Which graph shows a set of ordered pairs that represents a function?

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

pantera1 [17]

Answer:

The height of the pile is increasing at the rate of $\mathbf{ \dfrac{20}{56.25 \pi} \ \ \ \ \ ft/min}$

Step-by-step explanation:

Given that :

Gravel is being dumped from a conveyor belt at a rate of 20 ft³ /min

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

we know that radius r is always twice the diameter d

i.e d = 2r

Given that :

the shape of a cone whose base diameter and height are always equal.

then d = h = 2r

h = 2r

r = h/2

The volume of a cone can be given by the formula:

$V = \dfrac{\pi r^2 h}{3}$

$V = \dfrac{\pi (h/2)^2 h}{3}$

$V = \dfrac{1}{12} \pi h^3$

$V = \dfrac{ \pi h^3}{12}$

Taking the differentiation of volume V with respect to time t; we have:

$\dfrac{dV}{dt }= (\dfrac{d}{dh}(\dfrac{\pi h^3}{12})) \times \dfrac{dh}{dt}$

$\dfrac{dV}{dt }= (\dfrac{\pi h^2}{4} ) \times \dfrac{dh}{dt}$

we know that:

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

So;we have:

$20= (\dfrac{\pi (15)^2}{4} ) \times \dfrac{dh}{dt}$

$20= 56.25 \pi \times \dfrac{dh}{dt}$

$\mathbf{\dfrac{dh}{dt}= \dfrac{20}{56.25 \pi} \ \ \ \ \ ft/min}$

The height of the pile is increasing at the rate of $\mathbf{ \dfrac{20}{56.25 \pi} \ \ \ \ \ ft/min}$

8 0

3 years ago

Find the midpoint of the segment with the given endpoints.

andrew-mc [135]

To solve for the midpoint of the segment we use the equation that is given as:

(x1 + x2 / 2) , (y1 + y2 / 2)

For the points given,

(x1 + x2 / 2) , (y1 + y2 / 2)
(3+ 2 / 2) , (-5 + 9 / 2)
(5/2 , 2) or (2.5 , 2)

Hope this answers the question. Have a nice day. Feel free to ask more questions.

7 0

3 years ago

Read 2 more answers

Give at least three examples of how earlier periods made use of the accounting process? How did the accounting process help such

Ksju [112]

Answer:

i am not sure of these answer but what i know i am gonnna share eith you

Step-by-step explanation:

. The people relied on primitive accounting methods to record the growth of crops and herds. Because there was a natural season to farming and herding, it was easy to count and determine if a surplus had been gained after the crops had been harvested or the young animals weaned.

2. The use of the words "debit" and "credit" in accounting goes back to the days of single-entry bookkeeping, which had as its chief objective keeping track of amounts owed by customers (debtors) and amounts owed to creditors.

3. Accounting as an ad-hoc ordering system devised by the merchant. Its regular use provides the merchant with continued information about business, and allows to evaluate how things are going and to act accordingly.

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2 years ago

Which measurement is the best estimate for the mass of an apple?

Taya2010 [7]

It would be A because an apple can't be 150 g that's way to heavy same for 150kg

3 0

3 years ago

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Write the relation as a set of ordered pairs. WILL MARK BRANLIEST!! PLEASE HELP ASAP!!!!

dsp73

Answer:

Option a.

Step-by-step explanation:

An ordered pair is written in the following form: (x, y). It means, first the independent variable and secondly the dependent variable.

In the diagram, the first circle represents the independent variable, and the second circle represents the dependent variable.

Then, the set of ordered pairs is (From left to right)

(-3, 3) ; (0, 0) ; (2, -2).

So the correct option is option a.

8 0

3 years ago

Read 2 more answers