Fifth Grade Math

--> Fifth Grade Math:Let us see one example of fifth grade math,we can solve one problem here, 1. Find the value of s in the given expression if t = 10. s= t
Solution
Given t = 10
The equation is s = t
s = t + 12
Substitute the value of t
s= 10+12
s = 22.Let us now learn the definition of an acute angle,acute definition- The acute angle is the type of angle which measures the angle between 0 to 90 degree and less than the 90 degree. I hope the above explanation was useful.

Regular Polygon

Regular Polygon:A polygon is a 2-dimensional object; it is a plane shape with straight sides.Commonly A Regular Polygon has included the following two conditions: All sides are equal, and all angles are equal.Examples for regular polygons: Like that triangles, squares (quadrilateral), pentagons, hexagons and so on.The area of polygon measures the size of the region enclosed by the polygon. This is usually expressed in terms of some square unit.The area regular polygon is equal to the number of triangles formed by the radii times their height.Hope you like the above example of Regular Polygon.

Area of a Circle

Area of a circle:Introduction to area of a circle:Area is the measure of surface occupied by an object. The standard unit for measurement of area is metres quare (m2).However the area of smaller dimensions can be expressed in mm2 or cm2. The areas of large dimensions can be expressed in acre or hectare.We can find the area of a circle by using the formula as, A=πr2.Here r is the radius of a circle.It is easy to find the area of a circle by applying the formula given above.Hope you like the above example of Area of a circle.Please leave your comments, if you have any doubts.

Algebra equation

Algebra equation solver:Let us understand what we mean by the concept of algebraic equation.Every algebraic equation of degree n ≥ 1 has a root real or complex.An algebraic equation solver is a statement where two algebraic expressions are equal.We can understand this concept better with the help of an Algebra equations examples.
Some Problems:

1) Sum of a number and three is 5

Solution: x+3 = 5 where x is the number

Vertical Tangent

Vertical Tangent:

In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that "just touches" the curve at that point (in the sense explained more precisely below). As it passes through the point where the tangent line and the curve meet, or the point of tangency, the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point.


In mathematics, a vertical tangent is tangent line to be vertical. Since a vertical line contain infinite slope, a function whose graph contain a vertical tangent be not differentiable on the point of tangency. During the definition of the slope, vertical lines are excluded. Although from a simply geometric point of view, a curve might contain a vertical tangent. Imagine of a circle (with two vertical tangent lines). We still contain an equation, namely x=c, except it be not of the form y = ax+b.In fact, such tangent lines contain an infinite slope.
Limit Definition of Vertical Tangent

A function ƒ have a vertical tangent on x = a. Condition the difference quotient use to identify the derivative have infinite limit:

[lim_(h->0)(f(a+h)-f(a))/(h)=+oo] (or [lim_(h->0)(f(a+h)-f(a))/(h)=-oo]

The first case corresponds toward an upward-sloping vertical tangent, with the second case toward a downward-sloping vertical tangent. Easily speaking, the graph of ƒ have a vertical tangent at x = a condition the derivative of ƒ on a be either positive or negative infinity.



Used for a continuous function, it is often possible toward detect a vertical tangent through taking the limit of the derivative.

if [lim_(x->a)f'(x)=+oo]

After that ƒ have to contain an upward-sloping vertical tangent at x = a. In the same way, if

if [lim_(x->a)f'(x)=-oo]

then ƒ have to contain an downward-sloping vertical tangent at x = a. Within these situations, the vertical tangent toward ƒ appears since a vertical asymptote on the graph of the derivative.Let us now look at few examples of Vertical Tangents.

Examples of Vertical Tangent

Example 1 for vertical tangent

The function

[f(x) = root(4)(x)]

have a vertical tangent at x = 0, while it is continuous also

[lim_(x->0)f'(x)=lim_(x->0)(1)/root(4)(x^2)=oo]

[g(x)=root(4)(x^2)]

Have a vertical cusp on x = 0, given that it be continuous,

[lim_(x->0)g'(x)=lim_(x->0)(1)/root(4)(x)=+oo]

[lim_(x->0^-)g'(x)=lim_(x->0^-)(1)/root(4)(x)=-oo]

Example 2 for vertical tangent

What value of x does the function (you mean the graph of the equation) 5x^2+2xy+y^2=36 have a vertical tangent line?

Solution

5x^2 + 2xy + y^2 = 36
and put y = -x
5x^2 - 2x^2 + x^2 = 36
4x^2 = 36
x^2 = 9
x = +3,-3


Hope you like the above example of Vertical Tangent.Please leave your comments, if you have any doubts.

Angles

Angles:


In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (see "Measuring angles", below). Where there is no possibility of confusion, the term "angle" is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity).

The word angle comes from the Latin word angulus, meaning "a corner". The word angulus is a diminutive, of which the primitive form, angus, does not occur in Latin. Cognate words are the Greek (ankylοs), meaning "crooked, curved," and the English word "ankle." Both are connected with the Proto-Indo-European root *ank-, meaning "to bend" or "bow".

Let OA and OB two half lines with common end point O. The half lines OA and OB are the sides of an angle and the point O is the vertex of the angle. An angle is an amount of rotation of a half-line (or ray) in a plane about its end point from an initial position to a terminal position.We usually come across the questions such as how to measure an angle,what are the various methods to measure and angle etc,the explanation to these questions is given below.



Measurement of angle

The amount of rotation from initial side to terminal is called the measure of an angle.
Positive and Negative angles

Angles that are formed by counter clockwise (anti clockwise) rotation, such as the one shown in fig (ii) are said to be positive or to have positive measure.
Angles that are formed by a clockwise rotation, like the one in fig(iii) are said to be negative or to have negative measure.
Lines at right angles

The lines are said to be at right angles if the rotating half line (or ray) from starting from initial position to the final position describes one quarter of a circle.


Hope you like the above example of Angles.Please leave your comments, if you have any doubts.

Coefficients

Coefficients:

Introduction to coefficient:

In simple terms the meaning of a coefficient is,a factor that contributes to produce a result.In mathematics, a coefficient is a multiplicative factor in some term of an expression (or of a series); it is usually a number, but in any case does not involve any variables of the expression. For instance in

7x2 − 3xy + 1.5 + y

the first three terms respectively have coefficients 7, −3, and 1.5 (in the third term there are no variables, so the coefficient is the term itself; it is called the constant term or constant coefficient of this expression). The final term does not have any explicitly written coefficient, but is usually considered to have coefficient 1, since multiplying by that factor would not change the term. Often coefficients are numbers as in this example, although they could be parameters of the problem, as a, b, and c in

ax2 + bx + c

when it is understood that these are not considered as variables.Also it is defined as the number in front of the variable is called as coefficient. For example 2x is the given expression here the coefficient is 2. The coefficient is usually in numeral with the variable. The expression contains variable and coefficient of the variable.The other way we can learn about a coefficient is by solving few example problems related to coefficient.
Example Problem for the Coefficient:

Example 1:

Find the coefficient of the variables in the given expression:

X + 2y

Solution:

Given that X + 2y

Here x and 2y is the expression with the coefficient

The coefficient of x is 1

The coefficient of y is 2.

Example 2:

Find the coefficient of variables in the given expression:

Y2 + 2y + 3xy +1

Solution:

Given that Y2 + 2y + 3xy +1

Here y2 , 2y, 3xy, is the expression with the coefficient and 1 is with out variable

The 3xy having two variables that two variable consider as a one variable

1 is the constant term of the given expression

The coefficient of y2 is 1

The coefficient of 2y is 2

The coefficient of 3xy is 3

Example 3:

Find the coefficient of variables in the given expression:

Z5 + z + y +6y

Solution:

Given that Z5 + z + y +6y

Here z5, z, y, 6y is the expression with the coefficient

The coefficient of z5 is 1

The coefficient of z is 1

The coefficient of y is 1

The coefficient of 6y is 6.
Example Problem for the Coefficient:

Example 4:

Find the coefficient of variables in the given expression:

X3 + y 5 +2xy + 5yx

Solution:

Given that X3 + y 5 +2xy + 5yx

Here X3, y 5, 2xy, 5yx the expression with the coefficient

The coefficient of x3 is 1

The coefficient of y5 is 1

The coefficient of 2xy is 2

The coefficient of 5yx is 5.

Example 5:

Find the coefficient of variables in the given expression:

100x2 + 2z3 + 102z

Solution:

Given that 100x2 + 2z3 + 102z

Here 100x2, 2z3, 102z the expression with the coefficient

The coefficient of 100x2 is 100

The coefficient of 2z3 is 2

The coefficient of 102z is 102.