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Yogita Ingle 5 years, 7 months ago
According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r ≤ b.
The basis of the Euclidean division algorithm is Euclid’s division lemma. To calculate the Highest Common Factor (HCF) of two positive integers a and b we use Euclid’s division algorithm. HCF is the largest number which exactly divides two or more positive integers. By exactly we mean that on dividing both the integers a and b the remainder is zero.
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Yogita Ingle 5 years, 7 months ago
The vertices of the triangle ΔABC are A (1, 2), B (- 3, 2) and C (3, - 2). The sides of the triangle are AB, BC, CA and we have to find the tangent ratio of the angle A.
The slope of the line AB is
m₁ = (2 - 2) / (- 3 - 1)
= 0 and
that of the line CA is
m₂ = (2 + 2) / (1 - 3)
= - 2
Then the angle A is determined from
tanA = (m₁ - m₂) / (1 + m₁m₂)
= (0 + 2) / (1 + 0)
= 2
Hence tanA = 2
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Yogita Ingle 5 years, 7 months ago
1x - 3y= 11 .......... (i)
5x+y= 7....... (ii)
Multiply equation (ii) by 3
15x + 3y = 21 ........... (iii)
Adding (i) and (iii), we get
16x = 32
x = 32/16 = 2
Put x = 2 in (i), we gwt
x - 3y = 11
2 - 3y = 11
-3y = 9
y = -3
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Yogita Ingle 5 years, 7 months ago
By elimination method :
8x+5y = 9---------(1) ×2
3x+2y = 4 -----(2). ×5
we get,
16x+10y = 18
15x+10y= 20
subtracting both the equations we get;
x = -2
Putting the value of x in (1)...
8×-2 +5y = 9
-16+5y = 9
5y = 9+16
5y = 25
y = 25/5
y = 5
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