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OverLord2011 [107]
3 years ago
5

What is the answer to 8 3n/12=13?

Mathematics
1 answer:
Greeley [361]3 years ago
7 0
Does this say 8 × 3n/12=13? I want to be sure so I don't give you the wrong answer.
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Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.
nignag [31]

Answer:

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

1) check divisibility for n=1, f(1)=(1)^{5}-1=0  (divisible)

2) Assume that f(k) is divisible by 5, f(k)=(k)^{5}-k

3) Induction,

f(k+1)=(k+1)^{5}-(k+1)

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

=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k

Now, f(k+1)-f(k)

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

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.

3 0
3 years ago
A stone dropped from a bridge strikes the water 2.2 s later. How high is the bridge above thewater
mina [271]
Since you are giving no information whatsoever, the formula could be:

S = (1/2)g.t², where s is the distance, 9 =9.8 m/s² and t = time
S = (1/2).(9.8)(2.2)² ans S= 23.7 meters
7 0
3 years ago
PLEASE ANSWER FAST!!!! On Friday, Susan bought a dress for 35% off the regular price of $70.00. The next day, the dress that Sus
attashe74 [19]

Answer:

She would have saved 14 dollars more

Step-by-step explanation:

Hope this helps and plz mark brainliest :)

6 0
3 years ago
Read 2 more answers
1
fredd [130]
Hi there I know the answer but it was confusing so it has to be D or B
6 0
2 years ago
PLEASSEE HELPPPP HURRRY FIND THE SURFACE AREA HURRRYY
Aleksandr [31]

Answer:

The answer is 48.9 cm^2.

Step-by-step explanation:

Let's find the surface areas of the faces other than the base;

triangle area: b x h / 2

4 x 7 = 28, 28/2 = 14

in this case, there are three faces, so 14 x 3 = 42, and we add that with the base to get 48.9

:) hope this helps!

8 0
3 years ago
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