In your garden, sandy soil can be corrected by adding what?

an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

4 years ago

An HR director numbered employees 1 through 50 for an extra vacation day contest. What is the probability that the HR director w

blsea [12.9K]

Multiples of 13 from 1-50 : 13 , 26 , 39
total number from 1-50 : 50
no. of employees who is not a multiple of 13 : 50-3= 47
Probability = 47/50
I’m not sure if this is correct :( I tried hahaha

7 0

3 years ago

Classify the angle pair using all names that apply

Nesterboy [21]

Answer:

Vertical and supplementary

4 0

3 years ago

Read 2 more answers

I need help with this plzzz theres also a part 2 b

Artemon [7]

Step-by-step explanation:

Because the line doesn't start at 0 (right at the bottom) and that shows that it is not directly proportional to x.

Hope it helped.

8 0

3 years ago

Simplify (3√-5 +2)(4√-12 -1)<br> Thank you in advance<br> Full steps so I can understand!

Shkiper50 [21]

Answer:

12√60 - 3√-5 + 8√-24 -2

Step-by-step explanation:

Use the distributive property

Multiply each by the other term outside their parantheses

for example multiply 3√-5 by 4√-12 and 3√-5 by -1.

5 0

3 years ago

Read 2 more answers