In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
It can be expressed in equation form as,
a2 + b2 = c2
Where, a and b are the sides of a right triangle
c is the hypotenuse of the right triangle
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A projection on a plane, using lines perpendicular to the plane
Graphic communications has many forms. Orthographics is one such form. It was developed as a way of communicating information about physical objects. It is part of a universal system of drawings. House plans - one well known drawing format, are a form of othographic projection. In simple terms, orthographic drawings are views (front, side, top, and so on) of an object. An orthographic view is only one side. It takes several views to show all the object. Before getting to views, it is useful to look at another type of drawing. Pictorial drawings show several sides at the same time. Many people find pictorial drawings easier to understand. They do not provide as much information as orthographic views. The most commonly used pictorial drawing for technical information is called isometric drawings. Isometric drawings were developed to approximate perspective, but are much easier to draw. For a square box, all the sides are drawn as vertical lines, or at 30 degrees to the horizontal.
Match the orthographic drawing to the isometric drawing.
A ) Figure 4 B ) Figure 2 C ) Figure 3 D ) Figure 1
Steps to derive
1 An orthographic drawing shows the top view, front view and right-side view of a three-dimensional figure. 2 Develop a three-dimensional figure from the orthographic views. 3 Top view forms the base of the structure. A three-dimensional structure is developed from the orthographic views. 4 Figure 2 gives the isometric drawing of the structure developed from orthographic drawing.
Hence the right answer is Option B
In our next blog we shall learn about "alphabet of lines"
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Regression is the measure of the average relationship between two or more variables in terms of the original units of the data. This can be represented by an equation of a straight line which can be obtained by the method of least squares. The equations are of two forms as y on x and x on y. To obtain them we use the following normal equatons.
(i) Regression line y on x: It is given by y = hx + k.
Their normal equations are:
Σy = hΣx + nk ……………… (1)
Σxy = hΣx 2 + kΣx …………. (2)
By solving (1) and (2), we arrive at the required equation y = hx + k
(ii) Regression line x on y: It is given by x = hy + k.
Their normal equations are:
Σx = hΣy + nk ……….. (1)
Σxy = hΣy 2 + kΣy ………… (2)
By solving (1) and (2), we arrive at the required equations x = hy + k
In our next blog we shall learn about converting 1 meter in feet
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A line plot is defined as a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer numbers.
A line plot shows data on a number line with the symbol x or other marks to show frequency.
In the applications of line plot, we have also created the scatter plot analysis. I we go in the wrong path or plotting the extra values or plotting the values in different place or leaving some values when we plotting make great difference in the diagrams.
Line Plot Maker - Making a Number Line Plot:
To define the scale which we use, if the data is described as 100 the scale is increased by 10. So that we define the scale as 10 for 100
Next we have to draw the horizontal line to across the paper.
Break the grid as per the required scale.
Place the data values of x in the x-axis and y in the y-axis.
X
X X
X X X
X X X X X X
0 1 2 3 4 5 6 7 8 9 10
In our next blog we shall learn about converting 1 meter to feet
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The word fraction has been derived from the Latin word fractus, means broken
A Fraction means a part of a group or a region or a whole.
Fractions having the same(common) denominators but different numerators are known as like fractions.
Fraction is defined as an element of quotient field. Fraction can be represented as " a / b " here fraction variable 'a' denotes the value called as numerator and fraction variable 'b' denotes the value called as denominator and the denominator 'b' is not equal to zero.
Fractional functions:
The fraction rule is used in following functions,
Addition
Subtraction
Multiplication
Division
In our next blog we shall learn about misleading graphs
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The solving change of base formula is known as formulas which it permits us to rework a logarithm by means of the logs that may be is written with different base.
The change of base formula is given by,
Log a x = log b x / log b a
Here, assume that a, b and x are positive where a≠1 and b≠1.
Problem
Solve log 16 32
Change of base formula => loga x = logbx / logba
log 16 32 = log 2 32 / log 2 16
= 5 / 4
Thus a formula that allows you to rewrite a logarithm in terms of logs written with another base. This is especially helpful when using a calculator to evaluate a log to any base other than 10 or e.
In our next blog we shall learn "how to simplify radicals"
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In our previous blog we learned about Factor of 28. Today let us learn about "Factor of 72"
Like concepts presented throughout the Montessori classroom, even those more abstract concepts of Mathematics have been made concrete for the children in our classrooms. Beginning with simple number concepts like understanding quantity and identifying numerals, the Math materials include advanced presentations in cubing numbers, factors, fractions, and mathematical operations.
Factor Tree can be started by taking Different factors. The factor trees can be different but we will see that the Prime Factorization will remain same.
Steps to draw the Factor Tree of 72
Step 1: We start by building a Factor Tree of 72 by dividing 72 by smallest prime number that is 2.
Step 2: since 72 is 2 x 36 we write both these factors under 72 and circle 2 since it is prime.
Step 3: Since 36 is even number so we divide 36 again by 2 we get 2 x 18
Step 4: writing both factors 2 and 18 under 36 and circling 2 as it is again prime
Step 5: Then splitting 18 as 2 and 9 and writing the factors under 18 again circling the prime factor 2.
Step 6: Since now 9 is not divisible by 2 so we see next prime number that is 3
Step 7: On dividing it by 3 we get 3 which is the last and final factor.
Note: we keep on continuing these steps until we get all prime numbers in bottom row.
The Graphical representation of the factors of any number is called a Factor Tree
Factor Tree can be started by taking Different factors. The factor trees can be different but we will see that the Prime Factorization will remain same.
Steps to draw the Factor of 72
Step 1: We start by building a Factor Tree of 72 by dividing 72 by smallest prime number that is 2.
Step 2: since 72 is 2 x 36 we write both these factors under 72 and circle 2 since it is prime.
Step 3: Since 36 is even number so we divide 36 again by 2 we get 2 x 18
Step 4: writing both factors 2 and 18 under 36 and circling 2 as it is again prime
Step 5: Then splitting 18 as 2 and 9 and writing the factors under 18 again circling the prime factor 2.
Step 6: Since now 9 is not divisible by 2 so we see next prime number that is 3
Step 7: On dividing it by 3 we get 3 which is the last and final factor.
Note: we keep on continuing these steps until we get all prime numbers in bottom row.
In the above figure on the left side we see all the prime factors
So the prime factorization can be written as product of all Prime factors
72= 2 x 2 x 2 x 3 x 3
In simplified form it can be written in form of Exponents
72= 2^3 x 3^2
I hope the above explanation was useful.Keep reading and leave your comments.
Let us learn about "change of base formula"
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