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zvonat [6]
3 years ago
10

There are 5 gears connected in a row, the first one is connected to the second one, the second one is connected to the third one

, and so on.
If the first gear is rotating clockwise, what direction is the fifth gear turning?
Mathematics
1 answer:
IrinaVladis [17]3 years ago
5 0

Answer:

fifth gear is also rotating clockwise

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2 years ago
A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int
Wittaler [7]

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:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}

By expanding the previous equation:

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)

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

V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0

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

c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}

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

V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}, where c(0) = 0 \frac{pounds}{gallon}.

\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}

The solution of this equation is:

c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})

The salt concentration after 8 minutes is:

c(8) = 0.166 \frac{pounds}{gallon}

The instantaneous amount of salt in the tank is:

m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds

3 0
3 years ago
3<br> What is the difference of<br> 21<br> ?<br> 4
PilotLPTM [1.2K]

Answer:

The difference is 4–3. If you want the difference between 3 and -4, then the difference is 7.

Step-by-step explanation:

6 0
3 years ago
Solve the equation for x. 1 3 (6x − 9) = −33
KIM [24]

Answer:

<u>x = 1.07</u>

Step-by-step explanation:

13 ( 6x - 9) = -33

78x  - 117 = -33            ( opening brackets and multiplying )

78x  = 84                     ( - 117 taken to the other side makes it positive)

  x  =  84 / 78

  x  =  <u>1.07</u>

7 0
3 years ago
Read 2 more answers
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