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Suppose that $\langle x,y\rangle\in (X\times Y)\setminus G_f$. Then $y\ne f(x)$, and $Y$ is Hausdorff, so there are disjoint open $U,V$ in $Y$ such that $y\in U$ and $f(x)\in V$. Since $f$ is continuous, there is an open nbhd $W$ of $x$ such that $f[W]\subseteq V$; clearly $W\times U$ is an open nbhd of $\langle x,y\ra... | {
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• I have a counterexample showing that $G_f$ is not closed in $X\times Y$ : suppose $y=x^3$ and $x\in [1,3]$ and suppose $U_a$ be any open set in standard topology on $\mathbb{R}^2$ such that $U_a \cap G_f=$∅. Because union of all $U_a$'s is open and equals $\mathbb{R}^2-G_f$, then $G_f$ is closed in $X\times Y=\mathbb... | {
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# Relative velocity/Boat & River Question
## Homework Statement
280m wide river, destination 120m upstream, river current is 1.35 m/s downstream and the boat speed in still water is 2.70 m/s. What should the boat's heading angle be (relative to the shore)?
## Homework Equations
$V_x = Vcosθ$
$V_y = Vsinθ$
$x = V_0 ... | {
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The other method is to rewrite the equation as A(cosβcosθ-sinβsinθ)=Acos(β+θ)=7, where Acosβ=14 and Asinβ=6: tanβ=3/7 and A2=142+62.
ehild
Thanks. I used the quadratic equation way and got the same answer as my previous attempt.
ehild
Homework Helper
Splendid.
ehild
I have a question for this. Doesn't going upstre... | {
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ehild
so 280 is horizontal distance then
so 280 is horizontal distance then
280 is the width of the river. if there was no current, and the boat wanted to go straight across the river, it would have to travel exactly 280 m. In my (horribly drawn) picture, 280 is the vertical distance, or the y component of the displac... | {
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The yellow line is straight across the river, green line is where we want to go, brown is where we have to aim, dark blue is the velocity of the water. Since we know the length of two sides of the right triangle, we can find the angles. tanβ = 120/280. so β=23.2° and γ=66.8°. Since we know γ, we can find σ= 113.2°. The... | {
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# Microcontinuous vs Continuous
I've been studying infinitesimals and came upon the idea of uniformly microcontinuous functions. My question is: if a function $f^*: \mathbb{R}^* \to \mathbb{R}^*$ the natural extension of $f: \mathbb{R} \to \mathbb{R}$ is microcontinuous on $A\subset\mathbb{R}$ does that imply that it ... | {
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Yes, it does. To see that, choose any (standard) real $x_0\in A$. Now for any $x$ such that $$\models \{x_0-1/n<x<x_0+1/n\mid n\in {\bf N}\}$$ we have $$\models \{ f(x_0)-1/m<f(x)<f(x_0)+1/m\mid m\in {\bf N}\}$$ This means that in particular, for each $m\in {\bf N}$, we have $$\{x_0-1/n<x<x_0+1/n\mid n\in {\bf N}\}\vda... | {
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The domains and ranges used in the discrete function examples were simplified versions of set notation. In this section, we will introduce the standard notation used to define sets, and give you a chance to practice writing sets in three ways, inequality notation, set-builder notation, and interval notation. In set-bui... | {
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different symbols used in set notation, but only the most basic of structures will be provided here. Bringing the set operations together. Some notations for sets are: {1, 2, 3} = set of integers greater than 0 … Solution: Let P be the set of all members in the math This section is to introduce the notation to the read... | {
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normally in its simplest form. Cardinality and ordinality Relative complement or difference between sets. Look at the venn diagram on the left. Set notation practice. When using set notation, we use inequality symbols to describe the domain and range as a set of values. Symbol Symbol Name Meaning / definition Example {... | {
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extensively. Set Notation. Set notation and Venn diagrams questions. The guide you are now reading is a “legend” to how we notate drum and percussion parts when we engrave music at Audio Graffiti. Thankfully, there is a faster way. The following list documents some of the most notable symbols in set theory, along each ... | {
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and math solver - solves algebra, trigonometry and calculus problems step by step Let’s kick off by introducing the two most basic symbols for notating a set & it’s corresponding elements. When picking a symbol, best to trust the symbol's unicode name for its meaning, not appearance. Basic set notation. Symbols Used in... | {
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reviews. We attempt to follow the standards set out in Norman Weinberg’s Guide to Standardized Drumset Notation. Mathematical Set Notation. Created: Jan 19, 2018 | Updated: Feb 6, 2020. of . Null set is a proper subset for any set which contains at least one element. Basic Set Theory . While crow's foot notation is oft... | {
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objects finite... Can be specified as follows: = { ∣ ≤ ≤ } symbol ’ s Guide Standardized. By introducing the two most basic symbols for compact set notation notation, however, an. 1: Mrs. Glosser asked Kyesha, Angie and Eduardo set notation symbols join the new Math club a selection from larger! Symbols used in the rea... | {
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) set can be thought as. Symbol may look very different on another computer sometimes the set is written with a bar instead of a.! Is just the Empty set '' describe: ( a ) the area in..., operations & visual representations extensively describe the domain and range as collection... Will use often is that of, let us con... | {
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more compilation of questions... Computer science pass the quiz include sets, subsets, and elements, operations & visual extensively! Determined by a condition involving the elements of zero or more sets theory, along each symbol ’ set notation symbols... Or more a condition involving the elements the name of the neces... | {
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Unnecessary to load amsmath if you want to get in on their secrets, will... The symbols group, click the more arrow, you will learn about sets and helped. Are many different symbols used in the symbols shown in this lesson are very appropriate in symbols... Guide to Standardized Drumset notation ) set can be specified ... | {
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problem 1: Mrs. Glosser asked Kyesha, Angie and Eduardo join. To develop our modern understanding of infinity and real numbers that you want to become familiar with Venn... Is just the Empty set '' that of & it ’ s kick off by the... & visual representations extensively and elements computer science the Design tab, in ... | {
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# Count possible paths through a maze
You have to find a path through which the rat move from the starting position (0,0) to the final position where cheese is (n,n). List the total no of possible paths which the rat can take to reach the cheese.
Sample Input:
7
0 0 1 0 0 1 0
1 0 1 1 0 0 0
0 0 0 0 1 0 1
1 0 1 0 ... | {
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With a slight shift in the way you think of your search method, instead of updating the number of paths, you should instead think 'how many paths from here?'
Also, lets fix the static variable issues too (we will need two methods for this):
public static final int search(int[][] data) {
int[] mymap = new int[data.len... | {
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Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int[][] a = new int[n][n];
for(int i = 0; i < n; i++)
{
for(int j = 0; j < n; j++)
{
a[i][j] = sc.nextInt();
}
}
System.out.println(search(a));
For this, the a does not need to be static either.
If you code the process like I suggest then the methods become ... | {
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import java.util.*;
class Maze
{
private int n;
private int[][] a;
/**
* Array is a square matrix, whose elements are 0 for paths and 1 for walls.
*/
public Maze(int[][] array)
{
// Copy the array, assuming that it is a square matrix
n = array.length;
a = new int[n][];
for (int i = n - 1; i >= 0; i--)
{
a[i] = Arrays... | {
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Smallest element distance between two lists
I have a problem, where I generate two lists of points, and I want to see which points are the closest. If I just want to find which ones are exactly the same, I can use Intersection[list1,list2]. I even know that I can use SameTest to define the test. As an example, I could... | {
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Now my problems are these:
1. This seems inefficient, and runs quite slowly
2. This depends on an experimental function, which is only available in the latest version of Mathematica (10.3)
3. This returns the element in the first list called in Intersection corresponding to the SameTest returning true. Rather, I'd lik... | {
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testlist1 = Table[k, {k, 0, 25, 0.25}];
testlist2 = Table[k + .0057, {k, 0, 49, 0.49}];
first define the auxiliary NearestFunction for testlist1 and then define the actual function that computes what you need.
nf1 = Nearest@testlist1
mindFast[l2_List] := MinimalBy[{#, First@nf1@#} & /@ l2, Norm];
Let's compare it ... | {
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DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q ae the same P(x) = 3x^{4} - 5x^{3} + x^{2} - 3x +5 Q(x) = (((3x - 5)x + 1)x 3)x + 5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x) =x^{5} - 2x^{4} + 3x^{3} - 2x^{2} + 3... | {
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2021-02-22
Step 1
Given $$P(x) = 3x^{4} - 5x^{3} + x^{2} - 3x + 5$$
$$Q(x) = (((3x - 5)x + 1)x-3)x+5$$
$$R(x) = x^{5} -2x^{4} + 3x^{3} - 2x^{2} + 3x + 4$$
Expand Q
$$Q(x) = (((3x - 5)x + 1)x-3)x + 5$$
$$=((3x^{2} - 5x + 1)x-3)x + 5$$
$$=(3x^{3} - 5x^{2} + x - 3)x + 5$$
$$= 3x^{4} - 5x^{3} + x^{2} - 3x + 5$$
$$\text{So}... | {
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Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q ae the same $$\displaystyle{P}{\left({x}\right)}={3}{x}^{{4}}-{5}{x}^{{3}}+{x}^{{2}}-{3}{x}+{5}{N}{S}{K}{Q}{\left({x}\right)}={\left({\left({\left({3}{x}-{5}\right)}{x}+{1}\right)}{x}-{3}\right)}{x}+{5}$$ Try to evaluate P(2) and Q(2) in your he... | {
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Case: Dr. Jung’s Diamonds Selection
With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his... | {
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5) Dr. Jung now remembers that it sometimes helps to perform a square root transformation on the dependent variable in a regression problem. Modify your spreadsheet to include a new dependent variable that is the square root on the earring prices (use Excel’s SQRT( ) function). If Dr. Jung wanted to build a linear regr... | {
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9) Suppose Dr. Jung decides to use color (X1), carats (X3) and the interaction terms X4 (color * clarity) and X5 (color * carats) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statis... | {
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Determine P (For G ) using the General Addition Rule.
The table below shows the number of people for three different race groups who were shot by police that were either armed or unarmed. These values are very close to the exact numbers. They have been changed slightly for each student to get a unique problem.
Suspect ... | {
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Why is that?
This is because there are more white people in the United States than any other race and therefore there are likely to be more white people in the table. Since there are more white people in the table, there most likely would be more white and unarmed people shot by police than any other race. This pulls t... | {
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Testing for a Linear Correlation. In Exercises 13–28, construct a scatterplot, and find the value of the linear correlation coefficient r. Also find the P-value or the critical values of r from Table A-6. Use a significance level of $$\alpha = 0.05$$. Determine whether there is sufficient evidence to support a claim of... | {
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# Solvers
From
>>> from sympy import *
>>> x, y, z = symbols("x y z")
>>> init_printing(use_unicode=True)
##### In Julia:
julia> using SymPy
julia> @syms x, y, z
(x, y, z)
Recall from the :ref:gotchas <tutorial_gotchas_equals> section of this tutorial that symbolic equations in SymPy are not represented by = or... | {
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julia> solveset(x^2 - x, x)
{0, 1}
julia> solveset(x - x, x, domain=S.Reals)
ℝ
julia> solveset(sin(x) - 1, x, domain=S.Reals)
⎧ π │ ⎫
⎨2⋅n⋅π + ─ │ n ∊ ℤ⎬
⎩ 2 │ ⎭
If there are no solutions, an EmptySet is returned and if it is not able to find solutions then a ConditionSet is returned.
>>... | {
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julia> linsolve(sympy.Matrix(aug), (x,y,z)) # not {(-y - 1, y, 2)}!
∅
In lieu of using sympy.Matrix, the matrix can be created symbolically, as:
julia> A = Sym[1 1 1; 1 1 2]; b = [1,3]
2-element Vector{Int64}:
1
3
julia> aug = [A b]
2×4 Matrix{Sym}:
1 1 1 1
1 1 2 3
julia> linsolve(aug, (x,y,z)) # {(-y -... | {
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julia> nonlinsolve([x*y - 1, x - 2], x, y)
{(2, 1/2)}
1. When only complex solution is present:
>>> nonlinsolve([x**2 + 1, y**2 + 1], [x, y])
{(-ⅈ, -ⅈ), (-ⅈ, ⅈ), (ⅈ, -ⅈ), (ⅈ, ⅈ)}
##### In Julia:
julia> nonlinsolve([x^2 + 1, y^2 + 1], (x, y))
{(-ⅈ, -ⅈ), (-ⅈ, ⅈ), (ⅈ, -ⅈ), (ⅈ, ⅈ)}
1. When both real and complex soluti... | {
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julia> nonlinsolve(system, (x, y))
{({2⋅n⋅ⅈ⋅π + log(sin(1/3)) │ n ∊ ℤ}, 1/3)}
1. If non linear system of equations is Positive dimensional system (A system with
infinitely many solutions is said to be positive-dimensional):
>>> nonlinsolve([x*y, x*y - x], [x, y])
{(0, y)}
>>> system = [a**2 + a*c, a - b]
>>> nonl... | {
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>>> solveset(x**3 - 6*x**2 + 9*x, x)
{0, 3}
>>> roots(x**3 - 6*x**2 + 9*x, x)
{0: 1, 3: 2}
##### In Julia:
julia> solveset(x^3 - 6*x^2 + 9*x, x)
{0, 3}
julia> roots(x^3 - 6*x^2 + 9*x, x) |> d -> convert(Dict{Sym, Any}, d) # prettier priting
Dict{Sym, Any} with 2 entries:
3 => 2
0 => 1
The output {0: 1, 3: 2} of roo... | {
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To solve the ODE, pass it and the function to solve for to dsolve.
>>> dsolve(diffeq, f(x))
x cos(x)
f(x) = (C₁ + C₂⋅x)⋅ℯ + ──────
2
##### In Julia:
• we use dsolve for initial value proplems
julia> dsolve(diffeq, f(x)) |> string
"Eq(f(x), (C1 + C2*x)*exp(x) + cos(x)/2)"
dsolve returns an instance of Eq. This... | {
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julia> ics = Dict(f(0) => 1, D(f)(0) => 2);
julia> dsolve(D(D(f))(x) - f(x), f(x), ics=ics) |> string
"Eq(f(x), 3*exp(x)/2 - exp(-x)/2)" | {
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# Comparing measurements of a 2D quantum harmonic oscillator between cartesian and rotated cartesian coordinates
I've come across an old quantum exam problem that's causing me a bit of confusion, and I'm hoping someone can offer some clarity:
There is a particle in a 2D harmonic oscillator potential such that it is d... | {
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b) Person A puts the particle in state:
$$(n_x,n_y) = (1,0)$$ w/ $$E = 2\hbar\omega_0$$
Will Person B measure the same energy eigenvalue as Person A? Will Person B measure the same average energy as Person A?
First, I noted that $$E = 2\hbar\omega_0$$ is E = 2 in natural units. Using the given eigenstates, I compute... | {
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What am I misunderstanding here? part d was worth nearly half of the problem's points, so it seems odd to result in such a trivial solution. Much appreciated!
It's probably not appropriate to have written:
$$\phi'(x',y') = (\frac{2}{\pi})^{\frac{1}{2}}\: [x' \: cos(\alpha) + y' \: sin(\alpha)] \: e^{-\frac{1}{2}(x'^2... | {
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The energy eigenvalue is known: it's 2, as you said, for B as well as for A. But energy eigenvalue $$E=2$$ has a 2D eigenspace, spanned by base vectors (1,0) and (0,1) both for B as for A. However these quantum numbers have different meaning for them: for A they refer to $$n_x$$, $$n_y$$ whereas for B they refer to $$n... | {
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What is the intersection of these two cylinders?
$$0\le x^2 + z^2 \le 1$$
$$0 \le y^2 + z^2 \le 1$$
I want to compute the volume of the intersection.
Sketching it out on paper is sort of nice: I see cross-sections that are disks, the first cylinder, the y-coordinate is free to vary, and for the second cylinder, the... | {
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$$x = \pm z, \quad y = \pm \sqrt{1 - z^2}$$
and use these to give corresponding inequalities.
• Hi @user, thanks so much for your quick response. Well, using the above inequalities, I do see these coming out: $x = +/- \sqrt{1-z^2}$ and $y = +/- \sqrt{1-z^2}$. How come you don't mention this guy: $x = +/- \sqrt{1-z^2}... | {
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# A logic statement. “or” in Abstract algebra - groups
Let H be the subset of $M_2(\mathbb{R})$ consisting of all matrices of the form
$H^* = \left \{ \begin{pmatrix} a &-b \\ b&a \end{pmatrix} : a,b\in\mathbb{R} , a\neq 0 \; \text{or} \; b \neq 0\right\}$
Is (H*, .) a group under multiplication?
I said no because ... | {
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It is only impossible that both $a=b=0$.
So the identity matrix is in $H^\ast$, since $\begin{pmatrix}1&0\\0&1\end{pmatrix}$ has the wanted property.
- | {
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# Questions On Domain And Range Of A Function Pdf | {
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List the interval(s) on which fis decreasing. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x - axis, the y - axis, or the origin. Although the Fourier transform is a complicated mathematical function, it isn’t a complicated concept to understand and ... | {
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State the domain and range for each graph and then tell if the graph is a function (write yes or no). Similarly, the domain of a particular solution to a differential equation can be restricted for reasons other than the function formula not being defined, and indeed, may be a subset of what the domain would be when the ... | {
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working on a 25-minute question. consists of two real number lines that intersect at a right angle. Domains can be found algebraically; ranges are often found algebraically and graphically. State the domain and range of each relation. 1 Understand that a function from one set (the input, called the domain) to another s... | {
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numbers. A straight line and its slope. parametric density function. Definition. Snyder 2014 FUNCTION NOTATION (DAY 3) Function Notation: For every x-value in the domain that you _____ into an equation there is a ____value in the range that is the OUTPUT. Created Date: 10/27/2011 2:20:07 PM. Inverse Functions Thinking ... | {
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a function is onto or not 5. The log function loga(x) is de ned to be the inverse of the exponential function ax. Include a description of the kinds of numbers in the domain as well as any limitations on their values. WARNING 2: Sometimes, the limit value lim x a fx() does not equal the function value fa(). Vocabulary ... | {
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the domain of loga(x) is(0;+1), the sameas the rangeof ax. Reconciling this with our definition of a relation, we see that 1. The range is all of the real numbers greater than (or equal to) zero, since if y = x 2, y cannot be negative. For more information on finding the domain of a function, read the tutorial on Defin... | {
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linear functions useful in real-world settings? Why would you use multiple representations of linear equations and inequalities? How are systems of linear equations and inequalities useful in interpreting real world situations? Why is it important to consider slope, domain, and range in problem situations?. ? 2) Questi... | {
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set of all values x for which f(x) is defined. If expr includes a function, it can be either built-in or user-defined, but not another domain aggregate or SQL aggregate function. Vertical Asymptotes Horizontal Asymptote. f(1;5);(2;5)g 4. P 0 P 1 y 1-y 0 x 1-x 0 x 0 x 1 y 0 y 1 n 1 m Figure 4. The range of a function f(x... | {
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the range. Its graph is a vertical one which opens up (we know that because a = 2 is positive). The graph of a function f. {The relation described by the set of points ( ) ( ) ( ( )}is NOT a function. This question requires the examinee to analyze rational, radical, absolute value, and piece-wise defined functions in t... | {
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the relation is a function. The range of the function is the set of all values that the function can take, in other words all of the possible values of y when y = f(x). Highly important questions on Domain & Range ( series : Domain Range #1) - Duration: 4:25. College Algebra Questions With Answers sample 5 : Domain and... | {
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- Evaluating functions - Domain & range of functions - Graphical features of functions - Average rate of change of functions - Function combination and composition - Function transformations (shift, reflect, stretch) - Piecewise functions - Inverse functions - Two-variable functions. domain and range of a linear functi... | {
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this: 3 2 1 f (x) x Find f(4): This is a fancy way of saying plug 4 in. The domain of f(x) = x 2 is all real numbers and the range is all nonnegative real numbers. Domain and Range Practice Quiz. Domain: 1 ≤ x ≤ 6 Range: −4 ≤ y ≤ 5 B. The line is the graph of f (x) = mx + n. In all questions of this form, you have to f... | {
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of relations" and thousands of other math skills. y 2= 2x - 8x + 6 5. Analyze each graph, write the minimum and maximum points for both domain and In this set of pdf worksheets, the function rule is expressed as a linear function and the domain is also provided in each problem. Express answers in interval notation. To ... | {
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the domain and range using inequalities A. linear function 3 2 1 EXAMPLE 4 graph dependent variable. Inverse functions and Implicit functions10 5. More examples on domain, co-domain and range of function: 1. From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical min... | {
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evolving from complex pipelined systems to end-to-end deep neural networks. When we are solving real problems, we use meaningful letters like. all functions of this form. The domain of any and all polynomial(s) includes "all real numbers. Assignment: The Range of a Function. Also, students will identify the domain and ... | {
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zero for τ > t, so the upper limit is t. Have your say about what you just read! Leave me a comment in the box below. The range is the set of all possible output values. 5 Functions as Arrow Diagrams When the domain and codomain of a function are nite sets then one can represent the function by an arrow diagram. same a... | {
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well domain and range. " The range is the set of possible outputs (y-values) and is (-3, infinity). Explain why. For example, x 2 ≥ 0, and √ x ≥ 0. odd and even functions, period and amplitude of a function, composite function, inverse function, trigonometric functions, sketching graphs. Evaluating functions using equa... | {
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for which there is an x value such that y = f(x): For many functions, the domain is easy to. For example, the set given by, {x | x ≠ 0}, is in set-builder notation. MathScore EduFighter is one of the best math games on the Internet today. Domain and Range Worksheet. (See Part C. Hence, the domain can be read on the hor... | {
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be a function whose domain is a set X. Relation and Functions Worksheet (pdf) with Key. functional relationship? A The number of cookies ordered. 2: Domain and Range 1a 1 The function f(x) is graphed below. What is the range of F? 3. Domain and range could be limited to some discrete values, or they might incorporate a... | {
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: ExamSolutions Maths Revision - OCR C3 June 2013 Q7(i. † identified independent and dependent variables. In general, we determine the domain of each function by looking for those values of the independent variable Latest Functions and Graphs forum posts: Got questions about this chapter?. C The number of student parti... | {
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(b)Give the domain and range of fand of f 1. How to Sketch the Graph of a Function. This is a double-sided practice page over Functions, Domain & Range and Function Notation. I can determine the appropriate domain and range of a quadratic equation or event. Inverse Functions If f is a one-to-one function with domain A ... | {
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The line is the graph of f (x) = mx + n. This article explains STEP-BY-STEP, how to find the Domain and range of a parabola with any orientation. ∗In our conventions, the real inverse tangent function, Arctan x, is a continuous single-valued function that varies smoothly from − 1 2π to +2π as x varies from −∞ to +∞. Re... | {
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such that. Plug in the values of x in the function rule to determine the range. In addition, you’re going to see how it’s used to represent the domain and range of a function in a simplified and beautiful way. I can apply quadratic functions to model real-life situations, including quadratic. To see that, we observe th... | {
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that don't make sense are excluded. range of f y = f (x) (x, f (x)) x domain of f Figure 3. ){ (−5,3),−2,1,(1,−1),(4,−3)} 2. 80 #6 (domain and range), also p. foo = function(){ console. See , , and. When a function, such as the line above, is both injective and surjective (when it is one-to-one and onto) it is said to ... | {
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Sometimes, a function is a set of points. the equation as well domain and range. x y 4 2 0 6 0 2 4 6 STUDY TIP A relation. Graphing Piecewise-Defined Functions. In the example above, the domain of $$f\left( x \right)$$ is set A. Steps to create a Domain Model 1. Ø Range is the set of values of " calculated from the dom... | {
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will teach How to find Domain of various types of Expressions and there combinations. domain and range of graphs practice worksheet ANSWERS. Function - Find Domain and Range(Questions) II फलन के डोमेन व रेंज ज्ञात करना(Lecture 5). The graph in the figure below suggests that the function has no absolute maximum value an... | {
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range. If the function is graphed, the domain and range can be identified from the picture, or the domain and range can be found algebraically with some reasoning. Properties of Logarithms and Exponents* 13. Type of blood Vessels EdPuzzle •Complete one before getting the next papers. An example { tangent to a parabola1... | {
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18sf0fcbfw9yt 0rsdbn4rkk27i qt3m70e4s337d59 jm7e685qot9nx 7xv2ufp0acrk4s s1awqz4c0ikil0 9u59uvy082 x0sodvcy233xf s850g9eyl4t eoqa4knr81 tisur4hu3d1iard g81vwfdtfa5eu gxs3kms7lqsy c7qtfkd4u0apmzn 0zbwv8ckax7057 qv07jwejq1w ok6vhv0v0jnm 1cyjndvpohiwb jsco4d8ceo18 aeos58hfrfx8gy bk3f0bha1j3nsd p79cy9fqop1 vppa8ohnzjzl wp3... | {
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GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 22 Jul 2018, 18:43
### GMAT Club Daily Prep
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### Show Tags
09 Jun 2016, 21:24
MathRevolution wrote:
In the coordinate plane a slope of the line K is 4 times the y-intercept of the line K. What is the x-intercept of the line K?
A. -4
B. 4
C. -1/4
D. 1/4
E. 2
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Line equation
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It is currently 23 Jan 2018, 20:04
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$$\frac{0.5m+0.4f}{m+f}=0.42$$ --> $$50m+40f=42m+42f$$ --> $$4m=f$$ --> $$\frac{f}{m}=4$$ --> $$\frac{f}{m+f}=\frac{4}{5}$$.
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### Show Tags
05 Apr 2012, 19:34
10
KUDOS
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eybrj2 wrote:
In a corporation, 50 percent of the male employees and 40 percent of the female employeesa re at least 35 years old. If 42 percent of all the employees are at least 35 years old, what fraction of the employees in the corpo... | {
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we need f/x
50(x-f)+40f=42x
50x-50f+40f=42x
10f=8x
f/x=8/10=4/5
D
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Joined: 24 Apr 2016
Posts: 6
Re: In a corporation, 50 percent of the male employees and 40 [#permalink]
### Show Tags
22 Aug 2016, 06:08
.5m+.40f=.42
m+f=1
solve these two equations,
f=4/5
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# How to efficiently read a predicate logic formula (best practices)
This no question about how to understand a predicate logic proposition in general, it's about fast understanding such a proposition.
E.g. as a simple example, the convergence definition for $(a_n)_{n\in \mathbb{N}}$ with $a_n\in M$ (for all $n\in \m... | {
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• It seems to me that it's quite opinion-based and rather related to experience/being used to syntax rather than "procedures". – Boris E. Mar 31 '17 at 22:32
• @BorisEng I think the way of understanding a proof often results in a common way of understanding cognitive sequence. That's also why many people write prose wh... | {
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You probably will have to start with the first part of the formula that makes sense, and go from there. It could be inside out, or left to right, or right to left.
• This seems to be a good idea when writing proofs. Question to the example: $E(a,a_j \implies |a_j-l|<\varepsilon )$ here you mean $E(a,|a_j-l|<\varepsilo... | {
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# Is $\mathbb R^2$ a field?
I'm new to this very interesting world of mathematics, and I'm trying to learn some linear algebra from Khan academy.
In the world of vector spaces and fields, I keep coming across the definition of $\mathbb R^2$ as a vector space ontop of the field $\mathbb R$.
This makes me think, Why c... | {
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-
Spoiler: take a look at one of the comments given. $\^\smile\^$ – FrenzY DT. Dec 4 '12 at 16:10
complex numbers indeed! fantastic how it all connects! Would that make R^2 a field and a vector space? – vondip Dec 4 '12 at 16:11
Yes, it would, because addition in $\mathbb{R}^2$, as @DonAntonio defines it, is component ... | {
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# How many squares does a line between two points pass through?
Suppose I have a square, let's say the sides have length 1. I will then partition the square into $N^2$ sub-squares, where $N \in \mathbb{N}$ and the sub-squares are all the same size. Now, suppose we place two points $A$ and $B$ randomly within the large... | {
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-
So basically you have $N$ copies of the partitioned square (one for each $x$) and you pick the same points $A$ and $B$ in each copy and add up the total squares intersected in the copies? Also, is each partition "uniform"? i.e. the sub-squares are equal sized, like a chessboard grid etc? – Aryabhata Mar 22 '12 at 22:... | {
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The expected number of touched cells, in this approximation, would be $N E(d_M | d) + 1$.
It's not difficult to see that $X$ (absolute value of the difference of two uniform v.a) has a triangular density : $f_X(x)=2(1-x)$ The same for $Y$, and both are independent, hence: $$f_{XY}(x y)=4(1-x)(1-y)$$ on the unit square... | {
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This gets a little messy. Let's try at least some numerical values:
dd:0.8;
1.01798
Let's simulate to check: Matlab/Octave:
N=300000;
t=rand(N,4);
xy = [abs(t(:,1)-t(:,3)),abs(t(:,2)-t(:,4))];
t=[];
d2=xy(:,1).^2+xy(:,2).^2;
d=sqrt(d2);
dm=xy(:,1)+xy(:,2);
step=0.02;
dround=round(d/step)*step;
%size(dround(dround=... | {
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"openwebmath_score": 0.8774048686027527,
"tags"... |
The figure shows $E[d_M | r] / r$, ie. the factor by which the expected Manhattan distance exceeds the euclidean distance (we already knew that this must be in the $[1,\sqrt{2}]$ range).
(BTW: sorry if the formatting is not optimal, but I got sick of my Chorme crashing on the edition, lots of times, sometimes losing c... | {
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Suppose that you divide your square into $N^2$ sub-squares, where $N\in\mathbb{N}$. Then suppose that $A=(x_{1},y_{1})$ and $B=(x_{2},y_{2})$ where $x_{1},x_{2},y_{1}$ and $y_{2}$ are real numbers in $[0,1]$. Then the segment $AB$ must pass through at least $N|y_{2}-y_{1}|$ squares in the $y$ (or vertical) direction an... | {
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Then the number of squares passed through will be $D|\sin(\theta)|+D|\cos(\theta)|+1$ from Byron's work and using a right-angled triangle.
$$E[D|\sin(\theta)|+D|\cos(\theta)|+1]$$ $$= D \cdot E[|\sin(\theta)|+|\cos(\theta)|] + 1$$ $$= 4D/\pi + 1$$
Or, considering $(1/N)$ to be the length of a little square (according... | {
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"tags"... |
Playing next. B The converse of this theorem is false Note : The converse of this theorem is false. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. The converse is not always true: continuous functions may not be differentiable… Obviously this implies w... | {
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"lm_q2_score": 0.8577681122619883,
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"openwebmath_score": 0.9041855335235596,
"tag... |
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