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hodyreva [135]
3 years ago
7

Express the area of the entire rectangle.

Mathematics
1 answer:
Elza [17]3 years ago
7 0

Answer:

Step-by-step explanation:

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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
PLEASE HELP ME
balandron [24]
75 ÷ 15 = 5
Riley can cut 5 strips of ribbon each 15 inches long
4 0
3 years ago
Haily walked 15 miles in 9 hours. What was her walking rate in miles per hour? Express your answer in simplest form
Pachacha [2.7K]

Answer:

1.67

Step-by-step explanation:

you should do 15 ÷ 9 and you get 1.6666666667 and when you simplify that you get 1.67

6 0
3 years ago
Read 2 more answers
Their is no point for brainly if you need to sign in I don't wanna be mean tho
Nesterboy [21]

but it helps with homework and learning how to do stuff you dont know how to do

3 0
3 years ago
Which graph represent me y= y=3√x-5 ( I can’t add all 4 of the graphs because it won’t let me attach 2 photos) BUT I REALLY NEED
Andrews [41]
I think this is the graph for your answer, for the next question like this, try to use "Desmos"

7 0
3 years ago
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