If you are in a great deal of Dept but want to save for an emergency fund, you should

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

3 years ago

Put these numbers in order from least to greatest 12%, -1/2, 0, -0.22, 0.56

uysha [10]

Answer: -1/2, -0.22, 0, 12%, 0.56

Step-by-step explanation:

-1/2 is equal to -0.50, making it the number with the least value.

-0.22 is closer to 0 than -0.50, meaning it is greater then -0.50 and less than 0.

0 is between the negative and positive numbers, giving it the spot that it has.

12% is equivalent to 0.12, meaning it is more than 0, and less than 0.56, which is the greatest number.

0.56 has more value than any other number in the problem, meaning it goes last in the order.

8 0

3 years ago

describe how do you know if two lines are parallel if all you knew were the equations of the two lines

Marrrta [24]

Two lines are parallel if they intersect.

7 0

2 years ago

Read 2 more answers

Lucy deposits $7000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in th

Fofino [41]

7000*.03*6=?? Step 1. multiply 7000*.03=210 Step 2. multiply 210*6=1260. the answer is $1,260.00

5 0

3 years ago

A model airplane is built at a scale of 1 inch to 6 feet. If the model plane is 8 inches long, how many feet long is the actual

noname [10]

The airplane is 48 feet long in real dimensions.

To find out how long the airplane actually is, we can use the scale and input our amount of inches that it is measured by.

So, 1 inch equals to 6 feet.

Our model plane is 8 inches.

Now, we plug it in.

8 inches = 6(8)

8 inches = 48 feet

Therefore, the length of the real airplane is 48 feet.

48 feet

5 0

3 years ago

Read 2 more answers