maths

W is directly proportional to F.When, W = 24, F = 6Find the value of W, when F = 10

W∝FW = KFWhen, W = 24             F = 624 = 6K÷64 = KW = 4KW = 4x10W = 40

Directly Proportional

Inversely Proportional

R ∝ 1 ÷√F R = K ÷ √F  When R = 32             F = 1632 = K ÷√1632 = K ÷ 4      x4128 = KR = 128 ÷ √F16 = 128 ÷ √F         x√F16 x √F = 128        ÷16√F = 8        x^2F = 6

R is inversely proportional to the square root of F.When R = 32, F = 16Find the value of F, when R = 16

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Finding the LCM and HCF

area of a triangle

A = (a x b x sin C) ÷ 2       re-arrangeA = (c x a x sin B) ÷ 2A = (9 x 15 x sin 110°) ÷ 2A = (135 x sin 110°) ÷ 2A = 126.8585038 ÷ 2A = 63.4292519A ≈ 63.4 cm^2 (3 s.f.)

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Caption: : The equation you need is A = (a x b x sin C) ÷ 2

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Big ConeV = (ᴨ x r^2 x h) ÷ 3V = (ᴨ x 12^2 x 10) ÷ 3V = (ᴨ x 144 x 10) ÷ 3V = 1440ᴨ ÷ 3V = 480ᴨSmall ConeV = (ᴨ x r^2 x h) ÷ 3V = (ᴨ x 6^2 x 5) ÷ 3V = (ᴨ x 36 x 5) ÷ 3V = 180ᴨ ÷ 3V = 60ᴨ480ᴨ - 60ᴨ = 420ᴨFrustum Volume = 1319.468915                                      ≈ 1319.5 cm^3 (1 d.p.)

Frustums

Caption: : volume of a cone = (ᴨ x r^2 x h) ÷ 3

Surds

e.g. Simplify      √75*Highest root that is a factor of the number in the surd*= √(25 x 3)= √25 x  √3= 5√3

e.g. Multiply        √6 x √3*Multiply the numbers in the surd by each other, and outside ones are times by each other*= √18=√(9 x 2)= √9 x √2= 3√2