Suppose the sand in a sand box with length 14 feet, width 8 feet, and height 1.5 feet is to be removed. The density of the sand (in pounds per cubic feet) h feet from the bottom is given by δ(h)=2.5−h. Find the work required to completely empty the sandbox.

The work required is  

Explanation:

  The volume of the sand box is mathematical represented as

Substituting 14 feet for L,  8 feet for W into the equation

The force as a result of the sand in the disk is mathematically represented as

     Substituting (2.5-h)  for

Now the work that is required to lift the sand from h = 0 to a height of  h=1.5 m is mathematically represented as

Now above is the formula for change in work done in order to obtain the workdone we integrate

they are non-matter

explanation:

they are non-matter. basically, any type of energy or any abstract concept is an example of something that does not matter. other examples include dreams, magnetism, radio, and hate

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west