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erma4kov [3.2K]
3 years ago
10

Giving brainiest+points need explanation on this one my answer is 25 is it right?

Mathematics
1 answer:
Sergio [31]3 years ago
4 0
Yes, the answer of 25 is correct.

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Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)
notka56 [123]

Answer:

The answer is True

Step-by-step explanation:

A <em>mathematical induction</em> consists in only 2 steps:  

<u>First step</u>: Show the proposition is true for the first one valid integer number.

<u>Second step</u>: Show that if any one is true then the next one is true  

Finally, if first step and second step are true, then the complete proposition is true.

So, given 2*n^3+3*n^2+n

First step: using and replacing n=2 (the first valid integer number >1)

2*(2)^3 +3*(2)^2+2=30

\frac{30}{6} =5

As the result is an integer number, so the first step is true.

Second step: using any next number, n+1, let it replace

2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)

As the First step is true, we know that

2*n^3+3*n^2+n=6*k,

So let it replace in the previous expression

6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]

Finally

\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)

where the last expression is an integer number

So the second step is true, and the complete proposition is True

5 0
2 years ago
What does it mean to find the point P on GK such that 3(GP)=2(PK
Stolb23 [73]
This means that point P lies on GK where the ratio between the length of GP to the length of PK is:
GP/PK = 2/3

To better understand this, assume that the length of GK is 5 cm. Applying the given ratio, we will find that:
GP = 2 cm and PK = 3cm
4 0
2 years ago
Equation.<br> 1. h - 9= 2h - 1
lora16 [44]
H= -8. H-2h= 9-1; -h=8; h= -8
4 0
2 years ago
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Find the midpoint of the segment below and enter its coordinates as an ordered pair. If necessary, express the coordinates as fr
Vladimir [108]
The correct answer is (5/2, -7/2)
3 0
2 years ago
Giving brainliest for CORRECT awnser.
Alona [7]

Answer:

i think i am not sure

i am soo sorry if i gave it wrong but i think its A

Step-by-step explanation:

4 0
3 years ago
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