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3 years ago

What is an function because I don’t know what is it is so help me

1 answer:

6 0

is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

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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

Find the value of 40% of 1KM (in m)

labwork [276]

40% of 1 km in meters is 400 meters

<h3>What is percentage :</h3>

Percentage simply means per 100. Percentage can be express as decimal or fraction.

For example 25% of 80 can be found as follows:

25 / 100 × 80 = 2000 / 100 = 20

From the example, 25% of 80 is 20 .

Therefore, 40% of 1 km(m) can be found as follows:

Let's convert km to metres.

1000m = 1km

40% of 1000

40 / 100 × 1000 = 40000 / 100 = 400metres

Therefore, 40% of 1 km in meters is 400 meters

learn more on percentage here: brainly.com/question/19540991?referrer=searchResults

5 0

2 years ago

Read 2 more answers

What can be used to determine the length of segment AB?

Vikki [24]

It depends on what you mean by "what can be used", you can use a protractor or ruler since it's a line segment. OR you can use the formula a^ + b^ = c^ to find out all the measurements.......

If you still can't find it, then, you can try to find the other measurements around that specific line segments. And it DEPENDS on what you choose to find the length of this segment.

( There's no picture on my screen, so I'm guessing that you didn't put any.. )

Well, I hope this can help you :3

STAY SAFE!! :)

6 0

3 years ago

A taxi charges a pick-up fee p!us a charge per mile. Maria paid $15.00 for a 7 mile rode. To my paid $19.50 for a 10 mile ride.

lukranit [14]

Answer:

The y-intercept in coordinate form is (0, 4.5) and represents the taxi pick-up fee. The equation is y=1.5x + 4.5.

Step-by-step explanation:

This question is asking for the slope and y-intercept of a linear equation. A linear equation makes a straight line based on a constant rate of change. For this problem, the cost per mile is the slope, while the independent variable 'x' is the number of miles and the dependent variable 'y' is the total cost. In order to first find slope, you need to use the two points given (7, 15) and (10, 19.5) to set up a change in y / change in x, or (19.5-15)/(10-7) or 4.5/3 which is 1.5. So the slope, or cost per mile is $1.50. To find the y-intercept (b), or the cost of the pick-up fee, simply fill in your equation y=1.5x + b with your other variables and solve for 'b'. So, 15 = (1.5 x7) + b. or 15 = 10.5 +b, subtract 10.5 from both sides of the equation to get b=4.5.

5 0

3 years ago

You and your four friends are going to a concert. The total price for the tickets was $118.75 which includes a $10 service fee.

Alex787 [66]

Answer:475

Step-by-step explanation:

118.75 is the cost whitch includes a 10$ service fee

118.75x10=475

8 0

2 years ago