Como calcular la cantidad de horas por proyecto si un contratista tiene 5,000 horas-hombres y el costo es de $10 y $12 por proyecto para un total de $55.000 horas-homres

Each project has 2.500 man-hours

Step-by-step explanation:

Available man hours: 5000

For two projects          Costs $

X: project A                     10

Y: project B                     12

Approach:

X + Y = 5000 => X = 5000 - Y

10 * X + 12 * Y = 55000

replacing:

10 * (5000 - Y) + 12 * Y = 55000

50000 - 10 * Y + 12 * Y = 55000

2 * Y = 55000 - 50000

Y = 5000/2

Y = 2500

For X:

X = 5000 - 2500

X = 2500

The number of hours available for each project are:

Projects Man            hours

X: project A              2500

Y: project B              2500

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this