What is the domain of the relation below?

Mathematics

2 answers:

Sunny_sXe [5.5K]3 years ago

4 0

Answer:

it should be all real number

Step-by-step explanation:

Pie3 years ago

3 0

Answer:

A. x ≤ 5

Step-by-step explanation:

We know that finding the domain consists of finding where the function has an x value, so that rules out answer choice B which uses y, that gives the range.

Since the graph cuts off at a point (x = 5), We can confer that the domain is not all real numbers, so that eliminates D.

Now when you look at the graph, you can see that at x = 5, the x values start becoming smaller, so that rules out answer choice C which states that the x values at 5 start to get larger.

The answer is A because it includes x = 5, and the x values of the graph progressively get smaller.

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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

11Alexandr11 [23.1K]

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.)$