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rjkz [21]
3 years ago
7

Write three consecutive numbers starting with number n+1, where n is natural number. Find the sum of those numbers and prove tha

t it is divisible by 3.
Mathematics
1 answer:
netineya [11]3 years ago
5 0

Consecutive numbers differ by one, which means that if you start with a certain integer x, you obtain the next integer by adding one.

So, if you start with n+1, the three consecutive numbers are

n+1,\quad (n+1)+1 = n+2,\quad (n+2)+1 = n+3

The sum of these three numbers is

(n+1) + (n+2) + (n+3) = 3n+6

This number is divisible by 3 because you can write it as

3n+6 = 3(n+2)

Note that this is true in general: the sum of three consecutive numbers is always divisible by three, because it is three times the middle number.

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Solve the differential equation by variation of parameters.<br><br> y''+y=secx
suter [353]

Answer:y=

Acosx+Bsinx +cosx ln(cosx)+x sinx

Step-by-step explanation:

given  equation y''+y=secx

auxiliary  equation

p^2+1=0\\p=\pm i

so CF is y=Acosx+Bsinx

now

y_1(x)=cosx \ \ \ \ y_2(x)=sinx\\{y_1}'(x)=-sinx \ \ \ \ {y_2}'(x)=cosx

using wronskian formula

W=\begin{vmatrix}cosx &sinx \\ -sinx & cosx\end{vmatrix}

          =cos^2x+sin^2x=1

now f(x)=secx

u=-\int \frac{f(x)y_2(x)}{W(x)}dx \ and \ v=\int \frac{f(x)y_1(x)}{W(x)}dx

u=-\int \frac{secx\times sinx}{1}dx \ and \ v=\int \frac{secx\times cosx}{1}dx

u=-\int tanx dx \ and \ v=\int {1}dx

u=ln(cosx) \ \ \ and \ \ v=x

now particular integrals are

PI=cosx ln(cosx)+x sinx

total solution

y= C.F+P.I

y=Acosx+Bsinx +cosx ln(cosx)+x sinx

8 0
3 years ago
PLEASE HELP ME WITH MY PROBLEM!!! 50 POINTS!!!
Molodets [167]

Well he started off right by solving for y=y to find the abscissa of the intersection points between the two points,but then he assumed that their ordinate (y coordinates) are both zero,which is incorrect obviously. To find their ordinate,all we have to do is plug the x values into any of the two equations, since they both will pass through that point ੴ

y = 4 x+ 1 \\ y = 4(3) + 1  \\ y = 12 + 1 \\ y = 13

y = 4x + 1 \\ y = 4( - 2) + 1 \\ y =  - 8 + 1 \\ y =  - 7

I chose to plug the values in the second linear equation, since it's easier to compute

<h2>Points:</h2>

<h2>( 3 , 13 ) ( -2 , -7 )</h2>
5 0
2 years ago
What is the value of x?<br><br> 6<br> 8<br> 10<br> 12
Novosadov [1.4K]

we know that

The sum of exterior angles of any polygon is 360 degrees

so

(62+66+77+59+12x)=360\\( 264+12x)=360\\ 12x=360-264\\12x=96\\x= 8\ degrees

therefore

<u>the answer is</u>

the value of x is 8\ degrees

6 0
3 years ago
Read 2 more answers
two angles are a linear pair. the measure of the first angle minus 39 is equal to twice the measure of the second angle. What ar
baherus [9]

Step-by-step explanation:

Linear pairs = 180°!!!!!

  1. 1st angle is 2[x]-39 2nd angle is just x
  2. soooo add the x. 3x-39=180
  3. 3x=141 x=47

X is just the second angle!!!!!

lol. i toonk geo last year and i cant believe i still remember all this hopefully i got it right!

8 0
3 years ago
Consider the given function and the given interval. f(x) = (x − 4)2, [3, 6]
s2008m [1.1K]

Answer:

f average = 1

smaller value c = 3

larger value c = 5

Step-by-step explanation:

6 0
3 years ago
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