# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 Re: Exercises » In triangle ABC » 2022-04-24 20:43:58

The given paragraphs deal with 2 topics, measurement of Square Meter and Exterior angle bisector of the triangle. The exterior angle bisector of a triangle divides the other facet outwardly within the quantitative relation of the perimeters containing the angle.
In a triangle MNO, MP is that the external bisector of angle M meeting NO created at P. IF MN = ten cm, MO = 6 cm, NO - 12 cm, then realize OP.
Solution:
(NP/OP)  = (MN/MO)
NP = NO + OP= twelve + OP
(12 + OP)/OP = 10/6
6 (12 + OP) = ten OP
72 + six OP = ten OP
72 = ten OP - six OP
4 OP = seventy-two
OP = 72/4
= 18 cm
I get few details of calculation of square meter from https://ksa.mytutorsource.com/blog/how-to-calculate-square-meter/.
Some tools used for measurements like metric tape, meter stick, ruler, etc. Use mensuration tape or ruler from one corner to the opposite corner. You'll be able to modify centimeters into meters by inserting the percentage point to the left by 2 numbers (1 centimeter = zero.01 meters). If measurements are in sq. feet then they will be born again from sq. feet to face meters by multiplying the previous by zero.093 (1 area unit = zero.093 sq. meters). If measurements are in sq. yards, then you may get to multiply them by zero.84. If you have got a fancy form, break it into smaller shapes like triangles and rectangles.

## #2 Re: Exercises » congruent » 2022-04-14 21:53:41

The Question states that Prove that if two right-angled triangles: ABC, XYZ
have the same perimeter and the same area, then they are congruent.

Solution:
Assuming that AB = kXY
Assuming areas are equal, which means AB x BC = XY x YZ
AB = XY x YZ / BC
Putting AB = kXY
kBC = YZ
Let perimeter be
P => CA = P - AB - BC
(P - AB - BC) ^2 = BC ^2 + AB ^2
P^2 = 2P.BC + 2P.AB + 2.AB.BC
Similarly, P^2 = 2P.YZ + 2P.XY + 2.XY.YZ
YZ + XY = AB + BC
This proves areas and perimeters of the two are equal
Put k=1 in which case, AB=XY and BC = YZ and the triangles are congruent
Note: Two segments are congruent if and only if they have equal measures. Two triangles are congruent if and only if all corresponding angles and sides are congruent.

## #3 Re: Exercises » Geometry For You » 2022-04-11 19:34:51

According to the Question
In order to solve the questions, a little background information of angles and Pythagorean theorem is required.

59: Write the area A of a square as a function
of its perimeter P.
Given that the perimeter of the square = P
Therefore, length of one side of the square = P/4
Area of square = x ^2
A = P²/16

60. Write the area A of a circle as a function
of its circumference C.
Given Circumference = C
Therefore, Radius of the circle = C/2π
Area of a circle = π(C/2π)²
A = C²/4π

61. Path of a Ball You throw a baseball to a child
25 feet away. The height y (in feet) of the baseball is
given by y = − (x^2) /10 x^2 + 3x + 6 where x is the horizontal
distance (in feet) from where you threw the ball.
Can the child catch the baseball while holding a baseball glove
at a height of 5 feet?
y= - (25^2) 10/ 25^2 + 3*25 + 6
6250/625+81
Y =91

Also you can find it here: [mytutorsource.hk/blog/properties-of-right-angle-triangle-and-how-to-apply-pythagorean-theorem]

## #4 Re: Exercises » X / 5 + (5x10-45) » 2022-04-10 21:57:44

According to the Question:
X / 5 + ( 5 x 10 - 45) / 10 = ?
Solution:
x/ 5 + 50 - 45 / 10
X / 5 + 5 / 10
2 x + 5 / 10

I find Math fun because Math issues aren't simple to solve, but figuring out the solution may be quite rewarding. Remind kids that some issues are simpler to solve than others, and that figuring it out is part of the fun. Bring a feeling of adventure and inquiry to math class. Math promotes critical thinking and problem-solving abilities. Learning to look at an issue and come up with a strategy, whether it's a math problem or a life problem, is a crucial ability to have. You might think of arithmetic as searching for an answer in a book or on a worksheet, but it always begins with a question or a thought. Students' curiosity and enthusiasm are piqued when they are encouraged to begin by wondering.

## #5 Re: Help Me ! » Circle Problems » 2022-03-21 02:33:51

Hello,
The chord of a circle (mytutorsource.com/blog/chord-of-a-circle) is a line segment that links or unites two points on a circle's circumference.
According to the question,
C 1:  (x + 2) ^ 2 + (y + 4) ^ 2 = 64
C 2: (x - h) ^ 2 + (y - 1) ^ 2 = 81
Distance between the center of the circles = 13

Possible Values of h
You have already calculated that as h = -14 and h = 10
For Part 2,  If a segment connecting the centers is drawn, let A be the intersection of the segment with C1 and B be the intersection of the segment with C2. Find AB.
You may calculate the coordinates of A and B individually by substituting for y in each circular equation. This will also provide you with the coordinates for the second place on AB where it intersects C2. Since AB is the line that defines each circle's diameter, the tangents must pass through A and the second point, so you have everything you need to write the equations for these new circles' center and circumference point.

## #6 Re: Jai Ganesh's Puzzles » Trigonometry » 2022-03-15 19:47:55

ganesh wrote:

Hi pamshaw,

This topic is for 'Ganesh's puzzle.'

You can use 'Help me' or 'This is Cool' or 'Games and Puzzles'

Ganesh"s puzzles are posted by .me and others reply.

I have made amply clear now.

Acknowledge!

## #7 Re: Jokes » Short Funny Jokes - 60 » 2022-03-15 02:27:40

Hello,
What’s the best thing about Switzerland?
I don’t know, but the flag is a big plus.

I invented a new word!
Plagiarism!
A bear walks into a bar and says, “Give me a whiskey and … cola.”
“Why the big pause?” asks the bartender. The bear shrugged. “I’m not sure; I was born with them.”

Did you hear about the actor who fell through the floorboards?
He was just going through a stage.

Where are average things manufactured?
The satisfactory.

How do you drown a hipster?
Throw him in the mainstream.

How do you keep a bagel from getting away?
Put lox on it.

Why don’t Calculus majors throw house parties?
Because you should never drink and derive.

Why should the number 288 never be mentioned?
It’s two gross.

What did the left eye say to the right eye?
Between you and me, something smells.

What do you call a fake noodle?
An impasta.

What did the 0 say to the 8?
Nice belt!
What do you call a pony with a cough?
A little horse.

What’s orange and sounds like a carrot?
A parrot.

## #8 Re: Jai Ganesh's Puzzles » Trigonometry » 2022-03-15 02:26:26

ganesh wrote:

Hi pamshaw,

This is a section exclusively for 'Ganesh's Puzzles'. Post in 'Games and Puzzles' in future.

Hello Ganesh!
First of all thank you so much for your words it's mean alot to me. Secondly I find it helpful and just share the importance of trigonometry in our life and its applications in various important fields that make our life easier. After reading the following stuff:
mytutorsource.qa/blog/applications-of-trigonometry-in-real-life
https://www.mathisfunforum.com/viewtopic.php?id=2966
https://www.mathisfunforum.com/viewtopic.php?id=17410
http://www.mathisfunforum.com/viewtopic.php?id=17125

## #9 Re: Jai Ganesh's Puzzles » Trigonometry » 2022-03-13 23:37:52

Hello,
What an interesting trigonometry question.
tan² θ +1 = sec² θ, θ = 30°

For easier to write, assuming for  θ to be x
Prove that tan ^2 x + 1 = sec ^2 x.
LHS = tan ^2 x + 1
= sin^2 x / cos^2 x + 1
= sin^2 x/ cos^2 x + cos^2 x/cos^2 x
= (sin^2 x + cos^2 x)/ cos^2 x
= 1/cos ^2 x
= sec^2 x Hence, Proved.

## #10 Re: This is Cool » Are these unique numbers? » 2022-03-03 19:11:14

The problem here is the discussion is about numbers and multiplication. There is an example of the number 36 that if you multiply two numbers and then multiply the result with the two, you will get the number 36. The question that comes from here is there any number that follows the same pattern in any number of digits? If not, then why?
The discussion on this point is accepted with open arms in the community; the community answers the question with proof of the existence of certain other numbers on a variety of numerics.
a = 7, b = 5 , n = 5                    175 = 1 x 7 x 5 x 5
a = 2, b = 8, n = 8                     128 = 1 x 2 x 8 x 8
a = 3, b = 5, n = 9                     135 = 1 x 3 x 5 x 9
a = 4, b = 4, n = 9                     144 = 1 x 4 x 4 x 9
Starting with the acceptance that several digits can exist in the pattern discussed in the problem proves an abundant variable available that you can find. Though there was some difficulty in understanding the equation, the community did find the solution keeping the context that the number can be in any range and giving the result lies the numbers in the statement.

## #11 Re: Exercises » Find the real solutions » 2022-03-03 01:07:15

The problem statement here is a mathematical equation for which we have to find the answer for two equations given in the statement. The statement is basically logarithm equations that are integrated into the arithmetic situation.
Discussion on the problem highlights some important points of the equation, and the solution solved gives a few pointers as well to the community. They found some issues with the solution and highlighted them. The discussion also points out that the community has found some steps that can improve the results of the equation.
The community provides the solution of the equation by solving the equation step by step, helping the little bright minds to understand the steps and get up to speed with brilliant minds. The equation solution is very well explained for those who are not bright and sharp to understand things on the go and for those who can make sense of things on the  go.
With all the explanation, the equations solutions, the graphical presentations, the real solution of the equations have been provided, and all the necessary means and explanations have already been pointed out here,
X = \frac{-1}{2} + \frac{\sqrt{5}}{2} \implies x = 11.618...

## #12 Re: Exercises » X / 5 + (5x10-45) » 2022-02-28 23:08:41

Solution:

x/5+(5 .10-45)/10

By multiplying:
To get the simplest form first of all we will multiply 5 with 10.

x/5+(5 .  10-45)/10

x/5+(50-45)/10

By multiplying 5 with we got 50

By subtracting:

To make it simpler we will subtract 45 from 50.

x/5+(50-45)/10

x/5+5/10

Reducing the fractions with 5.

x/5+5/10

x/5+1/2

The real reason to reduce the fraction is to rewrite it in the simplest way.

Finding the common denominator:

x/5+1/2

x/5+(5 .1/2)/10

Combining the fractions with a common denominator:

x/5+(5 .1/2)/10

(x+5 .1/2)/5

By multiplying the number:
(x+5 .1/2)/5

(x+5/2)/5

(x+5/2)/5

## #13 Re: Help Me ! » Where do I start on Mathisfun.com? » 2022-02-28 22:53:06

If you are looking forward to taking admission in data science, you must have to be good in math. And if you are not good at math this will be a bumpy ride. Because every single algorithm is created with math functions. Usually, in Data science most of the math is based on statistics but not completely. In data science three topics that come up consistently are:
Statistics
Calculus
Linear algebra
Statistics is also divided into two branches which are inferential and descriptive. Statistics is used in a large number to develop new algorithms and applications. This also helps to create a summary image of an industry’s process flow.
Calculus is the math branch that studies the changes and optimizes the result at the end. If you don’t have knowledge of calculus it will be difficult to find better outcomes and fix the issue.
Last but not least is linear algebra. To deal with a problem it provides fast speed. Also helps to understand the different algorithms. It can be accessed in Python using the NumPy library. With the combination with Calculus, it helps us decision-making in vectors and matrices.

## #14 Re: Help Me ! » even and composed functions » 2022-02-28 20:10:37

In math functions that satisfy particular symmetric relations by taking additive inverse are known as even function and odd functions. They are very important in theory of Fourier series and power series. It is also very important in many areas of analysis of mathematics.
Even Functions
A function f will be even if the x and –x holds for all in the domain of f
f(x) = f(-x)
In geometry even function’s graph is symmetric with respect to axis Y. This means after reflecting with the Y-axis no change will happen in the graph.
X2, |x| and cos x are some examples of even functions.
Odd Functions
A function f will be odd if the x and –x holds for all in the domain of f
-f(x) = f (-x)
In geometry, an odd function’s graph has rotational symmetric with respect of origin. This means after rotation of 180° with origin no changing will happen in the graph
x, x³ and sin x are some example of odd function

## #15 Re: This is Cool » Important Laws/Principles in Physics » 2022-02-27 20:59:47

The discussion here lists different laws that explain most things happening around us. Among the listed laws, the first one is Newton's law of motion, further divided into three laws, first, second, and third; each has its significance and application in the daily world. Newton's law influenced modern physics and asked the world to upgrade the basics.
The following law in the list is Kepler's law of planetary motion; they are also divided into three more laws that explain planetary movements. Its usefulness applies to the motion of natural and artificial satellites. The next law is Kirchhoff's law which explains the circuits and the current flow through them just like the rest of the laws; this has its limitations.
Columb's law for the electric charges gas laws was proposed over time and included Boyle's law, Charle's law, and Avogadro's law. There is an ideal gas equation that is derived from the gas laws. The community finds this information interesting and useful; there are further laws of thermodynamics and Newton's gravitational law on the forum explaining each.

## #16 Re: This is Cool » Infinite Platonic Shapes?? » 2022-02-27 19:30:28

The discussion here on this link is about the author's calculations during his equations and table calculations. He found some interesting properties in the spiritual and extended them with the listed formula and calculations. But to his dismay, the procedure gave negative values when he used y = 1; the value for vertices and super vertices comes out to be negative. He further asked for linking the data with pascal's triangles.
The discussion on the forum starts with the comments on the statement of his occasional mathematician doing it for fun. The argument proceeds with the complexity of the question and the terms related to the octal and tetra vertices. Further, it was pointed out that this solid doesn't represent any regular solid and does not obey Euler's relation. To understand all this and your calculation, I had to draw 2D images, called Schlegel diagrams, where I made the drawing and placed vertices with nine edges, then I ended up with the F = 6, which Euler's relation would predict.

## #17 Re: Introductions » Hello please need help from math experts very necessary topic » 2022-02-25 00:49:57

While getting admission in 11th grade you must think about what subjects you are going to choose. A student should choose the subjects in which he is good and interested. You have to choose your subjects wisely because your future depends on them. Math is a tough subject. If you are looking forward to going to engineering, many engineering-related courses require good math. If you are learning math and you couldn't understand it, there are two options. First, try to get tuition from someone. Some people learn fast from books and some from teachers. If you learn quickly from a person then you can continue learning in math. Otherwise, it would be better for you to change to go with the 2nd option. Which is the change of subject. You can choose a field in which math is optional. For example, in the medical field, you can choose biology instead of math. In the end, no one is perfect and math is a difficult subject. To be good at math you have to work hard and keep practicing. Because Practice is math’s 2nd name.

## #18 Re: Jokes » More Miscellaneous Jokes - 27 » 2021-12-20 21:06:31

1.       Two guys are standing in line to enter heaven. One turned around and asked the other how he died. "I froze to death. How about you?" "I had a heart attack." "How did that happen?" "Well, I suspected my wife was cheating on me. So after work I went straight home. I ran upstairs to find my wife sleeping by herself. Then I ran back downstairs and looked in all the hiding spots. When I was running back up the stairs, I had a heart attack." "That's ironic." "Why?" "If you would've looked in the fridge, we'd both be alive."
2.       Question: What is the color of the wind? Answer: Blew.
3.       Do not be racist; be like Mario. He's an Italian plumber, who was made by the Japanese, speaks English, looks like a Mexican, jumps like a black man, and grabs coins like a Jew!
4.       The energizer bunny was arrested on a charge of battery.

## #19 Re: This is Cool » Important Laws/Principles in Physics » 2021-12-16 21:57:04

Some basic principles of Physics:
Phase
In physics, a common principle lies regarding phase. A phase is a region of space throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization, and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water.
Heat Transfer
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and energy transfer by phase changes. Engineers also consider transferring mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.
Wave
A wave is a propagating dynamic disturbance of one or more quantities, sometimes described by a wave equation. In physical waves, at least two field quantities in the wave medium are involved. Waves can be periodic, in which case those quantities repeatedly oscillate about an equilibrium value at some frequency.
Sound
In physics, sound is a vibration propagating as an acoustic wave through a transmission medium such as a gas, liquid, or solid. In psychology, the sound is the reception of such waves and their perception by the brain.
Temperature
Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy when a body is in contact with another that is colder or hotter. Temperature is measured with a thermometer.

## #20 Re: Exercises » About the Exercises » 2021-12-16 02:04:37

I find arranging new things very fascinating. That is because back in my time, it was everything to be done by yourself. Thus, most of us did not consider doing all the hard work for a little pleasure. Having short math exercises is always fun. The best thing I remembered was solving different word problems from a dedicated book. And this was around ten years ago. Back then, technology was not as such as it is now. Technology has advanced so much that creating such exercises is easy and accessible.
Thus, I love the idea of generating creative and indulging short exercises regarding math concepts such as algebra, basic word problems, trigonometry, etc. However, there is one thing which we need to adapt, and that comes from the idea of websites. They have everything arranged in different sections for easy identification. Thus, having math problems, we must arrange them in specific sections only; thus, people easily begin an exercise knowing where their interest and strength lies.