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3 years ago

Find the area and perimeter of a rectangle with a length of (6x2-10) and a width of (4x+3)

Mathematics

1 answer:

mestny [16]3 years ago

5 0

Answer:6x2=12-10=2 and 4×+3=12

Step-by-step explanation:

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Evaluate each expression please help(the crossed out ones are irrelevant)

olga nikolaevna [1]

9. 31 + 5 = 36
10. 16 - 4 = 12
12. 9
13. 44 + 34 = 78
14. 101 - 1 = 100

15. -539 ???
16. 15 ??
17. |-435| = 435

7 0

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

Harry cycles 8 kilometres in 30 minutes.<br> Calculate his average speed, in km/h

Lerok [7]

8 km / 0.5 hr
= 16 km/h

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2 years ago

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Write three items that a fraction can represent.

natka813 [3]

The first thing that fraction can can represent is Pizza, pie,and onions. Because you can cut the pizza, the pie, and the onion into different or equal spaces. Hoped it helped.

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3 years ago

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Group of kids rode horses to canyon. 20 eyes 30 legs between them. How many horses

Solnce55 [7]

If all were kids, there would be 20 legs. A horse has 2 more legs than a kid. The extra 10 legs can be attributed to there being 5 horses.

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2 years ago