Amodel train engine was moving at a constant speed on a straight horizontal track. as the engine moved along, a marble was fired into the air by a spring in the engine's smokestack. the marble, which continued to move with the same forward speed as the engine, rejoined the engine 1 sec after it was fired. the measure of the angle the marble's path made with the horizontal was 58degrees. use the information to find how high the marble went and how fast the engine was moving.

Alex drew a circle with right triangle prq inscribed in it, as shown below: the figure shows a circle with points p, q, and r on it forming an inscribed triangle. side pq is a chord through the center and angle r is a right angle. arc qr measures 80 degrees.

What is [tex] {7}^{98 + \sqrt{4} } - 3 \times (64 \div 2 + 4 - 36) \times a = a + 36[/tex]?

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).