exercise 3.6 class 10 math unit 3 variations | k-method | sir Abbas

Описание: exercise 3.6 || Q 1(i, iii, iv) || k-method || unit 3 maths 10th || exercise 3.6#abbasmaths
Mathematics 10th
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Maths 10th by
Muhammad Abbas
محمدعباس
Unit-3 یونٹ۔3
1-VARIATIONS
تغیرات
اُردو اور انگلش میڈیم طُلباء کیلئے
Both for urdu and English medium students.
In this unit, students will learn how to
define ratio, proportions and variations (direct and inverse).
s find 3 rd, 4th, mean and continued proportion.
à apply theorems of invertendo, alternendo, componendo, dividendo
and compo.
Define joint variation.
solve problems related to joint variation.
use k-method to prove conditional equalities involving proportions.
a solve real life problems based on variations.
2-Ratio, Proportions and Variations.
نسبت,تناسب اور تغیرات
Define (a) ratio, (b) proportion and (c) variations.
(i) Ratio نسبت
A relation between two quantities of the same kind is called
ratio. If a and b are two quantities of the same kind and b is not zero, then the ratio of a ani
b is written as a :b or in fraction a/b
Remember that:
(i) The order of the elements in a ratio is important.
(ii) In ratio a : b, the first term a is called antecedent and the second term bi
called consequent.
VARIATIONS تغیرات
The word variation is frequently used in all sciences. There are two types of
(i) Direct variation.
تغیر راست
(ii) Inverse variation.
تغیر معکوس
Direct Variation
تغیرراست
If two quantities are related in such a way that increase (decrease) in one quantity
causes increase (decrease) in the other quantity, then this variation is called direct variation
In otherwords, if a quantity y varies directly with regard to a quantity x. We say that y
is directly proportional to x and is written as yo x or y = kx. i.e., = k, k#0.
The sign « read as "varies as” is called the sign of proportionality or variation, while
k#0 is known as constant of variation.
Faster the speed of a car, longer the distance it covers.
The smaller the radius of the circle, smaller the circumference is.
Inverse Variation
تغیرمعکوس
If two quantities are related in such a way that when one quantity increases, the other
decreases is called inverse variation,
In otherwords, if a quantity y varies inversely with regard to quantity x. We say that y
1 k
is inversely proportional to x or y varies inversely as x and is written as yo
For y = x
i.e.,
xy = k, where k#0 is the constant of variation.
Proportion
تناسب
A proportion is a statement, which is expressed as an equivalence of two ratios.
If two ratios a : b and c:d are equal, then we can write a : b=c:d
Where quantities a, d are called extremes, while b, c are called means.
Symbolically the proportion of a, b, c and d is written as
a : b::c:d
or
a : b = c : d
Joint variation
مشترک تغیر
A combination of direct and inverse variations of one or more than one variables
forms joint variation.
If a variable y varies directly as x and varies inversely as z.
Y∝x and also y∝1/z
In joint variation, we write it as y =k x/z
Where k + 0 is the constant of variation.
Theorems on
Proportions
تناسب کے مسئلے
If four quantities a, b, c and d form a proportion, then many other useful properties
may be deduced by the properties of fractions.
(1) Theorem of
Invertendo
مسئلہ عکس نسبت
If a : b=c:d, then b:a=d:c
(2) Theorem of
K-Method (k-طریقہ)
(1) Use k-method to prove conditional equalities involving proportions.
If a : b:c:d is a proportion, then putting each ratio equal to k
a = bk and c= dk
Using the above equations, we can solve certain problems relating to proportions more easily.
This method is known as k-method.
Exercise 3.5
Q-4,5,6 Joint variation
مشق۔3.5
سوال-6,5,4
مشترک تغیر

MCQs unit-3
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ڈئیر سٹوڈنٹس آپ کو اگر یونٹ۔3 مشق-3.6 سوال ۔1 کلاس دھم میں کسی طرح کا کوئی بھی پرابلم ہو تو آپ بے جھجھک ہو کر مجھ سے بات کر سکتے ہہں یا کمینٹس میں لکھ سکتے ھیں۔میرا کنٹیکٹ نمبر یہ ھے (03460476001)
Dear students if you have any problem in maths 10th class unit 3
Exercise 3.6 Q-1 You can discuss me on contact no.(03460476001) or write your problem in comments on youtube link#abbasmaths