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DiKsa [7]
2 years ago
8

Maria's luggage travels 36 m in 3 minutes. What is the speed of the conveyer belt in kilometers per hour?

Mathematics
1 answer:
creativ13 [48]2 years ago
6 0

Answer:

0.72 km per hour

Step-by-step explanation:

First, find the speed in meters per hour. Create a proportion where x is this speed:

\frac{36}{3} = \frac{x}{60}

3x = 2160

x = 720

So, the speed is 720 meters per hour. Convert this to kilometers per hour by dividing 720 by 1000, since there are 1000 meters in a kilometer:

720/1000

= 0.72

So, the speed of the conveyer belt is 0.72 km per hour

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Step-by-step explanation:

Let <em>x</em> be the width and <em>y </em>the length of the rectangular field.

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20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30

Because the length is always positive the only point we take is x=30. We thus test the intervals (0, 30) and (30, \infty)

C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0

we see that total cost function is decreasing on (0, 30) and increasing on (30, \infty). Therefore, the minimum is attained at x=30, so the minimal cost is

C(30)=20(30)+\frac{18000}{30}\\C(30)=1200

The least cost of fencing for the rancher is $1200

Here’s the diagram:

3 0
3 years ago
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