Practice Mathematics III questions with answers and explanations.
Subtract 11 from both sides and divide by 3: x = (29-11)/3 = 6.
By Vieta’s formula, the sum of the roots equals the coefficient 19.
aₙ=a₁+(n−1)d=10+(16−1)×6=100.
An antiderivative is 3/2 x²+1x. At x=4, the value is 28.0.
The dot product is 3×3+2×5=19.
Percentage=(14/29)×100=48.28.
Subtract 10 from both sides and divide by 2: x = (20-10)/2 = 5.
By Vieta’s formula, the sum of the roots equals the coefficient 16.
aₙ=a₁+(n−1)d=9+(15−1)×5=79.
Choose an option to check your answer.
The sum is n(n+1)/2=10, so the mean is 10/4.
Choose an option to check your answer.
There are 2 favourable outcomes out of 9 equally likely outcomes, so P(red)=2/9.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
