Is -74.58 an integer

How do the physical and chemical properties of the elements change?

My name is Ann [436]

Answer

Step-by-step explanation: within a group

4 0

3 years ago

Read 2 more answers

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

The base of each pyramid is an isosceles triangle. Which has the greater surface area?

Semenov [28]

The base is the greatest surface area

8 0

3 years ago

PLEASE HELP!! I NEED HELP WITH THIS PROBLEM!

valkas [14]

His basic salary is $ 2,500, his commission on sales is 3% (on sales only)
At the end of te month he got $3,040

Let x be the TOTAL sales performed during this month, so the money generated from sales (only) is (x).(3%), Hence the equation:

2500 + (x).(3%) = 3040
2500 + x(0.03) = 3040
x(0.03) = 3040-2500
x(0.03) = 540

and x = 540/0.03
x = $18,000

5 0

4 years ago

cuboid of length 24cm and volume 768cm^3 the width and hight are not equal.give a pair of possible values for their length.

Brilliant_brown [7]

Answer:

Possible values of dimensions are (24,16,2) or (24,8,4)

Step-by-step explanation:

We are given the volume of the Cuboid and length . We are required to find the possible values of width and height from this information.

Let us say that the width is x and height is y

Length = 24

Volume of a cuboid = length * width * height

Volume = 768

768=24*x*y

$xy=\frac{768}{24}\\xy=32\\$

xy=32

Now the possible factors of 32

32=1*32 ( Which shall not be taken into consideration as length is already given as 24 and width or height can not be more length)

32=2*16

32=4*8

Hence the possible values width are 8, 16 and that of height 4 and 2

Hence the possible values of dimensions are (24,16,2) or (24,8,4)

3 0

3 years ago