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3 years ago

Someone plzzzzzz!!!!!

Mathematics

2 answers:

LuckyWell [14K]3 years ago

8 0

Answer:

Yes it does

Step-by-step explanation:

4 x -2 = -8

Alex777 [14]3 years ago

5 0

Answer:

yes

Step-by-step explanation:

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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

A rock drops from a height of 60m. how long does it take for it to hit the ground?

laila [671]

To solve for the time an object takes to hit the ground, the equation

y = y₀ + v₀t + ½gt², or just 0 = y₀ +½gt² since there is no initial velocity and the final y position is 0 (since it is on the ground). Therefore, t = (−2y₀/g)^½.

(-2*60/-9.8)^½ = 3.50 seconds.

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3 years ago

Write the expression a2b3c2d in expanded form.

Zanzabum

Answer:

a*2+b*2+c*2+d

Step-by-step explanation:

If i's meant to be Pythagorean theorem, a*a+b*b=c*c

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3 years ago

Which would be the best trend line for the given data set?

PSYCHO15rus [73]

I believe the correct answer would be a if it’s not remove my answer

6 0

3 years ago

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Which point is located at (–1, 3)? On a coordinate plane, point A is 1 unit to the right and 3 units down. Point B is 3 units to

Marizza181 [45]

Answer:

Point C.

Step-by-step explanation:

When the x-value is negative, the point is moving left. In this case, the point is moving left 1.

When the y-value is positive, the point is moving up. In this case, the point is moving up 3.

Only Point C fits the description.

4 0

3 years ago