Let a, b be real numbers. consider the equation z = ax+by. prove that there are two 3-vectors v1, v2 such that the set of points [x, y, z] satisfying the equation is exactly the set of linear combinations of v1 and v2. (hint: specify the vectors using formulas involving a, b.)

Given the points a(-2, 1) and b(8, 6), find the coordinates of the point c on directed line segment ab, that partitions ab in the ration 2: 3.

Long division the problem is 40 ➗ 348 = ?

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 (%).