Algebra, arithmetic, reasoning.
An antiderivative is 1/2 x²+5x. At x=2, the value is 12.0.
The dot product is 1×3+6×5=33.
Rewrite the value using base 2: 4 = 2^2. Matching exponents gives x = 2.
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Use the circle-area formula A = πr². Substituting r = 6 gives A = π × 6² = 36π.
Percentage=(8/23)×100=34.78.
Subtract 7 from both sides and divide by 6: x = (37-7)/6 = 5.
By Vieta’s formula, the sum of the roots equals the coefficient 17.
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Use the circle-area formula A = πr². Substituting r = 5 gives A = π × 5² = 25π.
aₙ=a₁+(n−1)d=5+(8−1)×4=33.
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The sum is n(n+1)/2=28, so the mean is 28/7.
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There are 5 favourable outcomes out of 11 equally likely outcomes, so P(red)=5/11.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
