What is the slope of the line in the graph? On a coordinate plane, a line goes through points (negative 2, negative 1) and (0, 1
2 answers:
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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:
Answer:
The height of the next door building is 41.7 feet
Step-by-step explanation:
* Lets study the situation in the problem
- The man standing on the roof of a building 64.0 feet high
- The angle of depression to roof of the next door building is 34.7°
- The angle of depression to the bottom of the next door building
is 63.3°
- We need to find the height of the next door building
* Lets consider the height of the man building and the horizontal
distance between the two building formed a right triangle and the
angle of depression is opposite to the side which represented the
height of the building
- Let the horizontal distance between the two buildings called x
# In the triangle
∵ The length of the side opposite to the angle of depression (63.3°)
is 64.0
∵ The length of the horizontal distance is x which is adjacent to the
angle of depression (63.3°)
- Use the trigonometry function tanФ = opposite/adjacent
∴ tan 63.3° = 64.0/x ⇒ use cross multiplication
∴ x (tan 63.3°) = 64 ⇒ divide both sides by (tan 63.3°)
∴ x = 64.0/(tan 63.3°)
∴ x = 32.1886 feet
- Lets use this horizontal distance to find the vertical distance between
the roofs of the two buildings
* Lets consider the height of the vertical distance between the roofs
of the two buildings and the horizontal distance between the two
building formed a right triangle and the
angle of depression is opposite to the side which represented the
vertical distance between the roofs of the two buildings
- Let the vertical distance between the roofs of the two buildings
called y
# In the triangle
∵ The vertical distance between the roofs of the two buildings is y
and opposite to the angle of depression (34.7°)
∵ The horizontal distance x is adjacent to the angle of
depression (34.7°)
∴ tan (34.7°) = y/x
∵ x = 32.1886
∴ tan 34.7° = y/32.1886 ⇒ use the cross multiplication
∴ y = 32.1886 (tan 34.7°)
∴ y = 22.2884 ≅ 22.3 feet
∴ The vertical distance between the roofs of the two
buildings is 22.3 feet
- The height of the next door building is the difference between the
height of the man building and the vertical distance between the
roofs of the two buildings
∴ The height of the next door building = 64.0 - 22.3 = 41.7 feet
