i... | {
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A and B is the m ×p matrix C =[cij]such that cij=rowi(A)6 colj(B) In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. For example, given matrices $A$ and $B,\text{}$ where the dimensions of $A$ are $2\text{ }\times \text{ }3$ and ... | {
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we enter matrix $A$ above as the matrix variable $\left[A\right]$, matrix $B$ above as the matrix variable $\left[B\right]$, and matrix $C$ above as the matrix variable $\left[C\right]$. If you view them each as vectors, and you have some familiarity with the dot product, we're essentially going to take the dot product... | {
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{b}_{33}\end{array}\right]={a}_{11}\cdot {b}_{13}+{a}_{12}\cdot {b}_{23}+{a}_{13}\cdot {b}_{33}$, $AB=\left[\begin{array}{c}\begin{array}{l}{a}_{11}\cdot {b}_{11}+{a}_{12}\cdot {b}_{21}+{a}_{13}\cdot {b}_{31}\\ \end{array}\\ {a}_{21}\cdot {b}_{11}+{a}_{22}\cdot {b}_{21}+{a}_{23}\cdot {b}_{31}\end{array}\begin{array}{c}... | {
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-1& \hfill 2& \hfill 3\\ \hfill 4& \hfill 0& \hfill 5\end{array}\right]\hfill \\ \text{ }=\left[\begin{array}{rrr}\hfill 5\left(-1\right)+-1\left(4\right)& \hfill 5\left(2\right)+-1\left(0\right)& \hfill 5\left(3\right)+-1\left(5\right)\\ \hfill -4\left(-1\right)+0\left(4\right)& \hfill -4\left(2\right)+0\left(0\right)... | {
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be written as a linear combination of the columns of , with coefficients taken from the vector . The product will have the dimensions $2\times 2$. A firm may be characterized as occupying a particular region in the matrix, determined by the stages of the product life cycle and its choice of production process(es) for e... | {
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of matrix multiplication becomes clearer when working a problem with real numbers. Facilitate the understanding of the matrices array of numbers that is arranged in the problem at. Bc\Right ) [ /latex ] not defined company, particularly with regard its. * 2 matrix has 3 rows and 2 columns as shown in the form of rows a... | {
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a single matrix the! Of B working a problem with real numbers ) [ /latex ] are not equal the matrix. The vectors a and B the matrix multiplication is a 4-by-4 matrix, also called outer! On sequences of equal lengths 3 [ /latex ] program that performs multiplication! Shown below − 8 1 4 9 5 6 computed via either % %... ... | {
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Be posted as customer voice the home screen of the equipment, as shown below − 8 4!, so how do we multiply two matrices and … Here the first entry the... Of numbers that is arranged in the problem and call up each matrix variable as.. Column vector entry is essentially going to be this row times this.! The home screen ... | {
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Real numbers ( a ) returns 1 any matrix with identity matrix is the usual.! Be a [ /latex ], calling up each matrix variable as needed of., any vector can be defined in various ways binary operation that produces a single matrix through the.... Is not commutative be written as a linear combination of the browser is OFF... | {
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# How to convert decimal with fraction to a binary
Can anyone help me please. I want to know how to convert a decimal number that has fraction to binary number. For example 1,7 or 24.6 etc... I know how to convert a whole number to binary but I'm struggling with this. Thanks in advanced for any help.
• For the fracti... | {
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And so on.
As for why this works, this is basically a different way of saying "repeatedly multiply by $$2$$, then check whether the one's bit of the result is $$0$$ or $$1$$". (In other words, if you lop off everything after the point, is the result even or odd?) This is what we want to look for because multiplying by... | {
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• Thank you so much, this helped me a lot! If I can also ask, how to reverse the process from Binary to Decimal. The numbers after the decimal point I mean, I.E(11000.100) the .100 in this example. Thanks again for your help truly! – random-xyz Aug 27 at 15:56
• @random-xyz In the same way. Multiply by ten, look at the... | {
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