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Ksivusya [100]
4 years ago
9

Prove that 3n< n! if n is an integer greater than 6.

Mathematics
1 answer:
Lera25 [3.4K]4 years ago
4 0
Let n=7. Then

3(7)=21

Assume the inequality holds for n=k, so that 3k. Then for n=k+1, you have, for k>7,

3(k+1)

so the statement is true.
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Two consecutive numbers can be represented by x and x - 1. The product of two consecutive numbers is equal to 35 more than eleve
USPshnik [31]

funzo


the numbers are x and x-1


a.

"product of them is equal to 35 more than 11 times sum of them" translated to maths is

(x)(x-1)=35+11(x+x-1)

we need to get it into standard form (0=ax^2+bx+c)

expand

x^2-x=35+11(2x-1)

x^2-x=35+22x-11

x^2-x=22x+24

x^2-23x-24=0


b.

factor

what 2 numbers multiply to get -24 and add to get -23?

-24 and 1

(x-24)(x+1)=0

set each equal to 0

x-24=0, x=24

x+1=0, x=-1

the solutions are 24 and -1


c.

if x=24, then x-1=23, the 2 numbers are 24 and 23


if x=-1, then x-1=-2, the 2 numbers are -1 and -2


since the question did not specify if the numbers had to be of a certain sign (positive or negative) or something like that, there are 2 pairs of consecutive numbers that satisfy the equation

4 0
3 years ago
Read 2 more answers
A block of ice melts 8oz every 5 minutes it began melting at 8:00am weighing 250 pounds at what specific time will it be complet
dimulka [17.4K]

Answer:

1:40 am the next day

Step-by-step explanation:

1 pound = 16 oz

The block of ice melts 1 pound or 16 oz in 10 minutes

10 x 250 = 2,500

It will take 2,500 minutes to melt completely.

2,500 divided by 60 = 41.66666 or 41 hours and 40 minutes              

60 minutes = 1 hour

1 day = 24 hours                    41.6666666 - 24 = 17.6666666

8 am + 17 hours and 40 minutes = 1:40 am the next day

6 0
4 years ago
How the position of the decimal point changes in a quotient as you divide by increasing powers 10
kirza4 [7]
The position of the decimal point changes in a quotient as you divide by increasing the powers 10.
6 0
3 years ago
How to share four sandwiches with six people
dimaraw [331]
Cut each sandwich into pieces of thirds
 4 sandwiches x 3 pieces = 12 total pieces
--------------------
12 / 6 = 2
Everybody would get 2 pieces
3 0
3 years ago
Mr Nersin likes to ride his bike. He rode for 1/2 hour. After a short rest, he rode 1/10 hour more. He traveled 4 miles in all.
vodomira [7]
The distance traveled by Mr.Nersin = 4 miles
The time for which Mr.Nersin rode first = 1/2 hour
The time for which Mr.Nersin rode after a short rest = 1/10 hour
Then
The total time for which Mr.Nersin rode = (1/2) + (1/10) hour
                                                                = (5 + 1)/10 hour
                                                                = 6/10 hour
                                                                = 3/5 hour
So
Average speed of Mr. Nersin = Distance traveled / Time taken
                                                = 4/(3/5) miles/hour
                                                = (4 * 5)/3 miles/hour
                                               = 20/3 miles/hour
                                                = 6 2/3 miles/hour
                                                = 6.67 miles per hour
So the average speed at which Mr.Nersin traveled is 6 2/3 or 6.67 miles per hour.
6 0
3 years ago
Read 2 more answers
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