Rehan proved by mathematical Induction that for all the positive Integers, n^3+ 2n is divisible by 3. Can you find an integer counterexample to show that this statement is not true? Explain.

Answers

Answer 1

Reproduce the proof. When n = 1, we have

n³ + 2n = 1³ + 2 = 3

which is clearly divisible by 3.

Assume n³ + 2n is divisible by 3. Then for the next natural number n + 1, we have

(n + 1)³ + 2 (n + 1) = n³ + 3n² + 3n + 1 + 2n + 2

= n³ + 2n + 3 (n² + n + 1)

The first two terms n³ + 2n are divisible by 3 according to our assumption, and 3 (n² + n + 1) is clearly a multiple of, and therefore divisible by, 3 as well.

So the claim that 3 divides n³ + 2n is true for all natural numbers n.


Related Questions

Use the graph below to fill in the blank with the correct number:
F(0)=

Answers

Answer:

f(0) = 1.

Step-by-step explanation:

f(0) means the value of f when x = 0.

From the graph this is 1.

The graphs of the equations 2x - By = 7 and Ax + 3y = 10 are both the same line. Find A and B.

Answers

Answer:

[tex]\bold{A = \frac{20}{7}}[/tex]

[tex]\bold{B = -\frac{21}{10}}[/tex]

Step-by-step explanation:

[tex]\underline{\mathrm{Same \:lines:}}\\\\y = \frac{2x}{\mathrm{B}} - \frac{7}{\mathrm{B}}\\\\ y = \frac{\mathrm{-A}x}{3} +\frac{10}{3}[/tex]

[tex]\mathrm{If\:they\:are\:in\:the\:same\:line,\:then\:the\:Slopes\:and\:Intercepts\:are\: Equal.}[/tex]

I= $50
P= $500
r= ?
t= 5 years

Answers

Answer:

2%

Step-by-step explanation:

Interest Rate = (Simple Interest × 100)/(Principal × Time).

50= 500(5)(r)

50= 2500r

50/2500= .02 or 2%

convert to 75 km/ into m/s

Answers

Answer:

1(kilometer/hour) = 1000(meters) / 3600(seconds) can also be expressed as 1(kilometer/hour) = 5/18 (meters/second), which is its simplified form. To convert km/h to m/s, directly multiply the given value of speed by the fraction 5/18

Step-by-step explanation:

so the answer wil be 20.8333 m/s

If you had half a dollar, three quarters, eight dimes, six nickels, and nine pennies, how much money would you have altogether?

Answers

Answer:

$1.69

Step-by-step explanation:

Half a dollar = $0.50

Eight dimes = $0.80

Six nickels = $0.30

Nine pennies = $0.09

Total = $0.50 + $0.80 + $0.30 + $0.09 = $1.69

Answer:

1.69

Step-by-step explanation:

Dev ordered 10 ink cartridges and 1 box of copy paper for his office. The box of copy paper cost $45. He had a coupon for $2 off each ink cartridge. He spent a total of $175.

Answers

Based on the cost of the copy paper and the discount on ink cartridges, the cost of the ink cartridge is $15 each.

First find the amount paid for the ink cartridges:

= Total spent - cost of copy paper

= 175 - 45

= $130

He got a discount of $2 per cartridge. For 10 cartridges he got a discount of:

= 2 x 10

= $20

The cost of each ink cartridge is:

= (Amount spent on ink cartridges + Discount) / Number of cartridges

= (130 + 20) / 10

= $15 each

In conclusion, each cartridge cost $15.

Find out more at https://brainly.com/question/22085332.

A helicopter floats 120m above a helipad, a dog is 85m from the helipad, if the dog could fly, how far would it have to fly to get to helicopter?

Answers

Answer:  35m

Step-by-step explanation:

can you please fin x and y

Answers

So we know that x = 90º because it is a right angle. And angle B also has to be 47º because it is a reflection of angle C. And all the angles of any triangle are equal to 180º, so if we do 180-(90+47)=43. So now we know that y=43º and x=90º Your welcome, please give me brainlest.

Find the equation of the linear function represented by the table below in slope-intercept form. x y -1 -4 3 -8 7 -12 11 -16

Answers

-15 the answer is 15

help plzz 78 % of R340 ,00 ​

Answers

Answer:

R26,520

Step-by-step explanation:

78÷100×34000. This is the explanation

at noon a contained 20 in of water after several hours it contained 16 in of water what is the percent decrease of water the tank

Answers

Answer:

20%

Step-by-step explanation:

20 x .2 =4

0.2 because its 20%

20-4=16

Find all missing angles

Answers

Answer:

10

Step-by-step explanation:

best guess ever

Help me! Quick! Please. 25 points

Answers

Answer:

A. would be correct

Step-by-step explanation:

if 1 package is $8 and 2 packages cost $16

the ratio would be $8:1 so the unit rate would be $8 per package

Please help me! I will mark brainliest if correct! (Question is in the image shown)

Answers

2nd one the combining with y one

Plzzzzzx help meeeeee

Answers

Step-by-step explanation:

first find out the area of sector ECF

π(10)² × 40°/360°

=100π×1/9

=100π/9 m²

now find the area of sector DCG

π(2)² × 40°/360°

=4π/9 m²*

so the area of the shaded region would be the big sector minus the small sector

so

100π/9 - 4π/9

=96π/9

=33.5 m² (3sig.fig.)

*Note that 4π/9 DOES NOT equal to 2π/3

4/9 DOES NOT EQUAL TO 2/3

evaluate the following using identity ( part 2 )
4. (0.4a + 1/4 b) (0.4a - 1/4b)
5. (x + 1/y) ( x-1/y)
6. (2/3x + 3/11y) (2/3x - 3/11y)​

Answers

Answer:

refer the attachment pls

please can i have help

Answers

Answer:

1:6ab  

2: c^6x

3: 10y^7x

4:3g^4 h^5 x^4

A tree that is 15 feet tall casts a 10 foot shadow. What is the length of the shadow of a nearby 21 foot tall tree?​

Answers

Answer:

16 ft is the 21ft tall tree.

Step-by-step explanation:

15:10

21 - 5 is 16

NEED ASAP
What are the coordinates of the midpoint of AB if A (4, 6) and B(-8, 2)?
o (6, 4)
O (-6, 4)
O (-2, 4)
o (2, 4)

Answers

Answer:

(- 2, 4 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

Here (x₁, y₁ ) = A (4, 6 ) and (x₂, y₂ ) = B (- 8, 2 )

midpoint = ( [tex]\frac{4-8}{2}[/tex] , [tex]\frac{6+2}{2}[/tex] ) = ( [tex]\frac{-4}{2}[/tex] , [tex]\frac{8}{2}[/tex] ) = (- 2, 4 )

Midpoint be p(x,y)

P(x,y)=

[tex]\\ \sf\longmapsto \left(\dfrac{4-8}{2},\dfrac{6+2}{2}\right)[/tex]

[tex]\\ \sf\longmapsto \left(\dfrac{-4}{2},\dfrac{8}{2}\right)[/tex]

[tex]\\ \sf\longmapsto (-2,4)[/tex]



Convert the following measurements into the indicated units:

Answers

Step-by-step explanation:

1) 2.057 kg

2)1.25× 10^-1 um

3)65.8km

4)2.78 × 10^2 mg

5)9.44 yards

6) 5.91ft

7)200000cm^3

8)1287.48km

find the measure of KH

Answers

Answer:

i dont know

Step-by-step explanation:

1) Solve 3x+2= 5.
A. Model 3 2 x+ = 5.
B. Perform the step to have the variables (circles) alone on one side.
C. Write the resulting step.
D. Divide the variables (circles) and numbers (squares) into equal groups.
E. Show the value of one group.

DO EVERY SINGLE ONE

Answers

Answer:

x = 1

Step-by-step explanation:

3x + 2 = 5

→ Minus 2 from both sides

3x = 3

→ Divide both sides by 3

x = 1

Percent of 51,300-45,800

Answers

Answer: the percent is 112.01. please mark brainliest

Step-by-step explanation:

work out

a) 4 1/3 x 6

b) 2 3/5 x 3 1/3

Answers

Answer:

a) 26

b) 26/3

Step-by-step explanation:

a) 4 and 1/3 = 13/3

13/3 x 6/1 = 13/1 x 2/1

b) 2 and 3/5 = 13/5, 3 and 1/3 = 10/3

13/5 x 10/3 = 13/1 x 2/3

Factor. Check by multiplying.
x²- 6x

Answers

[tex] {x}^{2} \times - 6x \\ = - 6 {x}^{3} [/tex]

- BRAINLIEST answerer

Which of these inequalities is graphed below


Y>2x-6
Y<2x-6
Y<2x-6
Y>2x-6



Answers

Answer:

D

Step-by-step explanation:

The line looks dotted (image quality isn't the best) so we can already exclude the inequalities with [tex]\le[/tex] or [tex]\ge[/tex]. At this point let's check an "easy" point, 0.0.

[tex](0)>2(0)-6 \rightarrow 0>-6[/tex] Which is indeed true. The correct answer is D

I don’t understand this :(

Answers

Answer:

3 < S < 17

Step-by-step explanation:

picture the 10 side as the bottom

the 7 side pivoting on the right end of the 10 leg

when it swings toward the left the shortest the third side can be is >3

when it swings to the right the longest the third side can be is <17

A group of students is going on an overnight camping trip. The cost of the campsite is $19 and the cost of food is $12 per person.
pls help me

Answers

Answer:

Step-by-step explanation:

12 times 19 equals 228 final answer 228

A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (2, 4).
The graph of the function is negative on (4, infinity).
The graph of the function is positive on (negative infinity, –7).
The graph of the function is negative on (–7, –1).

Answers

Answer:

C. The graph of the function is positive on (negative infinity, –7).

Step-by-step explanation:

With given conditions we can state:

The graph is positive between (-∞, -7)∪(-7, -1)∪(4, +∞), since it touches -7 and is positive either side of it.The graph is negative between (-1, 2) and (2, 4), since it touches 2 and is negative either side of it.Overall shape is U as leading coefficient is positive and is of even degree.

Comparing with the answer choices, correct choice is C.

Write an expression for the operation described below.
the product of r and s

Answers

Answer:

r + s

Step-by-step explanation:

the product of r and s

\/

Addition

\/

the product of r and s

\/

r + s

Have a nice day!

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- Heather

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