Senior-secondary mathematics task 176: Evaluate ∫₀^5 (4x+1) dx.
An antiderivative is 4/2 x²+1x. At x=5, the value is 55.0.
Practice china-gaokao-mathematics questions with answers and explanations.
An antiderivative is 4/2 x²+1x. At x=5, the value is 55.0.
The dot product is 4×2+2×4=16.
Rewrite the value using base 5: 3125 = 5^5. Matching exponents gives x = 5.
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Use the circle-area formula A = πr². Substituting r = 9 gives A = π × 9² = 81π.
Percentage=(10/35)×100=28.57.
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Use the circle-area formula A = πr². Substituting r = 8 gives A = π × 8² = 64π.
Percentage=(9/34)×100=26.47.
Subtract 9 from both sides and divide by 3: x = (24-9)/3 = 5.
By Vieta’s formula, the sum of the roots equals the coefficient 15.
aₙ=a₁+(n−1)d=8+(8−1)×4=36.
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The sum is n(n+1)/2=15, so the mean is 15/5.
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There are 2 favourable outcomes out of 8 equally likely outcomes, so P(red)=2/8.