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3 years ago

Pedro built nine bicycles in 25 hours, at this rate how many bicycles will he build in a 400 hour week

Mathematics

1 answer:

Veseljchak [2.6K]3 years ago

8 0

Answer:

144 bicycles

Step-by-step explanation:

Are you sure it's 400 hour week?

We can find his rate in bicycles per hour.

9 bicycles in 25 hours = 9/25 bicycles/hour = 0.36 bicycles/hour

Now we multiply the hourly rate by 400 hours to find the number of bicycles.

0.36 bycycles/hour * 400 hours = 144 bicycles

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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

4 years ago

What is the shape of the graph of the function? h(t) = 0.32 - 0.5t

allsm [11]

Answer:

Answer (a) is correct

Step-by-step explanation:

This is not the same function that was given to you in the problem.

As you have typed it, this function is linear. The one in the homework problem is exponential.

We will ignore the linear function h(t) = 0.32 - 0.5t.

We will focus on h(t) = 0.32 - 0.5^t.

If t = 0, then 0.5^t = 0.5 ^0 = 1, and so h(0) = 0.32 - 1 = -0.68 => (0, -0.68)

Continuing with a few other t values chosen at random:

h(1) = -0.18

h(2) = 0.07

Notice that h is increasing as x increases!

h(4) = 0.2575

and so on.

answer A is the correct one.

h(1) = 0.32 - 0.5^1 = 0.32 - 0.5 = -0.18

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3 years ago

A headache medicine has a flush rate of 25% after 24hrs since a patient took it. James was prescribed a 35mg dose of the medicin

Bess [88]

James will need 115.08mg of medicine at the start of day 6.

5 0

3 years ago

What's the radius of a circle with an area of 64 square feet

Ivenika [448]

Radius equals: 4.51

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3 years ago

What is the value of x in the figure below? A-9 B-14 1/3 C-45 2/3 D-81

laila [671]

Answer:

Step-by-step explanation:

3x9+ 27 + 8= 35

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3 years ago