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aleksley [76]
3 years ago
11

You are going on a field trip in a school bus. A special detector placed on one of the bus's tires counts the number of rotation

s completed by the tire during the journey. The tire's diameter is 1 meter, and it made 8000 rotations during the trip. How far did the bus travel? Give an exact answer.
Mathematics
2 answers:
andrey2020 [161]3 years ago
7 0

Answer:

25,120

Step-by-step explanation:

I got it on Khan Academy it says that this is the ansewr to the question

Hope this helps

Regards Jaygtgajm11

Akimi4 [234]3 years ago
6 0
The way tires on wheels work is that when the wheel turns one complete
turn, it moves (forward or backward) by a distance that's the circumference
of the tire.

Now, we know that the circumference of a circle is (π) times the diameter.
The diameter of the tire on this bus is 1 meter.  So its circumference is
(π · 1 meter), and every time it turns once, the bus moves 1 meter down
the road.

If the tire rotated 8,000 times, then the bus moved 8,000π meters,
or 8π kilometers.

THAT's the exact answer.  If you want to know how far that actually is,
then you take some number that's approximately π and multiply it by
8 km.  You can never get an exact answer like that, because you can
never write the exact value of π with digits.

In school, we often use  ' 3.14 ' for π .  If you do that, then the bus
traveled

                   (8 km) x (3.14)  =  25.1 kilometers .

When you do that, you have to remember that it's approximate.
If you want an exact answer, then you have to leave π in the answer.
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describe what would be true about the rate of change in a situation that could be represented by a graphed line and an equation
Andru [333]
If y=mx+b,

\frac { dy }{ dx } =m

You can't differentiate a constant, so dy/dx=m.
5 0
3 years ago
A travelling salesman sells milkshake mixing machines and on average sells 8.9 machines per month. He needs to sell at least 3 m
Goshia [24]

Answer:

0.67% probability he will have to shut down after this month

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given time interval.

On average sells 8.9 machines per month.

So \mu = 8.9

Using the Poisson distribution, what is the probability he will have to shut down after this month

If he sells less than 3 machines.

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = 0) = \frac{e^{-8.9}*8.9^{0}}{(0)!} = 0.0001

P(X = 1) = \frac{e^{-8.9}*8.9^{1}}{(1)!} = 0.0012

P(X = 2) = \frac{e^{-8.9}*8.9^{2}}{(2)!} = 0.0054

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0001 + 0.0012 + 0.0054 = 0.0067

0.67% probability he will have to shut down after this month

5 0
3 years ago
An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the ref
hichkok12 [17]

Answer:

P is exactly 3km east from the oil refinery.

Step-by-step explanation:

Let's d be the distance in km from the oil refinery to point P. So the horizontal distance from P to the storage is 3 - d and the vertical distance is 2. Hence the diagonal distance is:

\sqrt{(3 - d)^2 + 2^2} = \sqrt{(3 - d)^2 + 4}

So the cost of laying pipe under water with this distance is

800000\sqrt{(3 - d)^2 + 4}

And the cost of laying pipe over land from the refinery to point P is 400000d. Hence the total cost:

800000\sqrt{(3 - d)^2 + 4} + 400000d

We can find the minimum value of this by taking the 1st derivative and set it to 0

800000\frac{2*0.5*(3-d)(-1)}{\sqrt{(3 - d)^2 + 4}} + 400000 = 0

We can move the first term over to the right hand side and divide both sides by 400000

1 = 2\frac{3 - d}{\sqrt{(3 - d)^2 + 4}}

\sqrt{(3 - d)^2 + 4} = 6 - 2d

From here we can square up both sides

(3 - d)^2 + 4 = (6 - 2d)^2

9 - 6d + d^2 + 4 = 36 - 24d + 4d^2

3d^2-18d+27 = 0

d^2 - 6d + 9 = 0

(d - 3)^2 = 0

d -3 = 0

d = 3

So the cost of pipeline is minimum when P is exactly 3km east from the oil refinery.

3 0
3 years ago
Explain how you know that x^2-8x+20 is always positive. <br> Please help.
IRISSAK [1]

Answer:

if you rearrange to complete the square, you get (x^2-4)^2 +4

and seeing as anything squared will always be positive or zero, the lowest possible value for (x^2-4)^2 is 0, when x = 4

and 0 + 4 = 4, which is greater than 0, so positive

Step-by-step explanation:

4 0
3 years ago
The numbers of carrot muffins and walnut muffins sold at a cafeteria yesterday are
Mnenie [13.5K]

Answer:

36%

Step-by-step explanation:

9÷25

6 0
3 years ago
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