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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.

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.

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]

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.

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.

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!

Hello,

What a fun thread

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.

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

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.

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.

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...

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

Answer:

(x+5/2)/5

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.

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

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.

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.

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.

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.

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.

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