## Example : Logical Operators

// Working of logical operators#include <stdio.h>int main

**Output**

&& is 1 && is 0 || is 1 || is 0 ! is 1 ! is 0

**Explanation of logical operator program**

- && evaluates to 1 because both operands and is 1 .
- && evaluates to 0 because operand is 0 .
- || evaluates to 1 because is 1 .
- || evaluates to 0 because both operand and are 0 .
- ! evaluates to 1 because operand is 0 . Hence, ! is 1 .
- ! evaluates to 0 because is 1 . Hence, ! is 0 .

## What Does A Closed Dot Mean In Math

**closed****dot means****dot means****dots****means**

1) Draw a **number line**. 2) Put either an open circle or a **closed dot** above the **number** given. For and , use a **closed dot** to indicate the **number** itself is part of the solution. For < and >, use an open circle to indicate the **number** itself is not part of the solution.

One may also ask, what do open and closed circles mean in limits? An **open circle** represents a hole in a function, which is one specific value of x that **does** not have a value of f. With **limits**, the **limit** exists as long as the **limit** from the left is equal to the **limit** from the right.

Subsequently, one may also ask, is a closed dot a bracket?

You use **brackets** when you want to include the endpoint, and you denote this with a **closed** circle/**dot**. On the other hand, if you want to exclude the endpoint, you use a parenthesis, which is shown by an open circle.

What does a dot mean in a math equation?

In **mathematics** and scienceIn **mathematics**, a small middle **dot** can be used to represent product; for example, x y for the product of x and y. When dealing with scalars, it is interchangeable with the multiplication sign: x y means the same thing as x × y, but × is easily confused with the letter x.

## E In Scientific Notation And The Meaning Of 1e6

You don’t need a calculator to use E to express a number in scientific notation. You can simply let E stand for the base root of an exponent, but only when the base is 10. You wouldn’t use E to stand for base 8, 4 or any other base, especially if the base is Euler’s number, e.

When you use E in this way, you write the number *x*E*y*, where *x* is the first set of integers in the number and *y* is the exponent. For example, you would write the number 1 million as 1E6. In regular scientific notation, this is 1 × 106, or 1 followed by 6 zeros. Similarly 5 million would be 5E6, and 42,732 would be 4.27E4. When writing a number in scientific notation, whether you use E or not, you usually round to two decimal places.

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## Measurement Of Line Segment

A ruler is an instrument used in geometry. We use a ruler to draw a line segment. ;We use it also to measure length of a line segment.

A ruler is generally 1 ft long and is called One foot ruler. Sometime it is simply called scale. Some rulers are six inches long and are called half foot ruler. One edge of a ruler has scales marked in inches and the other edge has scales marked in cm.

We place the ruler with its edge along the line-segment AB with the zero mark of the ruler at the start point A of the line-segment. We read the mark on the ruler at the other endpoint B of the line-segment.

## Examples Of End Point In A Sentence

*end point **Curbed**end point **Washington Post**end point **The Arizona Republic**end point**Forbes**end point**The New Yorker**end point **oregonlive**end point **San Diego Union-Tribune**end point **courant.com*

These example sentences are selected automatically from various online news sources to reflect current usage of the word end point. Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

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## Addition And Subtraction Of Segments

Figure 4 illustrates three collinear points E, F, and G forming a segment.

Points E and G constitute the endpoints of the segment which is and point F in between divides into two segments: and . The sum of the lengths of and is equal to the length of . Therefore, ** + = ** . The expression represents a segment if point F is between Points E and G.

The following expressions are also true for the lengths of the segments:

**Find the length of in the figure.**

## Where Does Euler’s Number E Come From

The number represented by e was discovered by mathematician Leonard Euler as a solution to a problem posed by another mathematician, Jacob Bernoulli, 50 years earlier. Bernoulli’s problem was a financial one.

Suppose you put $1,000 in a bank that pays 100% annual compound interest and leave it there for a year. You’ll have $2,000. Now suppose the interest rate is half that, but the bank pays it twice a year. At the end of a year, you’d have $2,250. Now suppose the bank paid only 8.33%, which is 1/12 of 100%, but paid it 12 times a year. At the end of the year, you’d have $2,613. The general equation for this progression is:

where *r* is 1 and n is the payment period.

It turns out that, as n approaches infinity, the result gets closer and closer to e, which is 2.7182818284 to 10 decimal places. This is how Euler discovered it. The maximum return you could get on an investment of $1,000 in one year would be $2,718.

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## Example : Arithmetic Operators

// Working of arithmetic operators#include <stdio.h>int main

**Output**

a+b = 13a-b = 5a*b = 36a/b = 2Remainder when a divided by b=1

The operators +, – and * computes addition, subtraction, and multiplication respectively as you might have expected.

In normal calculation, 9/4 = 2.25. However, the output is 2 in the program.

It is because both the variables a and b are integers. Hence, the output is also an integer. The compiler neglects the term after the decimal point and shows answer 2 instead of 2.25.

The modulo operator % computes the remainder. When a=9 is divided by b=4, the remainder is 1. The % operator can only be used with integers.

Suppose a = 5.0, b = 2.0, c = 5 and d = 2. Then in C programming,

// Either one of the operands is a floating-point numbera/b = 2.5 a/d = 2.5 c/b = 2.5 // Both operands are integersc/d = 2

## That Is A Lot Of Adding Up

But we don’t have to add them up, as there is a “shortcut”, because …

… finding an Integral is the **reverse** of finding a Derivative.

Like here:

An integral of 2x is x2 …

… because the derivative of x2 is 2x

That simple example can be confirmed by calculating the area:

Area of triangle = *1***2** = *1***2** = x2

Integration can sometimes be that easy!

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## Now For An Increasing Flow Rate

Imagine the flow starts at 0 and gradually increases :

As;the;flow rate increases, the tank fills up faster and faster:

- Integration: With a flow rate of
**2x**, the tank volume increases by**x2** - Derivative: If the tank volume increases by
**x2**, then the flow rate must be**2x**

We can write it down this way:

The integral of the flow rate | ; |

## Naming Objects Using Endpoints

Many objects in geometry such as line segments, angles, polygons, etc., can be named using endpoints:

Points A and B are endpoints for the line segment below. The line segment is named by its endpoints, AB or BA.

A ray on the other hand, has only one endpoint as shown below. The ray is named using its endpoint as the first letter, AB.

An angle can be named using the common endpoint of the two rays, as shown below. Rays AB and BC share endpoint B and form an angle. This angle can be named as ABC or, using just its endpoint, as B.

A polygon is formed by three or more-line segments. The polygon below, called a quadrilateral, is formed by segments AB, BC, CD, and AD, called sides. Each side intersects two other sides, at each endpoint. One way to name a polygon involves listing the endpoints of the polygon in sequence; the polygon below can be named ABCD or BCDA, among other names.

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## What Does This C Symbol Mean

- 1Nov 17 ’18 at 2:11
- $\begingroup$$\mathrm_n^k$ refers to the binomial coefficient $\binom$.$\endgroup$Nov 17 ’18 at 2:11
- $\begingroup$The larger number appears on the top and smaller on the bottom for that symbol.$\endgroup$Nov 17 ’18 at 2:11
- 2$\begingroup$I will point out that there are a good dozen or so notations for the binomial coefficient. Some people notate it as $C^n_k$ while other people notate it as $C^k_n$, both to mean the algebraic expression $\frac$. It is unfortunate that there are so many conflicting notations, which is why I strongly recommend swapping to the superior and the seemingly more common notation $\binom$ to avoid confusion.$\endgroup$

## Definition Of End Point

Any of the two furthest points on a line segment. See: Line Segment · Line in Geometry · Search Index;

#### 7. Opposite Rays in Geometry: Definition & Example Video & Lesson

#### 8. What is Acute Angle? Definition, Facts & Example

Definition of Acute Angle explained with real life illustrated examples. In geometry, two rays sharing a common endpoint form an angle. define acute angle;

#### 9. Arc Math word definition Math Open Reference

Arc. Definition: A portion of the circumference of a circle. Try this Drag one of the orange dots that define the endpoints of the blue arc. The arc will change;

#### 10. K-5 Definitions of Math Terms

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## Terms You Need To Know

#### Point:

A point shows location and has no size or dimension. A point is represented by a dot and is usually named with a letter of choice. In the graphic below, the points are labelled by a nearby letter.

#### Line:

A line is a set of points extends in two opposite directions without end. A line is one-dimensional and has no width. It is identified by naming two points on the line or by writing a lowercase letter of choice after the line.

The notation, for example, AB , is read as line AB and refers to the line that has points A and B.

#### Plane:

A plane is a flat surface that has no thickness and extends without ending in ALL directions. It is a two-dimensional object. A plane is represented by a parallelogram and may be named by writing an uppercase letter of choice in one of its corners. I will go into detail about what a parallelogram is in future lessons. For now, think of a parallelogram as a window pane.For simplicity, you might want to think of a plane as an infinitely large sheet of paper.

The diagram below shows three points, a line, and a plane.

#### Line Segment:

A line line segment is part of a line having two points, called endpoints. It also has points between the endpoints. A line segment does not have a set of CONTINUOUS points like a line does. Endpoint means that a line has a beginning and an end. The notation for a line segment in a bar over any letter of choice. Say AB has a bar over it, you would read it as line segment AB.

#### Ray:

## How To Use ‘if And Only If’ In Mathematics

- M.S., Mathematics, Purdue University
- B.A., Mathematics, Physics, and Chemistry, Anderson University

When reading about statistics and mathematics, one phrase that regularly shows up is if and only if. This phrase particularly appears within statements of mathematical theorems or proofs. But what, precisely, does this statement mean?

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## Half Closed Interval Notation

Since we denote an open interval by and a closed interval by , we denote a half-closed interval by a mixture of those two notations. Imagine your interval has endpoints a and b:

- If a is included and b isnt, we can say the interval is [a,b).
- If b is included and a isnt, we write it as (a,b].

It looks like mismatched brackets, but its really just a clever way of denoting which side is in the interval and which side isnt.

Theres one more way of denoting open intervals which you may not have come across yet: with backward square brackets. Using that notation, your half closed intervals become a,b].

Here we use mathematical set notation to define these phrases:

## As A Degenerate Ellipse

A line segment can be viewed as a degenerate case of an ellipse, in which the semiminor axis goes to zero, the foci go to the endpoints, and the eccentricity goes to one. A standard definition of an ellipse is the set of points for which the sum of a points distances to two foci is a constant; if this constant equals the distance between the foci, the line segment is the result. A complete orbit of this ellipse traverses the line segment twice. As a degenerate orbit, this is a radial elliptic trajectory.

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## What Does Twice A Number Mean In Math

**4.3/5****Twice a number****means****Twice means****number****mean****twice****means**

“As many” **means** the same **number**. **Twice** as many **means** two times as many. From there we pretty **much** the **number** followed by ” as many”, Like “15 times as many” is a=15b.

Secondly, what does 5 more than twice mean? Next, “**twice** a number” **means** to multiply the number by 2 giving: 2×n or 2n or 2n. **Then**, “five **more than**” **means** to add **5** to what follows or: 2n+**5**.

Then, how do you write 5 more than twice a number?

Solution: Let g represent the **number** of groups in Ms. Jensen’s class. **Then** 2 · g, or 2g can represent “g groups of 2 students”. Search form.

## What Is An Endpoint And Do You Need An Endpoint Data Protection Solution

Jargon abounds in the technical world of IT, with obscure-but-precise language sometimes getting in the way of conceptual understanding. The term endpoint fits the bill. While it may make sense to a seasoned IT professional, the rest of us may need a little help. What exactly is an endpoint, why does it matter, and do you need an endpoint backup solution?

According to Wikipedia, Endpoint is a hardcore punk band from Louisville, Kentucky. A more common definition for endpoint in computer networking, architecture, and operations, however, is a mobile device such as a laptop, phone, or tablet.

The term has its origin in reference to computer networks. The endpoint is a device or node that connects to the LAN or WAN and accepts communications back and forth across the network. In a traditional sense, an endpoint can be a modem, hub, bridge, or switch. It also could be data terminal equipment or a host computer .

Yet today, endpoint is used most commonly in network security and end-user mobility circles to mean any device outside the corporate firewall. This could be laptops, tablets, or mobile phones on the edge of the network, which individuals connect to the central network.

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## Member And Pointer Operators

Operator name | ||
---|---|---|

Indirection | *a | |

Structure dereference | a->b | |

Structure reference | a.b | |

Member selected by pointer-to-memberb of object pointed to by a | a->*b | R&operator->*; |

Member of object a selected by pointer-to-memberb | a.*b |

RK::operator; | N/A |

explicitK::operatorR;since C++11 | N/A |

void*K::operatornew; | void*operatornew; |

voidK::operatordelete; | voidoperatordelete; |

Exception check | N/A |

Notes:

**^**The modulus operator works just with integer operands, for floating point numbers a library function must be used instead .

**^**About C++20 three-way comparison

**a***In the context of iostreams, writers often will refer to << and >> as the “put-to” or “stream insertion” and “get-from” or “stream extraction” operators, respectively.*

**b**

**a***According to the C99 standard, the right shift of a negative number is implementation defined. Most implementations, e.g., the GCC, use an arithmetic shift , but a logical shift is possible.*

**b****^**The return type of operator-> must be a type for which the -> operation can be applied, such as a pointer type. If x is of type C where C overloads operator->, x->y gets expanded to x.operator->->y.

**^**Meyers, Scott , “Implementing operator->* for Smart Pointers”,

*Dr. Dobb’s Journal*, Aristeia.

**^**The parentheses are not necessary when taking the size of a value, only when taking the size of a type. However, they are usually used regardless.

**^**C++ defines alignof operator, whereas C defines _Alignof. Both operators have the same semantics.

## What Are The Opposite Rays In Geometry

Opposite Rays are those 2 rays that start exactly from the same point but continues to the opposite direction. Take an example of the below Opposite Rays:

The start point for the Rays **ZX;**and;**ZY;**is;**Z, **and then they both go the opposite direction that makes 2 opposite rays: ZX and ZY.

#### Points to Remember about Opposite Rays

- Both Rays must Start from the same point
- Must go the opposite direction
- Must form a line

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