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3 years ago

Let f(x) = x + 7 and g(x) = x − 4. Find f(x) ⋅ g(x).

Mathematics

1 answer:

saveliy_v [14]3 years ago

6 0

For this case we have the following functions:

$f (x) = x + 7\\g (x) = x-4$

We must find the product of the functions:

$f (x) * g (x) = (x + 7) (x-4)$

We apply distributive property:

$f (x) * g (x) = x ^ 2-4x + 7x-28\\f (x) * g (x) = x ^ 2 + 3x-28$

Finally, the product of the functions is:

$x ^ 2 + 3x-28$

Answer:

$x ^ 2 + 3x-28$

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[a] Dye is removed from the pool at a rate of

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So the net rate of change of the amount of dye in the pool is given by the differential equation,

$\dfrac{\mathrm dq}{\mathrm dt}=-\dfrac{q(t)}{240}$

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[b] The ODE above is separable as

$\dfrac{\mathrm dq}q=-\dfrac{\mathrm dt}{240}$

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$\ln|q|=-\dfrac t{240}+C$

$e^{\ln|q|}=e^{-t/240+C}$

$\implies q(t)=e^{-t/240+C}=e^{-t/240}e^C=Ce^{-t/240}$

Now plug in the initial condition:

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$\implies\ln0.3=-\dfrac t{240}$

$\implies t=-240\ln0.3\approx288.953$

so the amount of dye in the pool is within the acceptable tolerance after about 289 min have passes, or about 4.82 hrs. So no, the filtration system is not up to the task.

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