Let us study the concept by finding the constant term in the expansion of (x3 – 1/x2)15 In (a + b)n the (r + 1)th term Tr+1 is given by –Tr+1 = nCr .an-r. br for r = 0, 1, 2, 3, 4, 5 … n Let constant terms occurs at (r+1)th term for ( x3 – […]
Explaining the concept by finding the range of 5 sinx + 12 cosx – 13 Comparing (5 sinx + 12 cosx) with (asinx + bcosx)a = 5b = 12√(a2 + b2) = √(52 + 122) = √(25 + 144) = √169 = 13 asinx + bcosx = √(a2 + b2)(asinx + bcosx) / √(a2 + b2) Putting values of a & b ==>5 sinx […]
Let us study a Circle inscribed in Equilateral Triangle and Square First let’s see the Circle in Equilateral Triangle By Pythagoras theorem in triangle BAP BA2 = AP2 + BP2 t2 = L2 + (t/2)2 L2 = 3t2 /4 L = √3 t/2 Again by Pythagoras theorem in triangle BOP BO2 = OP2 + BP2 (L – r) 2 = r 2 + (t/2) 2 r2 = (√3t/2 – r)2 – (t/2)2 […]
The square which is made in a circle such that all four vertices of a square touches circle is called Circumscribed square. By Pythagoras theorem in triangle BOC s2 = r2 + r2 s = √2r Areas In terms of radius ‘r’ In terms of side ‘s’ Area of square ABCD with side ‘s’ […]
The triangle which is made in a circle such that all three vertices of a triangle touches circle is called Circumscribed Triangle. Let us see the an example of Circumscribed equilateral triangle. By Pythagoras theorem in triangle BAP BA2 = AP2 + BP2 t2 = L2 + (t/2)2 L2 = 3t2 /4 L = √3 t/2 […]
The concept of ratio and proportion is one of the most essential concepts in maths. A ratio is a relationship between two numbers that defines the quantity of the first in comparison to the second. Ratios can be written in the fractional form. For example: 3:7 or 3/7. When quantities are proportional, their ratios are equal.
The terms mean, median and mode are used to describe the central tendency of a large data set. Range provides provides context for the mean, median and mode. Mean: It is the average of all the values of a dataset. Significance: While buying a car you are not interested in the no. of Kilometers car […]