All categories

3 years ago

Irrational numbers are _____ integers. a. always b. sometimes c. never

Mathematics

1 answer:

Butoxors [25]3 years ago

5 0

C) never integers
definition of integer: a whole number

You might be interested in

Williamston Daily is a new daily newspaper. When they first started printing three years ago they had 5900 home

Dominik [7]

Answer:

Step-by-step explanation:

4 0

3 years ago

The sum of the first n terms of a geometric series is 364? The sum of their reciprocals 364/243. If the first term is 1, find n

Afina-wow [57]

If the geometric series has first term $a$ and common ratio $r$ , then its $N$ -th partial sum is

$\displaystyle S_N = \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}$

Multiply both sides by $r$ , then subtract $rS_N$ from $S_N$ to eliminate all the middle terms and solve for $S_N$ :

$rS_N = ar + ar^2 + ar^3 + \cdots + ar^N$

$\implies (1 - r) S_N = a - ar^N$

$\implies S_N = \dfrac{a(1-r^N)}{1-r}$

The $N$ -th partial sum for the series of reciprocal terms (denoted by $S'_N$ ) can be computed similarly:

$\displaystyle S'_N = \sum_{n=1}^N \frac1{ar^{N-1}} = \frac1a + \frac1{ar} + \frac1{ar^2} + \cdots + \frac1{ar^{N-1}}$

$\dfrac{S'_N}r = \dfrac1{ar} + \dfrac1{ar^2} + \dfrac1{ar^3} + \cdots + \dfrac1{ar^N}$

$\implies \left(1 - \dfrac1r\right) S'_N = \dfrac1a - \dfrac1{ar^N}$

$\implies S'_N = \dfrac{1 - \frac1{r^N}}{a\left(1 - \frac1r\right)} = \dfrac{r^N - 1}{a(r^N - r^{N-1})} = \dfrac{1 - r^N}{a r^{N-1} (1 - r)}$

We're given that $a=1$ , and the sum of the first $n$ terms of the series is

$S_n = \dfrac{1-r^n}{1-r} = 364$

and the sum of their reciprocals is

$S'_n = \dfrac{1 - r^n}{r^{n-1}(1 - r)} = \dfrac{364}{243}$

By substitution,

$\dfrac{1 - r^n}{r^{n-1}(1-r)} = \dfrac{364}{r^{n-1}} = \dfrac{364}{243} \implies r^{n-1} = 243$

Manipulating the $S_n$ equation gives

$\dfrac{1 - r^n}{1-r} = 364 \implies r (364 - r^{n-1}) = 363$

so that substituting again yields

$r (364 - 243) = 363 \implies 121r = 363 \implies \boxed{r=3}$

and it follows that

$r^{n-1} = 243 \implies 3^{n-1} = 3^5 \implies n-1 = 5 \implies \boxed{n=6}$

5 0

2 years ago

Reupload of a question. I wasted my points on the other one.

mylen [45]

It would be ft3 because its a cone shape and you multiply the circumference by the height and you’ll get the volume

6 0

3 years ago

Fill in the blank with the correct response.<br><br> The slope of the graph of y = 5x is ___.

Ilya [14]

The answer 5 or 5/1

6 0

4 years ago

Read 2 more answers

What is 6 to the second power divided by 2 (3) plus 4

nikdorinn [45]

The answer is 10.

6^2/2(3)+4 is the formula

6^2=36
36/2(3)+4
2(3)=6
36/6+4
36/6
6+4
10

I did PEMDAS. P is for Parentheses. E is for exponents. M is for multiplication. D is for Division. A is for adding. S is for subtracting.

3 0

3 years ago

Read 2 more answers