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2 years ago

What is the correct answer to this?

Mathematics

2 answers:

ra1l [238]2 years ago

7 0

Answer:

33.4933 ≈ 33.5 mm³

Step-by-step explanation:

Given that,

→ Radius (r) = 2 mm

Formula we use,

→ 4/3 πr³

Let's solve for the volume of sphere,

→ 4/3 πr³

→ 4/3 × 3.14 × 2 × 2 × 2

→ 4/3 × 3.14 × 8

→ 4/3 × 25.12

→ 100.48/3

→ 33.4933

→ [ ≈ 33.5 mm³ ]

Hence, volume of sphere is 33.5 mm³.

Maksim231197 [3]2 years ago

4 0

Radius=r=2mm

Now

Volume

V=4/3πr³
V=4/3π(2)³
V=4/3π(8)
V=32π/3
V=33.49mm³

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nignag [31]

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we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

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$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

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