Whic of the following are valid names for the triangle below? Check all that apply.

Mathematics

1 answer:

emmasim [6.3K]3 years ago

4 0

Answer:

A, C, E

Step-by-step explanation:

As long as all the 3 letters(D, K, and M) are included, it should be a valid name. These are the 3 points in the triangle afterall.

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Which explicit formula generates the infinite sequence 2, 9, 28, 65, 126, ...?

Dimas [21]

1. The terms of a sequence are denoted by $u_{1} , u_{2}, u_{3}, u_{4}, u_{5},...$

2.
$u_{1} = 2 = 2*1

 u_{2} = 9 = 3*3
 
u_{3} = 28 = 4*7

u_{4} = 65 = 5*13

u_{5} = 126 = 6*21
$

3. so it is clear that the first columns add each time by one, and the second column add by 2, then by 4, by 6, by 8 and so on.

4. consider only the second column and how we get the terms, which we will call $t_{1} , t_{2}, t_{3}, t_{4}, t_{5},...$ :

$t_{1}=1

t_{2}=1+2

t_{3}=1+2+4=1+2+2*2

t_{4}=1+2+4+6=1+2+2*2+2*3=1+2(1+2+3)$

$t_{5}=1+2+2*2+2*3+2*4=1+2(1+2+3+4)$

5.
So

$u_{n}=(n+1)(1+2{1+2+3+....(n-1)})
 
 =(n+1)(1+2 [(n-1)n/2])

 = (n+1)(1+(n-1)n)
 
 =(n+1)( n^{2}-n+1 )
$

6. We can check: $u_{3} = (3+1)( 3^{2}-3+1 )=4*(9-3+1)=4*7=28$

7. Remark: Gauss addition formula: 1+2+3+....+n=n(n+1)/2

6 0

4 years ago

Read 2 more answers

A city had monthly rainfall amounts (in inches) of 0.75, 1.25, 0.33, 1.00, and 0.95. What was the difference between the highest

barxatty [35]

Answer:

0.92

Step-by-step explanation:

The highest rainfall was 1.25

The lowest rainfall was 0.33

1.25-0.33=0.92

6 0