MATHEMATICS HIGH SCHOOL

N ∈ lNWe set A= n(n²+11)
Show that A is divisible by 3
( n is natural number )
please try to help me in this i need it tomorrow plz...

Answers

Answer 1
Answer: @Konrad509's answer was fantastic. 

What you first need to know is this. 3 consecutive natural numbers multiplied by each other, for instance: (1*2*3) or (2*3*4) or (3*4*5) or (4*5*(2*3)) can be described using the abstract expression:

(n-1)n(n+1)

-------------

Now:

A=n(n²+11),

and:

n(n²+11)

=n(n²-1+12)

=n³-n+12n

=n(n²-1)+12n

=n(n+1)(n-1)+12n

=(n-1)n(n+1)+(4*3)n

-------------------------

So:

A=(n-1)n(n+1)+(4*3)n

Therefore, A is divisible by 3.
Answer 2
Answer: n(n^2+11)=\nn(n^2-1+12)=\nn(n^2-1)+12n=\n(n-1)n(n+1)+12n

(n-1)n(n+1) is the product of 3 consecutive natural numbers, so it has be to divisible by 3.

12n is also divisible by 3 because 12 is divisible by 3.

If both elements of the sum are divisible by 3 so the sum itself is divisible by 3 as well.

Related Questions

At a high school, the probability that a student takes a science class and a history class is 0.44. The probability that a student takes a science class is 0.68, and the probability that the student takes a history class is 0.56. What is the probability (rounded to the nearest hundredth) that a student takes a history class given that the student is taking a science class?0.44 0.65 0.30 0.79
What is the equation in point-slope form of the line that passes through the point (5,-5) and is parallel to the line represented by y = -8x - 2?​
Set A(18, 12), (20, 17), (24, 10), (25, 6), (28, 4), (30, 4), (32, 2), (34, 3)Set B(12, 18), (17, 20), (10, 24), (6, 25), (4, 28), (4, 30), (2, 32), (3, 34)a. Graph A, Set Ab. Graph A, Set Bc. Graph B, Set Ad. Graph B, Set B
Triangle inequality Theorem
Complete the inequality with >, <, or =.72 _____ 34

A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles?

Answers

Answer:

The amount of  wax that is needed to create one set of candles is:

                              27π cubic inches.

Step-by-step explanation:

  • The radius(r) of the smallest candle=0.5 inches.

Height(h) of smallest candle= 3 inches.

      Hence, Volume of smallest candle V_1 is:

                 V_1=\pi r^2h

  • Now the medium candle is one which is obtained by taking a scale factor of 2.

  Hence, radius of medium candle=2r

 Height of medium candle=2h

            Hence, Volume of medium candle V_2 is:

       V_2=\pi* (2r)^2* (2h)\n\nV_2=8\pi r^2h

  • Similarly the largest candle is one which is obtained by taking a scale factor of 3.

      Hence, radius of largest candle=3r

      Height of largest candle=3h

        Hence, Volume of largest candle V_3 is:

       V_3=\pi* (3r)^2* (3h)\n\nV_3=27\pi r^2h

The amount of wax required to create one set of candle is equal to total volume of all the three candles.

\text{Amount\ of\ wax}=V_1+V_2+V_3\n\n\n\text{Amount\ of\ wax}=\pi r^2h+8 \pi r^2h+27\pi r^2 h\n\n\n\text{Amount\ of\ wax}=36\pi r^2h

Now on putting the value of r and h in the expression we get:

\text{Amount\ of\ wax}=36* \pi* (0.5)^2* 3\n\n\n\text{Amount\ of\ wax}=27\pi\ \text{cubic\ inches}

                  Hence, the answer is:

                       27π cubic inches.
 it is 27 π cubic inches 

The number of wolves in a wildlife preserve is estimated to have increased continually by 3% per year. If the population is now estimated at 5,400 wolves, how many were present 10 years ago?

Answers

For the answer to the question above, Well, first let us put up a functional equation. 
Since this is an exponential function, it'll be: f(t)=54,000*1.03^t 
But we want to know how many wolves there were 10 years ago. 
For that, we simply "turn time around", as in: f(t)=54,00*1.03^-t 
This displays a decreasing number of wolves, as you turn back time. 

Now we simply calculate 54,000*1.03^-10 
which is approximately 40,200?

Be my best frienddd Ill make BrainLess! Which of the following organic compounds is the main source of energy for living things?

a.

carbohydrates

c.

nucleic acids

b.

lipids

d.

proteins

Answers

Answer:

A

Step-by-step explanation:

HOPE THIS HELPS :)

Express the quotient in simplest form.

Answers

express the qoutient of what?? I can help if you give me the problem :)

Suppose you know three minimum,lower quartile,median, upper quartile, and maximum values for a set of data. Explain how to create a box plot for the set of data.

Answers

Answer: First, draw and label a number line. Then plot the five values that are given above the line. Draw a box from the lower quartile to the upper quartile, with a line dividing it at the median. Then draw lines from the minimum and maximum values connecting to the box to form the whiskers.

Answer:

Create a number line and label it.

Above the number line, plot the five values.

Draw a box from the lower quartile to the upper quartile.

Divide the box at the median.

Connect the minimum and maximum values to the box.

Step-by-step explanation:

edg2020

If a car travels at a speed of 25 mi/h for t hours, then travels 45 mi/h for m hours. What does the expression 25t + 45m represent

Answers

The expression of 25t +45m shows the total number of miles driven at both speeds. In order to solve this equation you would need to know the total number of hours driven in order to multiply that by the appropriate speed in terms of miles per hour.
Other Questions
What is the common ratio of the geometric sequence 1, 4, 16, 64, ...? How many terms are there in the expression -2x + 8 - 6y + 8x + 11?
How do i identify the slope,y intercept,x intercept, and zero on a graph
Explain how the quotient of powers was used to simplify this expression 5^4/25=5^2
What is the solution of the system? Use elimination. 3x - 4y = 9-3x + 2y = 9