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Let get precalculus problems solved

Studying advanced form of secondary level algebra also known as preclculus, precalculus is one of the foundational mathematical discipline. Precalculus is described as introduction for analysis. It is also a relationship between algebra and calculus.

Get help with precalculus homework help free. Precalculus is deeply explained in algebra; it presents a complete view of the trigonometry, progressing from right triangle based definitions to functions of real numbers and their graphs. Also get information on algebra word problems free

Precalculus also describes about hyperbolas, circles, trigonometric ratios, limit of a function, etc.

About factors

What is factor by grouping?

In mathematics, factoring is one of the important topic in algebra. Given expression can be factored by using the method of factoring by grouping.

The given polynomial expression can be factored by different methods that are factoring by grouping, using trinomials by ac method, and group the polynomials more than two groups. Let us solve some example problems in factoring by grouping, also get help with differentiation rules

Different steps to solve factoring using trinomials ac method are,

• Given trinomials
• Given trinomials is in the standard form ax² + bx + c.
• Multiply the coefficients a and c in the expression.
• Different ways to get the product of ac, we multiply two integers.
• If we add a and c then we get the result as equals to b means choose that way.
• Factor the expression by grouping
  
• Solve the terms.

Learning work out percentages

Introduction to How to work out percentages

In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in French). It is often denoted using the percent sign, "%", or the abbreviation "pct". For example, 45% (read as "forty-five percent") is equal to 45 / 100, or 0.45. Let us see how to work out percentages.

When estimating percentages mentally, I usually don't worry about accuracy. As I practice mentally more and more, you cal also learn multiple meaning words activities I get closer to the exact number. (...science tells that accuracy depends on the measurement tool on hand: in this case, our brain). Or, if today I'm lazy to think, I just use a calculator, or fingers to count. It doesn't matter

Hope you liked the above post, learn more about Heptagon

Polynomial Equations

A Polynomial equations is an equation that can be written in the form
axn + bxn-1 + . . . + rx + s = 0,
where a, b, . . . , r and s are constants.

We call the largest exponent of x appearing in a non-zero term of a polynomial the degree of that polynomial.


A linear equation in two variables is an equation that can be written in the form
Ax + By = C, where A and B are not both 0.

This form is called the standard form of a linear equation.

Graphing linear equations involves three steps:-

Find three ordered pair solutions.
Plot the points found in step 1. The point lines up with both the x value of the ordered pair (x-axis) and the y value of the ordered pair (y-axis).

Draw the graph: A linear equation will graph as a straight line.

Will come next with Polynomial expression.

Area of a Square formula

Area is a quantit expressing the two dimensional size of a defined part of a surface, typically a region bounded by a closed curve. Area is an important invariant in the differentialgeometry of surface.


The area of a figure measures the size of the region enclosed by the figure. This is usually expressed in terms of some square unit. A few examples of the units used are square meters, square centimeters, square inches, or square kilometers.

The area of a square can be found by multiplying the base times itself. This is similar to the area of a rectangle but the base is the same length as the height.

The area of a square formula

Area = width × height

A hexagon is a polygon with six edges and six vertices.

The area of a hexagon can be found by the formula

A=ap/2,

where a is the apothem and p is the perimeter.

A triangle is a three-sided polygon.

The area of a triangle can be found from the below formula;

A = ½*base*height

AREA OF A TRIANGLE

There are several ways to compute the area of a triangle. For instance, there's the basic formula that the area of a triangle is half the base times the height. This formula works only when you know the height and base of the triangle.

There is another area of a triangle formula known as the Heron's formula which gives the area in terms of the three sides of the triangle, specifically, as the square root of the product s(s – a)(s – b)(s – c) where s is the semiperimeter of the triangle, that is, s = (a + b + c)/2.

This formula can be used when we know two sides and the included angle of the triangle. Suppose we know the values of the two sides a and b of the triangle, and the included angle C, then we can get the area of the same triangle by applying the above formula.

Let us now calculate area of a triangle in the below examples.

Example 1) Calculate area of a triangle with base as 12cms and height as 10cms

Area of a Triangle = ½* base*height

A = ½*12*10

A = 60cms

Example 2) Calculate area of a triangle with base as 5cms and height as 8cms

Area of a Triangle = ½* base*height

A = ½5*8

A = 20cms

COMPLEX NUMBERS

Complex Numbers Definition: A complex number is a number consisting of a real and imaginary part. Complex numbers are plotted on the complex plane, on which the real part is on the horizontal axis, and the imaginary part on the vertical axis. Two complex numbers are said to be equal if and only if their real parts are equal and their imaginary parts are equal.

Complex multiplication is a more difficult operation to understand from either an algebraic or a geometric point of view. Multiplying complex numbers is accomplished in a manner similar to multiplying two binomials. You can use the FOIL process of multiplication, the distributive property, or your personal favorite means of multiplying.

The conjugate of a complex number a + bi is the complex numbers a - bi.
For example, the conjugate of 4 + 2i is 4 - 2i.

Identity Definition

An identity is a relation which is tautologically true. This is usually taken to mean something that is true by definition, either directly by the definition, or as a consequence of it. An equation which is true for every value of the variable is called an identity equation. An inequality which is true for every value of the variable is called an identity inequality.

Identity definition: Identity definition is *An identity is an equality that remains true regardless of the values of any variable that appear within it, to distinguish it from an equality which is true under more particular conditions. ... The basic Number Properties (or laws) that apply to arithmetic operations are Commutative Property, Associative Property, Identity Property and Distributive Property. When a set possesses an identity element for a given operation, the mathematical system of the set and operation is said to possess the identity property for that operation.

To know more about what are pythagorean identities click here.

EQUATION OF LINE

The general equation of a line is given by: Ax +By = C

where A, B and C are constants and A and B cannot be both zero. Any straight line in a rectangular system has an equation of this form

The slope equation of a line m can also be written as follows: Y = mx + b where m is the slope of the line and b is the y intercept of the graph of the line.

The above form is called the slope intercept form of a line.
Given below is one solved example on equation of straight line.
1) Find equation of a line that has slope m = 4 and passes through the point (–1, –6). O

Here the value of slope is given; in this case, m = 4. Also, giving a point on the line, an x-value and a y-value for this line is being provided which is x = –1 and y = –6.

In the slope-intercept form of a straight line, We have y, m, x, and b. So the only thing that we don't have so far is a value for is b (which gives me the y-intercept). Then all we need to do is plug in what is being provided for the slope and the x and y from this particular point, and then solve for b:

y = mx + b (–6) = (4)(–1) + b –6 = –4 + b –2 = b

Then the line equation must be "y = 4x – 2".

There are different types of equations like Linear Equation, Quadratic equation etc.. I will be back on detail write on these shortly....

Linear programming

Here I come with another complex topic in math. I know that sounds boring but let us try to make it simpler so that we can understand the same.

Linear programming, sometimes known as linear optimization, is the problem of maximizing or minimizing a linear function over a convex polyhedron specified by linear and non-negativity constraints. Simplistically, linear programming is the optimization of an outcome based on some set of constraints using a linear mathematical model. Linear programming in which variables may take on integer values only is known as integer programming.

The Linear Programming plan helps to maximize the profit or else minimize the cost subject to the limitations. The profit or the cost is made up of unknown quantities. These unknowns are variables of the degree; one and they are called decision variables. The profit or else the cost are a linear function of these variables. These in equations are called constraints. The linear programming simplex (LPX) is to maximize or minimize the aim function subjected to the Linear Programming constraints.

This does not end here. Lot more to come so keep in touch…. Thank you for reading this post.

Prime Factorization

In our 6th class we all must have learnt about Prime Factors, Whole number, Prime numbers etc….

Today let us discuss about Prime Factorization:

Fist let us understand what is a Prime Number?

A Prime Number is a whole number, greater than 1, that can be evenly divided only by 1 or itself.

PRIME FACTORIZATION:-

Converting the composite numbers in to multiplication of numbers is known as factorization, simplifying till the prime numbers is known as prime factorization.

See the Image below:-


"Prime Factorization" is finding which prime numbers you need to multiply together to get the original number. Converting the composite numbers in to multiplication of numbers is known as factorization, simplifying till the prime numbers is known as prime factorization.
For e.g. the Prime factors of 6 are 2 and 3 (6 = 2*3). Here both have multiplicity 1.

Integers and Properties of Integers

I am sure we all are aware about integers; Let us recollect it again...

Integers: Integers are possitive and negative numbers. E.g. ...., -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6,..... Here each negative number is paired with a positive number the same distance from 0 on a number line.

Properties of Integers:

Below are some properties of Integers:

1. The sum of two integers is a integer
2. Addition on integers is cummutative, i.e a+b = b+a for all integers a,b
3. Addition of integers is associative, i.e. (a+b)+c = a+(b+c) for all integers a,b,c.
4. The integer zero, (0), is such that a+0 = a = 0+a for any integer a.
5. For any integer a, there correcponds an integer -a such that a+(-a) = 0 =(-a) +a
6. The product of any two integers is an integer.
7. Multiplication of integer is commutative i.e. a.b = b.a for any two integers a, b.
8. Multiplication of integers is distributive over addition i.e.
9. Multiplication of integers is associative, i.e. (a.b).c = a.(b.c) for all integers a,b,c.

a.(b+c) = a.b+a.c
(b+c) . a =b.a+c.a
for all integers a,b,c

10. The integer 1 is such that a.1 = a= 1.a for any integer a.


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Empirical Probability

Empirical probability, also known as relative frequency or experimental probability, is the ratio of the number favorable outcomes to the total number of trials, not in a sample space but in an actual sequence of experiments. In a more general sense, empirical probability estimates probabilities from experience and observation.

An advantage of estimating probabilities using empirical probabilities is that this procedure is relatively free of assumptions. For example, consider estimating the probability among a population of men that they satisfy two conditions:

1. they are over 6 feet in height;
2. that they prefer strawberry jam to raspberry jam.

A direct estimate could be found by counting the number of men who satisfy both conditions to give the empirical probability the combined condition. An alternative estimate could be found by multiplying the proportion of men who are over 6 feet in height with the proportion of men who prefer strawberry jam to raspberry jam, but this estimate relies on the assumption that the two conditions are statistically independent.

Subtraction

Subtraction is inverse function of addition. If any number that is added with its own inverse the result will be zero. If the number is subtracting with the lesser number then the result is positive. If the number is subtracting with the larger value then the result is negative value.

Subtraction is used to model four related processes:

1. From a given collection, take away (subtract) a given number of objects. For example, 5 apples minus 2 apples leaves 3 apples.

2. From a given measurement, take away a quantity measured in the same units. If I weigh 200 pounds, and lose 10 pounds, then I weigh 200 − 10 = 190 pounds.

3. Compare two like quantities to find the difference between them. For example, the difference between $800 and $600 is $800 − $600 = $200. Also known as comparative subtraction.

4. To find the distance between two locations at a fixed distance from starting point. For example if, on a given highway, you see a mileage marker that says 150 miles and later see a mileage marker that says 160 miles, you have traveled 160 − 150 = 10 miles.