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Naya [18.7K]
3 years ago
15

12x-20y=108 3x+ky=27 what is k

Mathematics
1 answer:
Sedaia [141]3 years ago
3 0

Let's look at the second equation and try multiplying it by 4:

4 * (3x + ky) = 4 * 27

Which gives us:

12x + 4ky = 108

This looks almost exactly like the first equation except that instead of -20y, there is 4ky. We could try making them equal to each other and solving for k:

-20y = 4ky

-20 = 4k

k = -5

Then, the answer is k = -5.

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A cone has a volume of 108 pi and a base diameter of 12. What is the height of the cone?
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Answer:

h  = 9 units of length

Step-by-step explanation:

Volume of a circular right cone is:

V(c)  = (1/3)*Area of the circular base * h

Where h is the height of the cone, then

V(c)  =  (1/3) * π * r² * h

And  we have that  V(c) = 108*π

Then:

108 * π  =  (1/3) * π * r² * h                  (1)

We know diameter of the circular base is 12 units, according to that

r =  d/2     ⇒  r = 12/2     r = 6 units

Then:

108 * π  [ cubic units ]  =  (1/3) * π * (6)² * h  [square units] [ units of length]

When simplifying we have to take into account that in order to keep last equation h needs to have units of length  

Therefore:

108  =  (1/3) * 36 * h

h = ( 108* 3 )/ 36

h  = 9 units of length

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