MathDB

4

Part of 2012 Hanoi Open Mathematics Competitions

Problems(2)

Q4 - Hanoi Open Mathematical Olympiad 2012 - Junior Section

Source:

6/10/2012
Q4. A man travels from town AA to town EE through B,CB,C and DD with uniform speeds 3km/h, 2km/h, 6km/h and 3km/h on the horizontal, up slope, down slope and horizontal road, respectively. If the road between town AA and town EE can be classified as horizontal, up slope, down slope and horizontal and total length of each typr of road is the same, what is the average speed of his journey? (A)  2km/h(B)  2,5km/h;(C)  3km/h;(D)  3,5km/h;(E)  4km/h.(A) \; 2 \text{km/h} \qquad (B) \; 2,5 \text{km/h} ; \qquad (C ) \; 3 \text{km/h} ; \qquad (D) \; 3,5 \text{km/h} ; \qquad (E) \; 4 \text{km/h}.
analytic geometrygraphing linesslope
x=\frac12$ ($\sqrt[3]{2+\sqrt3}+\sqrt[3]{2-\sqrt3} (HOMC 2012 Q4)

Source:

7/24/2019
What is the largest integer less than or equal to 4x3−3x4x^3 - 3x, where x=2+33+2−332x=\frac{\sqrt[3]{2+\sqrt3}+\sqrt[3]{2-\sqrt3}}{2} ?
(A) 11, (B) 22, (C) 33, (D) 44, (E) None of the above.
algebrafloor functionRadicals