15 pounds / 35 sandwiches ~ 0.43 pounds ham per sandwich
Step-by-step explanation:
a rectangular prism (like this brick) has the same basic structure as a cube (like a die) : it has 6 sides.
while a die has 6 equal sides, a rectangular prism has 3 pairs of equal sides :
top and bottom
left and right
front and back
all we have to do is calculate the areas of the 6 rectangles and add them up. that's it.
your remember, the area of a rectangle is
length × width
in our case we have
top and bottom : 2.5×11.5 × 2 = 28.75×2 = 57.5 in²
left and right : 2.5×5 × 2 = 12.5×2 = 25 in²
front and back : 11.5×5 × 2 = 57.5×2 = 115 in²
so, the total surface area of the whole block is
57.5 + 25 + 115 = 197.5 in²
Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.
Step-by-step explanation:
Salt in the tank is modelled by the Principle of Mass Conservation, which states:
(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)
Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

By expanding the previous equation:

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

Since there is no accumulation within the tank, expression is simplified to this:

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:
, where
.

The solution of this equation is:

The salt concentration after 8 minutes is:

The instantaneous amount of salt in the tank is: