Practice Mathematics III questions with answers and explanations.
Percentage=(10/25)×100=40.00.
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There are 2 favourable outcomes out of 10 equally likely outcomes, so P(red)=2/10.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=3x²+8x. Substituting x=2 gives 28.
An antiderivative is 2/2 x²+1x. At x=3, the value is 12.0.
The dot product is 2×4+2×6=20.
Rewrite the value using base 3: 27 = 3^3. Matching exponents gives x = 3.
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Use the circle-area formula A = πr². Substituting r = 3 gives A = π × 3² = 9π.
Percentage=(9/24)×100=37.50.
Subtract 5 from both sides and divide by 4: x = (49-5)/4 = 11.
By Vieta’s formula, the sum of the roots equals the coefficient 10.
aₙ=a₁+(n−1)d=4+(10−1)×6=58.
