Circles

Circles:
The different situations that can arise when a circle and a line
are given in a plane.
So, let us consider a circle and a line PQ. There can be three possibilities given
in Fig. below:

The line PQ and the circle have no common point. In this case,
PQ is called a non-intersecting line with respect to the circle. In above Fig. (ii), there
are two common points A and B that the line PQ and the circle have. In this case, we
call the line PQ a secant of the circle. In Fig. 10.1 (iii), there is only one point A which
is common to the line PQ and the circle. In this case, the line is called a tangent to the
circle.
The tangent to a circle is a special case of the secant, when the two end
points of its corresponding chord coincide.

Matrices

The knowledge of matrices is necessary in various branches of mathematics.

Matrices are one of the most powerful tools in mathematics.
This mathematical tool simplifies our work to a great extent when compared with other straight forward methods. The evolution of concept of matrices is the result of an attempt to obtain compact and simple methods of solving system of linear equations. Matrices are not only used as a representation of the coefficients in system of linear equations, but utility of matrices
far exceeds that use. Matrix notation and operations are used in electronic spreadsheet
programs for personal computer, which in turn is used in different areas of business
and science like budgeting, sales projection, cost estimation, analyzing the results of an
experiment etc. Also, many physical operations such as magnification, rotation and
reflection through a plane can be represented mathematically by matrices. Matrices
are also used in cryptography. This mathematical tool is not only used in certain branches
of sciences, but also in genetics, economics, sociology, modern psychology and industrial
management.

Example 1:
Consider the following information regarding the number of men and women
workers in three factories I, II and III
Men workers Women workers
I 30 25
II 25 31
III 27 26
Represent the above information in the form of a 3 × 2 matrix. What does the entry
in the third row and second column represent?

MATHEMATICS
Solution The information is represented in the form of a 3 × 2 matrix as follows:



30 25
A=25 31
21 26


The entry in the third row and second column represents the number of women
workers in factory III.

arithmetic reasoning help problems

Arithmetic reasoning help is for students who are preparing for test or competitive exams.We will have 4 options for each question ,in which we have to choose one correct answer.Let's see one of these kind of examples.

Question:-

A doctor can treat 4 cancer patients per hour; however stroke patients need 3 times as much of the doc's time. If the doctor treats patients 6 hours a day and has already treated 10 cancer patients and 3 stroke patients today, how many more stroke patients can the doctor treat?

A.1 B.2 C.3 D. 5

Answer:-

Let's see what is an expert online tutor explain us.

5,5' is the average of 5' and 6': (5 + 6)/2 = 5,5

One would expect that the height of the average is the average of the heights:Height converter will help us with this.

(110 + 170)/2 = 140



HEIGHT WEIGHT
5' 110
6' 170

?

I could just multiply 5x60 to find the LBS of a 5' person, why is this given? I tell you, that's "military math"...

Anyway, let's talk about that doctor:

"4 cancer patients per hour" => one quarter of an hour per cancer patient.

"3 times as much" for stroke patients => three quarters of an hour per stroke patient.

"has already treated 10 cancer patients and 3 stroke patients today" => has already consumed 10 quarters plus 3x3=9 quarters of his time. Makes 19 quarters altogether.

"the doctor treats patients 6 hours a day" => the doctors has 6x4=24 quarters of an hour at his disposal per day.

But he already spent 19 quarters => he has 24-19=5 quarters of an hour still available today.

How many stroke patients fit in 5 quarters of an hour? You already know from above that each stroke patient consumes 3 quarters.

So the answer is "c".

How to find the equation of a line which is passing through two points

Question:-

Find the equation of line passing through the points(-1,7)and (0,15)

Answer:-

Step 1:-

finding the slope of line = m

                      y2-y1     15-7         8
Formula to find slope ------- = ------- = ------ = 8
                      x2-x1     0-(-1)      0+1

so ,slope of a line is 8

step 2:-

The point slope form of equation (y-y1)=m(x-x1)

We know that (x1,y1) is (-1,7)

and m=8

So (y-7)=m-(x-(-1))

(y-7)=8(x+1)

y-7=8x+8
+7   +7
---------
y=8x+15

step 3:-

The equation of the line becomes

             y=8x+15

For more help on this,you can reply me.

How to find intersection point of two lines

Topic:-Intersection Point

a point where lines intersect

point - a geometric element that has position but no extension; "a point is defined by its coordinates"

Let's see how to find this intersection point of two lines

Question:-

Find the intersection point of two lines

3x+2y=5 and x+4y=0


Answer:-

Let's say


3x+2y=5 ---------> 1

x+4y=0 ---------->2


Take the equation 2

x+4y=0

x= -4y----->3

Substitute this in equation 1

We get

3(-4y)+2y=5

-12y+2y=5

-10y=5

y= 5/-10

y= - ½

Substitute this in 3

x= -4(-½)

x= 2

So ,The intersection point is

(2,-½)


For more help on this ,you can reply me.

a problem on inequality

Topic:-Inequality
What is inequality is defined along with a example in this math help
An inequality is a statement about the relative size or order of two objects, or about whether they are the same or not (See also: equality). Inequality rules are

• The notation a < b means that a is less than b.
• The notation a > b means that a is greater than b.
• The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size.

In each statement above, a is not equal to b. These relations are known as strict inequalities. The notation a < b may also be read as "a is strictly less than b".

Question:-

Solve the following inequality

y-7 > -12


Answer:-
 y-7 > -12

add 7 on both sides

y-7+7 > -12+7

 y > -5

So y є (-5,∞) is the Answer  

For more help on this ,Please reply me.

problem on Angular speed

Topic :- Angular speed of EarthThe Earth turns toward the east, we see the sky
turning toward the west at this same rate.Then how to find angular speed for it.Let's look at it.

Question:"Find the angular speed of the Earth's rotation on it's axis",
Answer:-

The earth rotate once about it's axis in 24 hours

That is 2π radians in 24 hours.

Therefore angular speed =


      2π
    ------  rad/hour
      24

    Lets see how to convert in seconds


       2π
  =  ----------
      24*60*60

  = 7.272*10-5rad/sec

So the angular speed of earth is7.272*10-5rad/sec
.

For similar kind of help ,you can reply me.