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2 years ago

Use the diagram and the value of x to find the measures of BCE and ECF.

Mathematics

1 answer:

stepan [7]2 years ago

7 0

Answer:

125° and 55°

Step-by-step explanation:

∠ BCE and ∠ ECF are adjacent angles and are supplementary, thus

10x + 15 + 5x = 180, that is

15x + 15 = 180 ( subtract 15 from both sides )

15x = 165 ( divide both sides by 15 )

x = 11

Thus

∠ BCE = 10x + 15 = 10(11) + 15 = 110 + 15 = 125°

∠ ECF = 5x = 5(11) = 55°

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2 years ago

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2 years ago

Water is added to a cylindrical tank of radius 5 m and height of 10 m at a rate of 100 L/min. Find the rate of change of the wat

nirvana33 [79]

Answer:

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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:

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

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

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

And replacing we got:

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

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2 years ago

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