How to Find Inverse Variation

The inverse variation is the product of two variables equals to a constant and the product is not equal to zero. Inverse variation is in the form of y =k/x. xy = k. Inverse variation in which value of one variable increases while the value of the other  variable decreases in value is known as an inverse variation. For example think a trip of 240 miles. Rate(mph)=>20,30,40,60,80,120 and time(h)=>12,8,6,4,3,2.The numbers can be explained. As the rate of speed increase, the numbers of hour require decrease. As the rate of speed decrease, the number of hour requires increase. contrasting in a direct variation, the ratio in each data is not equivalent. The product of the value in each is equal.

Problem on how to find inverse variation:-

Problem 1:-

If y is inversely proportional to find inverse variation x and y = 10 when x = 2. Find the value of y, when x = 15?

Let, k = x/y

Plug x = 2 and y = 10 in the above equation

k = 10/2

k = 5

Now the equation becomes 3 = x/y

Now, plug x = 15

3 = y/15

3 * 15 = y

So, y = 45 when x = 15

Problem 2:-

find inverse variation F vary inversely with the square of m. if F=15 when m=3,find F when m=5?

Solution:-

F=K/m2

15=K/32

15=K/9

K=135

F=135/m2

F=135/52

=135/25

=5.4..

Problem in Equation on how to find inverse variation:-

Find inverse variation problem:-

Complete the table in support of the positive values of x so that yoo (1)/(x^2)

Table

Find the x value using inverse variation method

Solution:-

If yoo (1)/(x^2)then y =(k)/(x^2)

But y =100 when x = 3

Therefore 100 =(k)/(9)

That is k = 900 so y =(900)/(x^2)

When x = 5, y =(900)/(25) = 36

If x = 10, y =(900)/(100) = 9

And if x = 15, y = (900)/(25) = 4

If y = 25, 25 =(900)/(x^2)

That is 25x2 =900

x2 =(900)/(25) = 36

Table

So that answer x = 6.

Algebra Probability Problems

Probability is used to find the possible outcomes in an event. It is defined as the ratio between the numbers of favorable outcomes to the total number of outcomes. The value of probability lies only between 0 and 1. It is not greater than 1.There are several types of probability. They are Conditional probability and Theoretical probability. Conditional probability occurs when an other event is already occurred and changed the sample space. Theoretical probability occurs based on the probability principles.

PROBABILITY BASIC PROBLEMS

Problem 1:

A number is drawn from 1 to 12 at random. What is the probability of finding a number 7.

Solution:

From 1 to 12 there will be 12 numbers. So the total outcome is 12. Number 7 occurs only once. So the favorable outcome is 1.

Hence the answer is 1/12

Problem 2:

A bag contains 7 black, 8 blue and 11 green marbles. A marble is drawn at random. What is P (blue)?

Solution:

Total marbles in the bag = 7+8+11 = 26

Out of which number of blue marbles = 8

So the probability P (blue) = 8/26 = 4/13

Problem 3:

A card is drawn from a well shuffled pack of cards. What is P (diamond)?

Solution:

A pack of cards will have a total of 52 cards.

So total outcomes = 52.

In a pack of cards number of diamonds = 13

So the probability P (Diamond) = 13/52 =1/4

PROBABILITY PRACTICE PROBLEMS

Problem 1:

A die is thrown twice. Find the probability that a sum of 6 occurs on the die.

Solution:

Let F be the event of getting a number 6 on the die.

F = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)}

So the probability = (5/36)

Problem 2:

The condition is two numbers appearing on throwing two dice are different. Find

the probability of the when a sum of 4 occurs on the die.

Solution:

Let E be the event of getting a sum of 4. Here the condition given is the numbers on each dice is different.

E= {(1, 3), (3, 1)}

So the probability= 2/36 = 1/18