Math, asked by philojohny, 6 months ago

आकाश को एटीटा बाय टू प्लस साइन स्क्वायर थीटा बाय टू माइनस टू साइन थीटा बाय टू इनटू कॉस थीटा बैटरी कॉल टू वन माइनस साइन थीटा in English



Answers

Answered by anandashish9525
0

Answer:

Geometry

Geometry Shapes Formulas for Class 9

Geometric Figure Area Perimeter

Rectangle A= l × w P = 2 × (l+w )

Triangle A = (1⁄2) × b × h P = a + b + c

Trapezoid A = (1⁄2) × h × (b1+ b2) P = a + b + c + d

Parallelogram A = b × h P = 2 (b + h)

Circle A = π r2 C = 2 π r

Algebra

Algebraic Identities For Class 9

\((a+b)^{2}=a^2+2ab+b^{2}\)

\((a-b)^{2}=a^{2}-2ab+b^{2}\)

\(\left (a + b \right ) \left (a – b \right ) = a^{2} – b^{2}\)

\(\left (x + a \right )\left (x + b \right ) = x^{2} + \left (a + b \right )x + ab\)

\(\left (x + a \right )\left (x – b \right ) = x^{2} + \left (a – b \right )x – ab\)

\(\left (x – a \right )\left (x + b \right ) = x^{2} + \left (b – a \right )x – ab\)

\(\left (x – a \right )\left (x – b \right ) = x^{2} – \left (a + b \right )x + ab\)

\(\left (a + b \right )^{3} = a^{3} + b^{3} + 3ab\left (a + b \right )\)

\(\left (a – b \right )^{3} = a^{3} – b^{3} – 3ab\left (a – b \right )\)

\( (x + y + z)^{2} = x^{2} + y^{2} + z^{2} + 2xy + 2yz + 2xz\)

\( (x + y – z)^{2} = x^{2} + y^{2} + z^{2} + 2xy – 2yz – 2xz\)

\( (x – y + z)^{2} = x^{2} + y^{2} + z^{2} – 2xy – 2yz + 2xz\)

\( (x – y – z)^{2} = x^{2} + y^{2} + z^{2} – 2xy + 2yz – 2xz\)

\( x^{3} + y^{3} + z^{3} – 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} – xy – yz -xz)\)

\( x^{2} + y^{2} = \frac{1}{2} \left [(x + y)^{2} + (x – y)^{2} \right ]\)

\( (x + a) (x + b) (x + c) = x^{3} + (a + b +c)x^{2} + (ab + bc + ca)x + abc\)

\( x^{3} + y^{3} = (x + y) (x^{2} – xy + y^{2})\)

\( x^{3} – y^{3} = (x – y) (x^{2} + xy + y^{2})\)

\( x^{2} + y^{2} + z^{2} -xy – yz – zx = \frac{1}{2} [(x-y)^{2} + (y-z)^{2} + (z-x)^{2}]\)<

Surface Area and Volumes

Shape Surface Area Volume

Cuboid 2(lb + bh +lh)

l= length, b=breadth, h=height

lbh

Cube 6a2 a3

Cylinder 2πr(h+r)

r = radius of circular bases

h = height of cylinder

πr2h

Cone πr(l+r)

r=radius of base

l=slant height

Also, l2=h2+r2, where h is the height of cone

(1/3)πr2h

Sphere 4πr2 (4/3)πr3

Heron’s Formula

\(Area ~of~ triangle~ using~ three~ sides =\sqrt{s(s-a)(s-b)(s-c)} \\)

Semi-perimeter, s = (a+b+c)/2

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