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3 years ago

12

Write the explicit formula that represents the geometric sequence -2, 8, -32, 128

1 answer:

lora16 [44]3 years ago

7 0

$a_{1}=-2 \\ \\ a_{2}=8 \\ \\ q= \frac{a_{2}}{a_{1}} \\ \\ q= \frac{8}{-2}=-4 \\ \\ a_{n}=a_{1}*q^{n-1} \\ \\ a_{n}=-2*-4^{n-1}$

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What is the domain of f(x) = cos(x)?

malfutka [58]

Answer:

Domain of the function f(x) = cos x : ( - infinity , + infinity)

Step-by-step explanation:

Let the given function f(x) = cos x

We need to find the domain set of the given function f(x) = cos x

Domain is the set of all possible value of x for which the function f(x) is defined.

Now, as the given function f(x) is defined for all the real values of x.

Domain of the function f(x) = cos x : ( - infinity , + infinity)

Hence, Domain : ( -∞ , +∞ )

Also, the graph of the given function f(x) = cos x is attached below :

Now, form the graph also we can see the graph of given function f(x) = cos x can attain all the real values starting from -infinity to +infinity

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Is the function in the table linear or nonlinear Why

Rashid [163]

Answer:

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Step-by-step explanation:

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LaShawn solved the equation below to the determine the solution. 3 x minus 8 = negative x + 4 (x minus 2) How many solutions doe

Phantasy [73]

Answer: D

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Step-by-step explanation:

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3 years ago

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2. In how many ways can 3 different novels, 2 different mathematics books and 5 different chemistry books be arranged on a books

insens350 [35]

The number of ways of the books can be arranged are illustrations of permutations.

When the books are arranged in any order, the number of arrangements is 3628800
When the mathematics book must not be together, the number of arrangements is 2903040
When the novels must be together, and the chemistry books must be together, the number of arrangements is 17280
When the mathematics books must be together, and the novels must not be together, the number of arrangements is 302400

The given parameters are:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

<u />

<u>(a) The books in any order</u>

First, we calculate the total number of books

$\mathbf{n = Novels + Mathematics + Chemistry}$

$\mathbf{n = 3 + 2 + 5}$

$\mathbf{n = 10}$

The number of arrangement is n!:

So, we have:

$\mathbf{n! = 10!}$

$\mathbf{n! = 3628800}$

<u>(b) The mathematics book, not together</u>

There are 2 mathematics books.

If the mathematics books, must be together

The number of arrangements is:

$\mathbf{Maths\ together = 2 \times 9!}$

Using the complement rule, we have:

$\mathbf{Maths\ not\ together = Total - Maths\ together}$

This gives

$\mathbf{Maths\ not\ together = 3628800 - 2 \times 9!}$

$\mathbf{Maths\ not\ together = 2903040}$

<u>(c) The novels must be together and the chemistry books, together</u>

We have:

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the novels in:

$\mathbf{Novels = 3!\ ways}$

Next, arrange the chemistry books in:

$\mathbf{Chemistry = 5!\ ways}$

Now, the 5 chemistry books will be taken as 1; the novels will also be taken as 1.

Literally, the number of books now is:

$\mathbf{n =Mathematics + 1 + 1}$

$\mathbf{n =2 + 1 + 1}$

$\mathbf{n =4}$

So, the number of arrangements is:

$\mathbf{Arrangements = n! \times 3! \times 5!}$

$\mathbf{Arrangements = 4! \times 3! \times 5!}$

$\mathbf{Arrangements = 17280}$

<u>(d) The mathematics must be together and the chemistry books, not together</u>

We have:

$\mathbf{Mathematics = 2}$

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the mathematics in:

$\mathbf{Mathematics = 2!}$

Literally, the number of chemistry and mathematics now is:

$\mathbf{n =Chemistry + 1}$

$\mathbf{n =5 + 1}$

$\mathbf{n =6}$

So, the number of arrangements of these books is:

$\mathbf{Arrangements = n! \times 2!}$

$\mathbf{Arrangements = 6! \times 2!}$

Now, there are 7 spaces between the chemistry and mathematics books.

For the 3 novels not to be together, the number of arrangement is:

$\mathbf{Arrangements = ^7P_3}$

So, the total arrangement is:

$\mathbf{Total = 6! \times 2!\times ^7P_3}$

$\mathbf{Total = 6! \times 2!\times 210}$

$\mathbf{Total = 302400}$

Read more about permutations at:

brainly.com/question/1216161

8 0

3 years ago

Please help ASAP give you 20 points and brainiest

GuDViN [60]

Answer:

Total charge= -25

Step-by-step explanation:

Given :

Charges of some ions

Aluminium +3

Phosphate -3

Chloride -1

Silver +1

To find total charge on 8 phosphate,7 chloride and 2 Aluminium atoms

Aluminium +3 × 2 =+6

Phosphate -3 × 8 = -24

Chloride -1 × 7 = -7

total charge=

+6-24-7 =+6 -31

= -25

6 0

4 years ago