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3 years ago

List THE numbers in order from least no greatest-65,34,7,-13,55,62,-7

1 answer:

ivann1987 [24]3 years ago

7 0

-65, -13, -7, 7, 34, 55, 62.
Here’s your answer^
Least to greatest

Always negative will be least and positive will be the greatest always.

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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

5+3=4d please help me

ad-work [718]

So the object of this problem is to find out the value of d.

To do this, first think about 5 + 3. This equals 8, right? So the value of d times 4 has to equal 8.

No other number besides 2 would make sense. 2 would equal d because 4 x 2 is 8, and 5 + 3 is 8.

So you would write the answer as:

5+3=4(2)

4 0

3 years ago

Read 2 more answers

a cheetah reaches a speed of 30 m/s as it chases its prey. What is the kinetic energy of the cheetah?

ZanzabumX [31]

Kinetic energy is in movement, so the answer is obviously the cheetah running :)

3 0

3 years ago

Disney held a breakfast for parents and their children to eat with Mickey and Minnie MouseAdult tickets cost $17.95 and children

ratelena [41]

This is a problem for 2 equations and 2 unknown.
so let x be the number of adults in the breakfast
y be the number of children present in the breakfast

so the total people attended is 500, in equation form
x + y = 500

and the total sales made by disney is $ 7355, in equation
17.95x + 12.95y = 7355

so we can solve the equation simultaneously so solve for the values of x and y

so the number of adults at the breakfast x = 176 adults and y = 324 children

5 0

3 years ago

Which of the following words correctly describe a triangle with two 45 angles?

Tom [10]

Well, first let's identify which answers are incorrect, then it will be easier to figure out which are correct.

A. Equilateral: An equilateral triangle is a triangle with 3 equal sides. Since there are 180 degrees in a triangle, an equilateral triangle would have three sides of 60 degrees, and none of 45 degrees. Answer? Incorrect.

B. Isosceles: An isosceles triangle has two sides that are equal. 45 and 45 are equal, therefore, this answer is: Correct!

C. Scalene: A scalene triangle has three unequal sides, therefore, this answer is incorrect.

D. Obtuse: An obtuse triangle has one angle that is more than 90 degrees, therefore, since 45 and 45 equal 90 already, this answer is: incorrect.

E. Right: A right triangle has one right angle (angle that equals 90 degrees) since 45 + 45 = 90, and 90 + 90 = 180, this answer is: Correct!

F. Equiangular: This last choice is practically the same as the first, therefore the answer is: incorrect.

The two correct answers are: B Isosceles, and E Right!

4 0

3 years ago

Read 2 more answers