Rules of Exponents

Topic: Exponents
Exponentiation is a mathematical operation, written aⁿ, involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication:

Here are some examples:

1.)Addition:An exponent can be added only when they have the same number.

For example: 2x1 + 2x1 = 4x1

   3x2 - 2x2 = 5x2


2.)Subtraction:The rule is same for subtraction.


3.)Multiplication:While multiplying, multiply the numbers and add the exponents.

For example: 3x1 * 2x1 = 6x2 (Add)

    4x2 * 3x3 = 12x5 (Add)


4.)Division:While dividing the exponents, the denominator takes the opposite sign and m

and mover to the numerator. The numbers should be divided as usual.

For example:

    36x8-4
 ___________ = 6x4
      64


     48x2+4
 ___________ = 8x6
     6x-4           

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problem on simple interest

Topic:- simple interest

Interest is a fee paid on borrowed assets. It is the price paid for the use of borrowed money or, money earned by deposited funds. Assets that are sometimes lent with interest include money, shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements.

Let's see a problem on this.

Question:

Greg invests $1200 at an annual rate of 6.5%. How long will it take until Greg earns $195 in interest?

Solution:

Formula to find the interest is

I = PTR/100

here p = profit=1200
   t = time
   r = rate=6.5

Substitute the values in formula,so that

        (1200 x T x 6.5)
195 = -----------------
             100

         T = 2.4

Greg will earn $195 in interest in 2.5 years.

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additoin of exponentials

Topic:- exponentials

Let's see what is exponent first, generally

BaseExponent

The exponent tells us how many times the base is used as a factor.

For example, to write 2 as a factor one million times, the base is 2, and the exponent is 1,000,000. We write this number in exponential form as follows:

2

1,000,000

read as two raised to the millionth power

This math help gives a example problem on addition of exponents.

Question:-

-3 z6(b3y2z2)

Answer:-

-3 z6(b3y2z2)
                   
Here we have 'z' for twice ,
So we can put them as 1 term by
additing the exponentials

we can add them by using exponent rule

formula of exponent

    am * a n = a m+n
So,
    -3 (z6+2*b3*y2)

    -3 (z8*b3*y2)

      -3z6+2*b3*y2 is the Answer

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Topic:Probability

Probability, is a way of expressing knowledge or belief that an event will occur or has occurred.

Here is some probability problems ,which help you to understand the concept much better.

Questions & Answers

1- Mr. Johnson taught a music class for 25 students under the age of ten. He randomlychose one of them. What was the probability that the student was under twelve?

Ans:-

The probability that the student was under twelve was 25/25, so P = 1.

2- The compact disk Jane bought had 12 songs. The first four were rock music. Tracks
number 5 through 12 were ballads. She selected the random function in her Compact
Disk Player. What is the probability of first listening to a balla?

Ans:-

The probability of listening to a ballad is 8/12, so P = 0.67.

I hope it helped you ,for more math help ,you can reply me.

Problem on Solving a Function and Show Graphical Representation for the Function

Relations and functions are the dependent concepts of math where the value of a variable is dependent on the other variable in the given function. It is expressed in terms of graphical representation as shown in the below example

Topic : Solving a Function and expressing graphically

In the given function variable 'x' is the independent value and y is the dependent one.

Problem : a) If y = √x −1, Find the values for x = 0, 1, 2, 3, 4.Round to three decimal places where necessary.
b) Explain why no negative values are chosen as values to substitute
in for x.
c) Draw a graphical representation for the values.

(a)Solution :

When x = 0
y = √x – 1
= √0 – 1
= 0 – 1
= -1

When x = 1
y = √x – 1
= √1 – 1
= 1 – 1 and y = -1 - 1
= 0 and y = -2

When x = 2
y = √x – 1
= √2 – 1
= 1.414 – 1 and y = -1.414 - 1
= 0.414 and y = -2.414

When x = 3
y = √x – 1
= √3 – 1
= 1.732 – 1 and y = -1.732 - 1
= 0.732 and y = -2.732

When x = 4
y = √x – 1
= √4 – 1
= 2 – 1 and y = -2 - 1
= 1 and y = -3

(b) Solution :
No negative values are chosen for x because square root of a negative
number is imaginary and is not defined in real space.

(c) Solution :

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A Question on Rightangle Triangle and Find length of a Side

On a Right angled triangle, number of theorem are derived. One such theorem is Mid point Theorem, with below example theorem is very well explained.

Topic : Right angle Triangle and Mid Point Theorem

Problem : Given angle C is a right angle, E is a midpoint of AC, F is the midpoint of BC, AF = √41, BE = 2√26, Find AB

Solution :













From the figure,
In ∆ACF
AC² + CF² = AF² (by Pythagoras Theorem)
AC² + (CB/2)² = (√41)² (as CF is half of CB)
AC² + CB²/4 = 41

Now in ∆ECB
EC² + CB² = EB²
(AC/2)² + CB² = (2√26)² (as EC is half of AC)
AC²/4 + CB² = 104

Now adding both the equations, we get
AC² + CB²/4 + AC²/4 + CB² = 41 + 104
(1+1/4)AC² + (1+1/4)CB² = 145
5AC²/4 + 5CB²/4 = 145
5/4(AC² + CB²) = 145
Now, in ∆ACB, AC² + CB² = AB²

So we get, 5/4 AB² = 145
AB² = 145 * 4/5
AB² = 116
AB = √116
AB = 2√29

Hope the above elaborated explanation will help you to understand mid point theorem and help you to solve similar kind of problems.

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