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Ask QuestionPosted by Harshita Bansal❤️ 5 years, 1 month ago
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Posted by Harshita Bansal❤️ 5 years, 1 month ago
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Posted by Ishika Dixit 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
T
he square root of a negative real number is called an imaginary quantity or imaginary number. e.g., √-3, √-7/2
The quantity √-1 is an imaginary number, denoted by ‘i’, called iota.
Integral Powers of Iota (i)
i=√-1, i2 = -1, i3 = -i, i4=1
So, i4n+1= i, i4n+2 = -1, i4n+3 = -i, i4n+4 = i4n = 1
In other words,
in = (-1)n/2, if n is an even integer
in = (-1)(n-1)/2.i, if is an odd integer
Posted by Nik . 5 years, 1 month ago
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Posted by Aleena Philip Shaji 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
Total no. of student=25
Let n(M)=student who studying mathematics
n(C)=student who studying chemistry
n(P)=student who studying Physics
∴n(M)=15,n(P)=12,n(C)=11,n(M∩P)=9,n(M∩C)=5,n(P∩C)=4,n(M∩P∩C)=3
Number of student who studying mathematics and physic but not chemistry
⇒n(M∩P)−n(M∩P∩C)
⇒9−3=6
Number of student who studying chemistry and physic but not mathematics
⇒n(P∩C)−n(M∩P∩C)
⇒4−3=1
Number of student who studying mathematics and chemistry but not physics
⇒n(M∩C)−n(M∩P∩C)
⇒5−3=2
∴No.of student who had taken two of the three subjects=6+1+2=9
Posted by Tilak Gupta 5 years, 1 month ago
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Posted by Soham Biswas 5 years, 1 month ago
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Posted by Dikshant Shokeen 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
Given : a circle of diameter 40cm,the length of a chord is 20 cm,
To Find : the length of the minor arc of the chord
Solution:
Chord Length = 20 cm
Diameter = 40 cm
Perpendicular from center on chord bisect the chord
Hence Half of chord = 10 cm
Radius = 40/2 = 20 cm
Sin ( 1/2 of chord angle ) = 10 /20
=> Sin ( 1/2 of chord angle ) = 1/2
=> Sin ( 1/2 of chord angle ) = Sin 30°
=> 1/2 of chord angle = 30°
=> chord angle = 60°
Minor arc angle = 60°
or another way to get angle
as Radius = 20 cm
Chord length = 20 cm
Hence it forms an Equilateral triangle
Hence angle formed by chord at center = 60°
Minor arc angle = 60°
length of the major arc of the chord = (60/360) * 2π * Radius
= ( 1/6 ) * 2π * 10
= 10π/3
= 50 * 3.14/3
= 10.47 cm
Yogita Ingle 5 years, 1 month ago
Diameter of the circle =40 cm
∴ Radius (r) of the circle = 40/2 =20 cm
Let AB be a chord (length = 20 cm) of the circle.
In △OAB, OA = OB = Radius of circle = 20 cm
Also, AB = 20 cm
Thus, △OAB is an equilateral triangle.
∴θ=60∘=π/3 radian
We know that in a circle of radius r unit, if an arc of length I unit subtends an angle θ radian at the centre, then θ=l/r
∴π/3 = arc AB/20
⟹arc AB = 20/ 3π cm
Posted by सत्य सनातन? 5 years, 1 month ago
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Posted by Priyanka Gurjar 5 years, 1 month ago
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Gaurav Seth 5 years, 1 month ago
In order to show that points (3, 0), (–2, –2), and (8, 2) are collinear, it suffices to show that the line passing through points (3, 0) and (–2, –2) also passes through point (8, 2).
The equation of the line passing through points (3, 0) and (–2, –2) is
It is observed that at x = 8 and y = 2,
L.H.S. = 2 × 8 – 5 × 2 = 16 – 10 = 6 = R.H.S.
Therefore, the line passing through points (3, 0) and (–2, –2) also passes through point (8, 2). Hence, points (3, 0), (–2, –2), and (8, 2) are collinear.
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Yogita Ingle 5 years, 1 month ago
We have this equation:
x + y = 1
x + y = 1
y = - x + 1
The slope of the tangent here is -1
And the slope of the line perpendicular to the tangent is 1
The line will pass through the focus y = x + c which will pass through (1,1)
The equation for this would be: y = x
The point of intersection of x + y = 1 and x = y can be obtained by:
y + y = 1
2y = 1
y = 1/2
The vertex for this is : (1/2, 1/2)
The distance between the focus and vertex is √[2x(1/2)²] = √2/2
The equation of parabola would be (y -1/2)² = (2x√2) x (x-1/2) y² + 1/4 - y = 2√2*x - √2
= 4y² - 4y - 8 x √2 *x + 4*√2 + 1 = 0
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