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3 years ago

Simplify. 5x^3/7x^3+x^4

Mathematics

1 answer:

gizmo_the_mogwai [7]3 years ago

5 0

Answer:

5x^6/7 + x^4

Step-by-step explanation:

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3 years ago

Kelly rows a boat at the rate of 7040 yards per hour. How fast did Kelly row in miles?

irakobra [83]

Answer:

4 mph

Step-by-step explanation:

yard → mile = divide the length value by 1760

7040 / 1760 = 4 miles per hour

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3 years ago

Carol sold twice as many magazine subscriptions as Jennifer. If Carol and Jennifer sold 90 subscriptions in all, how many subscr

goblinko [34]

Hello there!

Carol would have sold 60 subscriptions and Jenifer would have sold 30

The correct answer is option D, 60

I hope this help!

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3 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

If sin(x) = 0 and cos(x) = 1, what is cot(x)?

Nata [24]

Answer:

undefined

Step-by-step explanation:

Sin(x) = 0 where x = 0

Cos(x) = 1 where x = 0

Cot(0) is undefined

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3 years ago

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