Practice Mathematics II questions with answers and explanations.
Subtract 5 from both sides and divide by 7: x = (33-5)/7 = 4.
By Vieta’s formula, the sum of the roots equals the coefficient 16.
aₙ=a₁+(n−1)d=4+(16−1)×6=94.
The dot product is 3×3+3×5=24.
Subtract 4 from both sides and divide by 6: x = (22-4)/6 = 3.
By Vieta’s formula, the sum of the roots equals the coefficient 13.
aₙ=a₁+(n−1)d=3+(15−1)×5=73.
Choose an option to check your answer.
The sum is n(n+1)/2=36, so the mean is 36/8.
Choose an option to check your answer.
There are 3 favourable outcomes out of 10 equally likely outcomes, so P(red)=3/10.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=6x²+12x. Substituting x=3 gives 90.
An antiderivative is 3/2 x²+2x. At x=4, the value is 32.0.
