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2 years ago

What is the solution to the system of equations? Use the substitution method.

1 answer:

4 0

The answer is:
4x+2y=11} 4x+2y=11} x=2-2y
x-2=-2y } x+2y=2 } x=2-2(-3/6)
x=2-(-6/6)
4(2-2y)+2y=11 x=2-(-1)
8-8y+2y=11 x=3
8-6y=11
-6y=11-8
-6y=3/-6
y=-3/6=-1/2

So for my opinion the solution is A.(3,-1/2)

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And replacing we got:

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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:

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

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

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

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