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Anna71 [15]
3 years ago
8

eight wooden spheres with radii 3 in. are packed snugly into a square box 12 in. on one side. the remaining space is filled with

packing beads. what is the volume occupied by the packing beads? what percentage of the volume of the box is filled with beads?
Mathematics
1 answer:
ZanzabumX [31]3 years ago
3 0
Vbox-vspheres

vbox=, I assume we are dealing with l=w=h
so
v=lwh=12^3=1728

vsphere=(4/3)pir^3
r=3
vsphere=(4/3)pi3^3=4pi9=36pi
8 of them so
8 times 36pi=288pi or about 904.7786842338604526772412943845 cubic inches



vbox-sphere=1728-904.7786842338604526772412943845=823.2213157661395473227587056155
space filled by packing beads is about 823.22 cubic inches
beads percent is 823.2213157661395473227587056155/1728 times 100=47.64% filled by beads






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Answer:

y(x) = 0.0732x + 17.32

Step-by-step explanation:

The equation for the monthly charge has the following format

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Base charge of $17.32 per month.

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charge of 7.32 cents per kilowatt-hour

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Write an equation for the monthly charge y in terms of x, the number of kilowatt-hours used.

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tino4ka555 [31]

Hi! I'm happy to help!

To solve this, we first need to look at the perimeter equation:

P=2L+2W

We don't know our length, so we can represent it with x. Since our width is 2 feet shorter than x, we can represent it with x-2. Now, we plug these values into our equation:

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Let's simplify what the width is by multiplying:

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Now, we just need to solve for x in order to find our length and width.

First, we need to isolate x on one side of the equation. We can do this by adding 4 to both sides:

56=4x-4

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Now, all we have to do is divide both sides by 4 and x will be fully isolated:

60=4x

÷4  ÷4

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Now that we know x, let's plug this into our previous equations:

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<u>L=15</u>

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To verify our answers, we can plug this into our perimeter equation:

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After double checking our answers, we know that our length is 15 and our width is 13.

I hope this was helpful, keep learning! :D

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