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Fiesta28 [93]
3 years ago
14

Prove by mathematical induction. 2n<(n+2)!, for n ≥ 0, where n ∈ ℤ

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
6 0

The question is difficult for a beginner like me

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PLease help me ,really need help with explanation​
mylen [45]

a)

Check the picture below.

b)

volume wise, we know the smaller pyramid is 1/8 th of the whole pyramid, so the volume of the whole pyramid must be 8/8 th.

Now, if we take off 1/8 th of the volume of whole pyramid, what the whole pyramid is left with is 7/8 th of its total volume, and that 7/8 th is the truncated part, because the 1/8 we chopped off from it, is the volume of the tiny pyramid atop.

Now, what's the ratio of the tiny pyramid to the truncated bottom?

\stackrel{\textit{\Large Volumes}}{\cfrac{\textit{small pyramid}}{\textit{frustum}}\implies \cfrac{~~\frac{1}{8}whole ~~}{\frac{7}{8}whole}}\implies \cfrac{~~\frac{1}{8} ~~}{\frac{7}{8}}\implies \cfrac{1}{8}\cdot \cfrac{8}{7}\implies \cfrac{1}{7}

3 0
2 years ago
You get in an elevator and go down 8 floors. You exit on the 16th floor. Write and solve an equation to find what floor you got
disa [49]
So floor that you started is x
go down 8 means -8
end on 16

so
x-8=16
add 8
x=24

started on 24
3 0
4 years ago
My friend needs help on this problem, plz help, thank you
Dafna1 [17]

Answer:

3 = 95, 4 = 85, if a and b are parallel

Step-by-step explanation:

7 0
3 years ago
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Solve. Write your answer in interval notation.
lina2011 [118]

Answer: x < 3 or x ≥ 11

(-∞, 3) or [11, ∞)

Step-by-step explanation:

subtract 4 from each side

2x < 6 .     or .         3x  ≥ 33

x < 3 or x ≥ 11

make sure you have an OPEN DOT at 3 pointing to negative infinity and a CLOSED DOT at 11 pointing to positive infinity.  

3 0
3 years ago
If you spin the spinner 400 times, how many times can you expect it to land on an even number?
TiliK225 [7]
2/8 Hdhdjdjsksjsjsjsjsjsjsnsjsjjsksjsjsjs
3 0
3 years ago
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