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2 years ago

Given the definitions of f(x) and g(x) below, find the value of (gºf)(-5).

Mathematics

1 answer:

jolli1 [7]2 years ago

5 0

Answer:

(g ￮ f)(- 5) = 4

Step-by-step explanation:

evaluate f(- 5) then substitute the value obtained into g(x)

f(- 5) = (- 5)² + 6(- 5) + 3 = 25 - 30 + 3 = - 2 , then

g(- 2) = 2(- 2) + 8 = - 4 + 8 = 4

(g ￮ f)(- 5) = 4

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Step-by-step explanation:

For a tank similar to a cylinder the volume is given by:

$V = \pi r^2 h$

For this case we know that $r=5m$ represent the radius, $h = 10m$ the height and the rate given is:

$\frac{dV}{dt}= \frac{100 L}{min}$

For this case we want to find the rate of change of the water level when h =6m so then we can derivate the formula for the volume and we got:

$\frac{dV}{dt}= \pi r^2 \frac{dh}{dt}$

And solving for $\frac{dh}{dt}$ we got:

$\frac{dh}{dt}= \frac{\frac{dV}{dt}}{\pi r^2}$

We need to convert the rate given into m^3/min and we got:

$Q = 100 \frac{L}{min} *\frac{1m^3}{1000L}= 0.1 \frac{m^3}{min}$

And replacing we got:

$\frac{dh}{dt}=\frac{0.1 m^3/min}{\pi (5m)^2}= 0.0012732 \frac{m}{min}$

And that represent $0.127 \frac{cm}{min}$

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3 years ago

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Answer:

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