What fraction of this shape is shaded?

Mathematics

1 answer:

Vanyuwa [196]3 years ago

7 0

Answer:

1/3

Step-by-step explanation:

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There are 28.35 g in an ounce and 2.21 lb in a kilogram. Juanita converts 3 kilograms to ounces. Is her conversion correct? Expl

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3 kg = 105.82 ounces

Step-by-step explanation:

We have,

1 ounce = 28.35 g

and

1 kg = 2.21 lb

If we want to the value of 3 kg to ounces. The direct relation between kilogram to ounce is as follows :

1 kg = 35.274 ounces

It means,

3 kg = 105.82 ounces

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Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

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Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$