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Vladimir [108]
2 years ago
13

Find the surface area and volume of the shape.

Mathematics
1 answer:
frozen [14]2 years ago
7 0

Answer:

293.57

Step-by-step explanation:

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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
Add 408 to the difference of 7 000 and 3 096​
egoroff_w [7]

Answer:

4312

Step-by-step explanation:

7000-3096=3904

3904+408=4312

7 0
2 years ago
Round your answer to the nearest hundredth
nalin [4]

Answer:

A = arctan(BC/CA) = arctan(8/2) = 75.96 deg

Hope this helps!

:)

3 0
2 years ago
write the equation of the line parallell to the given line passing through the given point in slope intercept form y=-4x-2 (0, -
Finger [1]

Step-by-step explanation:

slope: -4

y + 1 = -4(x - 0)

y + 1 = -4x + 0

y = -4x - 1

4 0
3 years ago
Please help, thank you!
andrew11 [14]

Answer:

B

Step-by-step explanation:

11 13 18 19 22 25 29 32 37 37 38

find the median (25)

with 11,13,18,19,22 find the middle for that (18) Q1

with 29,32,37,37,38 find the middle for that (37)Q3

Q3-Q1

37-18=19

7 0
2 years ago
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