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pav-90 [236]
1 year ago
13

A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45

kmph in the same direction. In how much time will the train pass the jogger?.
Mathematics
1 answer:
Lapatulllka [165]1 year ago
5 0

The train will pass the jogger in 36 seconds.

Length of train = 120m

Speed of train = 45kmph

Distance by which the jogger is ahead of the engine of the train = 240 m

Speed of jogger = 9 kmph

To pass the jogger, the train will have to cover the length of the train and the distance by which the jogger is ahead of the engine of train.

Hence,

Distance = 120 + 240 = 360m

As,

Time = Distance/Speed

Relative speed of train w.r.t jogger = 45 - 9 = 36 kmph = 10 m/s

Hence,

Time = 360/10 = 36 seconds.

To learn more about train, here:-

brainly.com/question/21218609

#SPJ4

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NemiM [27]

Answer:

The minimum average cost is $643.75

It should be built 62.5 machines to achieve the minimum average cost

Step-by-step explanation:

The equation that represents the cost C to produce x DVD/BLU-ray players is C = 0.04x² - 5x + 800

To find the minimum cost differentiate C to equate it by 0 to find the average cost per machine and to find the value of the minimum cost

∵ C = 0.04x² - 5x + 800

- Differentiate C with respect to x

∴ \frac{dC}{dx}=0.04(2)x^{2-1}-5(1)x^{1-1}+0

∴ \frac{dC}{dx}=0.08x-5

- Equate \frac{dC}{dx} by 0

∴ 0.08x - 5 = 0

- Add 5 to both sides

∴ 0.08x = 5

- Divide both sides by 0.08

∴ x = 62.5

That means the minimum average cost is at x = 62.5

Substitute the value of x in C to find the minimum average cost

∵ C = 0.04(62.5)² - 5(62.5) + 800

∴ C = 643.75

∵ C is the average cost

∴ The minimum average cost is $643.75

∵ x is the number of the machines

∴ It should be built 62.5 machines to achieve the minimum

   average cost

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3 years ago
How is a 15% discount similar to a 15% decrease? Explain.
andrey2020 [161]
They are the same. Example: If something costs 100$ and you found a coupon to get a 15% discount you will save: 15$ and your cost will be 100$-15$=85$ Hope this helped! Have a great day!

7 0
3 years ago
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a bird of species a when diving can travel four times as fast as a bird of species b top speed if the total speeds of these two
weeeeeb [17]
X will be the speed of species b and 4x will be the speed of species a:

x + 4x = 180
5x = 180
x = 180 / 5
x = 36 m/h

If species b has a speed of 36 m/h, the speed of species a is 4 times that:

4 x 36 = 144 m/h.


Answer:

\boxed {\bf A~=~36~m/h~and~B~=~144~m/h}


Hope it helped,

Happy homework/ study/ exam!
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3 years ago
Please help I don’t understand number 16
Allisa [31]

Let's go step by step:

a) You are given four couples of x and y values which model the relationship between the number of drinks and their cost. So, the couple (x,y)=(0,0) means that if you buy zero drinks, you spend no money. That makes sense. The next information we have is (x,y) = (2,3), which means that two drinks cost 3 dollars, and so on.

So, you simply need to draw on the grid the four points

(0,0),\ (2,3),\ (4,6),\ (6,9)

b) The domain is the set of inputs. Since we only know the value of the function on four different points (we know the price for 0,2,4 and 6 drinks), the domain is discrete. In fact, a continuous domain must contain an interval (for example, [1,2] is a continuous domain), whereas if you pick a certain number of points (like in this case: we picked 0,2,4 and 6), the domain is discrete.

c) Once the points are drawn on the grid, you can see that they all lie on the same line. To find that line, we will only need two of those points (once two points are fixed, there is only one line passing through them). In general, the equation of the line passing through P = (P_x,P_y) and Q = (Q_x,Q_y) is

\cfrac{x-P_x}{Q_x-P_x} = \cfrac{y-P_y}{Q_y-P_y}

Let's choose, for example, the first two points. The equation is

\cfrac{x-0}{2-0} = \cfrac{y-0}{3-0} \iff \cfrac{x}{2} = \cfrac{y}{3} \iff y=\cfrac{3}{2}x

d) Now that we know the equation of the line, we can compute the cost of any number of drinks: the equation of the line is a function that associates a cost, y, with every possible number of drinks, x.

Of course, some associations will be odd - we can compute the cost of \sqrt{2} drink, but what would it mean?

Anyway, the question about the cost of two drinks seems more than reasonable, so let's see which y value is associate with the particular x value of 2:

y = \cfrac{3}{2} x \implies y = \cfrac{3}{2}\cdot 2 = 3

So, two drinks cost 3 dollars.

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