Postgraduate Mathematics II task 21: Enter the dot product of vectors (4,6) and (2,4).
The dot product is 4×2+6×4=32.
Practice China questions with answers and explanations.
The dot product is 4×2+6×4=32.
Rewrite the value using base 5: 3125 = 5^5. Matching exponents gives x = 5.
Choose an option to check your answer.
Use the circle-area formula A = πr². Substituting r = 9 gives A = π × 9² = 81π.
Percentage=(14/29)×100=48.28.
Subtract 7 from both sides and divide by 7: x = (63-7)/7 = 8.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=15x²+12x. Substituting x=4 gives 288.
The dot product is 3×4+5×3=27.
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 = 8 gives A = π × 8² = 64π.
Percentage=(13/28)×100=46.43.
Subtract 6 from both sides and divide by 6: x = (48-6)/6 = 7.