Mathematics in Daily Life

Introduction to Everyday Mathematics answers:-

Our life is intertwined with mathematics.

We use mathematics in our daily life.

We use mathematics  to measure the distance, the weights, to find volume, to know the time,  to measure temperature, to dilute liquids, to  make a concentrate of a solution etc. Understanding radian and degree measure is always challenging for me but thanks to all math help websites to help me out.


Use of mathematic in every day with answers

As soon as we get up in the morning, we look at the clock to know the time.

We measure the coffee and  count the slices of bread for the family.

When we go to the market to buy vegetables, we calculate the prices of the purchase.

As we walk home after purchase, we make a note of the day's temperature.

Cooking needs time management, weight management and volume management and temperature adjustment.

We need to pay for the ironed dress to wear for the office, pay for petrol for the motorbike  etc.

The office work also involves mathematical calculations, charts and graphs. Having problem with Radian Measure keep reading my upcoming posts, i will try to help you.


Use of mathematics outside home with answers


When we go shopping, we have to pay the bill, which is a  mathematical calculation.

Discount offered at the shops and taxes also involves calculations.

Buying and selling of various commodities involves profit or loss.

When you share your  food with friends, it involves fractions.

We convert money to bigger or smaller units.

We also convert measurements to higher or lower units in our daily life.


Mathematic in managing outside activities with answers


When we  build a house , we use the calculation called "Time and  Work".   This system is also used for many

other activities like mowing a garden, plucking tea leaf, harvesting a crop etc

We use the form "Time and distance" when we travel.

We use  the form 'Time and speed"  when we go up and down the stream and river.

We also use 'Time and speed" in sports activities, especially races.


Perimeter, area and volume in daily life with answers


If we want to fence our garden, we use the perimete formula of various shapes.

If we want to  have a lawn in our garden, we calculate the area of the lawn.

If we want to store our harvested grains, we use the volume formula.

If we want to pack the grains in sacks, we use the break-up of the volume to smaller volumes.

Thus we note that  purchases, sales, profits , losses, tax, discounts, time, weights, volumes, area, perimeter

work, speed etc are  used daily in our life .

Probability with Replacement

Introduction to Probability with replacement :

To calculate the probability of ball which is strained from a population by using explanation of probability and the calculations can be established by using the relative frequency definitions of probability. In a examination can have n equally likely conclusion, and that a 'success' can take place in s ways (from the n).

Then the probability of a 'success' = s / n


Probability with replacement Problem 1


A pitcher contains 7 orange and 4 green balls. Find the matching probabilities if the balls are replaced after every draw.

(a) Mutually orange

(b) a orange and a green

(c) both the identical color.

Solution:-

a.) Since the balls are restored after each draw,

P(s)is 7 in both cases since we replace it with in each case.

This is simply 7/11 * 7/11 = 49/121

b.) This should be 7/11 * 4/11 = 28/121

c.) As for P(c).

P(c) = (P(two orange and two green)) .,

so

P(two orange or two green) = P(two orange) + P(two green) = P(c)

P(two orange) is given by 49 / 121

P(two green) is given by 16 / 121

now by just plugging in it in the given function we get it as follows

= 49/121 + 16/121 = 65/121.

65 / 121 is the finalised answer. Please express your views of this topic Example of Theoretical Probability by commenting on blog.


Probability with replacement Problem 2


A population of 50 red mice, 200 green mice, selections with replacement:

a) Probability of 3 red mice in 3 selections

b) Probability of selecting, in order, red, red and then Green.

c) If, however, we are not interested in the order (i.e. red, red, green) but just the overall outcome (i.e. 2 red, 1 green), the probability is different:0

Solution:-

a) Probability of 3 red mice in 3 selections = (50/250) * (50/250) * (50/250)

= (1/5) * (1/5) * (1/5) = 0.008

b) Probability of selecting, in order, red, red and then green = (50/250) * (50/250) * (200/250)

= (1/5) * (1/5) * (4/5) = 0.032

c) If, however, we are not interested in the order (i.e. red, red, green) but just the overall outcome (i.e. 2 red, 1 green), the probability is different:0

Possible outcome of 3 selections with replacement

Rounding and Addition

Rounding is one of the major concepts in basic mathematics taught in the middle school but used throughout the growing years. Rounding is a process of changing a number by estimating its nearest value. If a number is followed by a number that is greater or equal to 5, the number can be rounded up and if a number is followed by a number that is less than 5, the number can be rounded down.
• Example 1: If he buys a full collection of Yonex badminton racquets, he will pay just Rs.155 per racquet. If he buys a full collection of Yonex badminton racquets , he will pay just Rs.160 per racquet
• Example 2: The mall has given away about 23% of discount on all fashion wear . The mall has given away about 20% of discount on all kid's fashion wear. Addition at times is done after rounding a number. Below are the steps to add a number after rounding.
• Round the number to its nearest value
• Add the numbers

Examples: 1.
She paid Rs.1190 to the trainer for teaching her tricep dips at home . She also paid Rs.2000 for her gym trainer. How much total she paid including trainer for teaching tricep dips at home and gym trainer. Rs.1190 + Rs.2000 Rs.1200 + Rs.2000 (Rs.1190 is rounded to Rs.1200) Rs. 3200 is the total amount she paid including trainers. 2. Mohan is planning to invest 24% of his salary in Gold. Mohan’s wife on the other hand is planning to invest 65% of her salary in gold. What is the total investment the family makes on gold? 24% + 65% 25 + 65% (24% is rounded to 25%) 90% of their total investment is made on gold. These are the basics about rounded and addition.

calculus derivative problems exam

Introduction for calculus derivative problems exam:

Two mathematicians, Namely Gottfried Leibniz and Isaac Newton, developed calculus. Calculus problems can be dividing into two branches: Differential Calculus problems and Integral Calculus problems. Differential calculus is use to measure the rate of change of a given quantity whereas the integral calculus is use to measure the quantity when the rate of change is known. The output of a function will change when we change the input value of a function. The measure of the change in the function is called as Calculus Derivatives.


Calculus derivative example problems:

The following solving problems are based on the derivatives.

Ex 1:

Determine the derivative dy/dx of the inverse of function f defined by

f(x) = (1/8) x - 2

Sol:

The first is used to find the inverse of f and differentiate it. To find the inverse of f we first write it as an equation

y = (1/8) x - 2

Solve for x.

x = 8y + 16.

Change y to x and x to y.

y = 8x + 16.

The above gives the inverse function of f. Let us find the derivative

dy / dx = 8


Ex 2:

Determine the critical number(s) of the polynomial function f given by

f(x) = x 4 - 108x + 100

Sol:

The domain of f is the set of all real numbers. The first derivative f ' is given by

f '(x) = 4 x^ 3 - 108

f '(x) is defined for all real numbers. Let us now solve f '(x) = 0

4 x^ 3 - 108 = 0

Add 108 on both sides,

4x^ 3– 108 108=108

4x^ 3= 108

x^ 3 = 27

x = 3 or x = -3

Since x = 3 and x = -3 are in the domain of f they are both critical numbers. Is this topic Limits of a Function in Calculus hard for you? Watch out for my coming posts.


Calculus derivative Practice Problems exam:


1) Determine the derivative dy/dx of the inverse of function f defined by

f(x) = x/2+ 3x/2 – 2

Answer:  dy / dx = 2


2) Determine the critical number(s) of the polynomial function f given by

f(x) = x^ 3 - 48x + 10

Answer:  X = 4 or X= -4

Five Thirty Eight

Introduction to five thirty eight:

Five thirty eight is represented in number form as 538. Thus five hundred thirty eight has five of hundred and three of ten and eight one. Thus the total sum of five hundred and three ten and eight ones is equal to five thirty eight. In this article we see about five thirty eight with some example problem related to five thirty eight. Is this topic Teaching Distributive Property hard for you? Watch out for my coming posts.

Five Thirty Eight:

Let us see the example problem of five thirty eight.

Example Problem – Five Thirty Eight:

Example 1:

Write the expand form of five thirty eight.

Solution:

We can split the five thirty eight as five hundred and thirty and eight.

Number form of five hundred is 500 and thirty as 30 and eight is 8.

Now we get the expand form of five thirty eight is added the five hundred and thirty and eight.

538 = 500 + 30 + 8

Answer: Expand form of five thirty eight is 500 + 30 + 8

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Five Thirty Eight:

Example 2:

Which of the following expression give the result as five thirty eight?

Option:

a)     500 – 30 + 8

b)    30 – 500 + 8

c)     500 + 30 + 8

d)    500 * 30 * 8

Solution:

Check the expressions which give five hundred fifty.

Option a: 500 – 30 + 8, give the result as 478.

Option b: 30 – 500 + 8, give the result as -442

Option c: 500 + 30 + 8, by adding the five hundred and thirty and eight give as result as five thirty eight.

Option d: 500 * 30 * 8, the product of 500 and 30 and 8 give the result as 120000

Hence the expression which has given in option c gives the result as five thirty eight

Answer: Option c - - - > 500 + 30 + 8

Now clear about the five thirty eight.

Multiplication Times Tables

Introduction for multiplication times tables:

Multiplication is the arithmetical operation of calculating one value with another value. This is a one kind of operations in basic arithmetic. Multiplication is nothing but the repeated addition. For example: 3 * 4 = 12 , so it represents 3 + 3 + 3 + 3  = 12, therefore for adding the number 4 simultaneously 3 times we get 12. Multiplication times tables is useful for making the multiplication process more easy. I like to share this Double Digit Multiplication Practice with you all through my article.

Multiplication Times Tables:

x	0	1	2	3	4	5	6	7	8	9	10	11	12
0	0	0	0	0	0	0	0	0	0	0	0	0	0
1	0	1	2	3	4	5	6	7	8	9	10	11	12
2	0	2	4	6	8	10	12	14	16	18	20	22	24
3	0	3	6	9	12	15	18	21	24	27	30	33	36
4	0	4	8	12	16	20	24	28	32	36	40	44	48
5	0	5	10	15	20	25	30	35	40	45	50	55	60
6	0	6	12	18	24	30	36	42	48	54	60	66	72
7	0	7	14	21	28	35	42	49	56	63	70	77	84
8	0	8	16	24	32	40	48	56	64	72	80	88	96
9	0	9	18	27	36	45	54	63	72	81	90	99	108
10	0	10	20	30	40	50	60	70	80	90	100	110	120
11	0	11	22	33	44	55	66	77	88	99	110	121	132
12	0	12	24	36	48	60	72	84	96	108	120	132	144

How to Find Answers Using Multiplication Times Tables:

First we have to see the numbers what we have to multiply. Let's take we have to multiply 8 and 8 so the answer can be easily found from the table. First we have to find 8 in the first column, and find 8 in the first row. Then we to see the intersecting cell. In the chart the intersecting cell of 8 and 8 has 64. So 64 is the answer for 8 times of 8. This is how we find the answers form multiplication from the multiplication times tables

Example problems using multiplication times tables

1) 7 x 7 = 49

2) 10 x 11 = 110

3) 8 x 1 = 8

4) 1 x 9 = 9

5) 5 x 6 = 30

6) 4 x 8 = 32

7) 3 x 2 = 6

8) 7 x 3 = 21

9) 8 x 3 = 24

10) 12 x 2 = 24

Distance of Earth from Sun

Introduction to distance of earth from sun:

Earth, as we all know, is the third planet from Sun. Earth revolves around Sun in an elliptical orbit. Due to the orbit of Earth being elliptical and not perfectly circular, the distance between Sun and Earth varies with the position of Earth.

Mean Distance between Earth and Sun
As it is very difficult to be able to continuously measure the distance between Earth and Sun, distances at the farthest and closest points are determined and the mean distance is calculated from them and used as a reference. These two points are:

Aphelion: Earth is farthest from Sun at Aphelion. This occurs during summer in the Northern Hemisphere - around the first week of July. The distance of Earth from Sun at Aphelion is about 152 million km (94.4 million miles).
Perihelion: Earth is closest from Sun at Perihelion. This occurs during winter in the Northern Hemisphere - around the first week of January. The distance of Earth from Sun at Perihelion is about 147 million km (91.3 million miles).
The mean distance between Earth and Sun (calculated from the mean of the distance at Aphelion and distance at Perihelion) is 149.5 million km.

Mathematically it can be expressed as:

Mean distance between Earth and Sun = (Distance at the farthest point or Aphelion + Distance at the closest point or Perihelion) / 2

= (152 + 147)/2 million km

= 149.5 million km

The exact value of the distance from Earth and Sun has been established as 149, 597, 870.7 kilometers (92,955,887.6 miles) and is also called 1 astronomical unit (or AU).

Implications on Distance of Earth from Sun

While we may think that Earth-Sun distance is critical in maintaining average temperatures on Earth and hence using a mean value would be misleading. But this is not true. The variation in distance due to the elliptical orbit is 5 million km. (This can be calculated by subtracting the distance at Perihelion from the distance at Aphelion. i.e. 152 – 147 million km.) This is a very small percentage of the actual distance between Earth and Sun (149.5 million km) and hence does not cause a significant change in the average temperatures on Earth.