Algebra, arithmetic, reasoning.
The dot product is 4×4+3×6=34.
Rewrite the value using base 5: 3125 = 5^5. Matching exponents gives x = 5.
An antiderivative is 3/2 x²+1x. At x=4, the value is 28.0.
The dot product is 3×3+2×5=19.
Rewrite the value using base 4: 256 = 4^4. Matching exponents gives x = 4.
Choose an option to check your answer.
Use the circle-area formula A = πr². Substituting r = 4 gives A = π × 4² = 16π.
Percentage=(5/30)×100=16.67.
Subtract 5 from both sides and divide by 6: x = (11-5)/6 = 1.
By Vieta’s formula, the sum of the roots equals the coefficient 12.
aₙ=a₁+(n−1)d=4+(16−1)×6=94.
Choose an option to check your answer.
The sum is n(n+1)/2=36, so the mean is 36/8.
f′(x)=3x²+10x. Substituting x=3 gives 57.
