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3 years ago

If arctan(3/5)=K Tan(k)=?

Mathematics

2 answers:

Marizza181 [45]3 years ago

4 0

Answer:

3/5

Step-by-step explanation:

hichkok12 [17]3 years ago

3 0

$arctan(x)=y$

this function is the inverse function of tan...

$arctan(x)=tan^{-1}(x)$

then...

$x=tan(y)$

in this case

$arctan(\frac{3}{5})=K$

$\frac{3}{5}=tan(K)$

$\boxed{\boxed{tan(K)=\frac{3}{5}}}$

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What is -6 divided by 3/7x

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Step-by-step explanation:

$- 6 \div \frac{3}{7x} \\ \\ = - 6 \times \frac{7x}{3} \\ \\ = - 2 \times 7x \\ \\ = - 14x$

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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:

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

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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:

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

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3 years ago

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o-na [289]

2 and 4.5 is not equivilant since 2 and 4.5 cannot go together (the 0.5 does not help and so it does not make it equivalent.)

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