For each home run hit in a baseball game, a

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

Please help me i really need help please help me

Lapatulllka [165]

Answer:

The total surface is 48 ft

Step-by-step explanation:

5 0

3 years ago

He earned a salary of $80,000 last year and sold stocks for $5,000. Which of the following types of income did Padraig have?

PSYCHO15rus [73]

Answer:

Step-by-step explanation:

There are 3 main types of income one can generate. They are termed as the earned income, the passive income and the capital gains income. Earned income is the compensation you get from working or offering a service. Passive income is the type of income you generate from what you own or your assets. Lastly, Capital gains income, also called "portfolio income", is the money generated from selling investments at a much higher price. Padraig have two type of income here. He had earned income by receiving the $80000 salary and he had capital gains income for selling stocks for $5000.

3 0

3 years ago

PLEASE HELP ME WITH THIS IT IS DUE RIGHT NOW

Ugo [173]

Step-by-step explanation:

1. Perimeter = 2 ( 5+4) = 18 cm

Area = 5 × 4 = 20 cm^2

2. Perimeter = 2 (5+5) = 20 cm

Area = 5 × 5 = 25 cm^2

3. Cups of seed needed per sq. meter = Area of the rectangle backyard

= 6 × 7

= 42 cups of seed

4. Feet of fence needed = Perimeter of the Square garden

= 2(8+8)

= 32 feet

5. Perimeter of rectangular quilt = 2 (4+6) feet

= 20 feet

6. Area of the room = 9 feet × 8 feet

= 72 feet^2

4 0

3 years ago

Find AC and FB. Points B, D, and F are midpoints of the sides of ACE. EC=40 and DF=18.

ANTONII [103]

The second option. A is 36 and B is 20. FD is half of AC, so 18*2 is 36. FB is half of EC, so it’s 20.

4 0

3 years ago

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