Practice Mathematics III questions with answers and explanations.
Subtract 3 from both sides and divide by 2: x = (21-3)/2 = 9.
By Vieta’s formula, the sum of the roots equals the coefficient 12.
aₙ=a₁+(n−1)d=2+(8−1)×4=30.
By Vieta’s formula, the sum of the roots equals the coefficient 18.
aₙ=a₁+(n−1)d=10+(7−1)×3=28.
Choose an option to check your answer.
The sum is n(n+1)/2=55, so the mean is 55/10.
Choose an option to check your answer.
There are 4 favourable outcomes out of 9 equally likely outcomes, so P(red)=4/9.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=9x²+16x. Substituting x=3 gives 129.
An antiderivative is 3/2 x²+3x. At x=4, the value is 36.0.
The dot product is 3×4+4×3=24.
Subtract 11 from both sides and divide by 8: x = (75-11)/8 = 8.
