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
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