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3 years ago

7

Simplify this expression. m13 × m6 =

2 answers:

My name is Ann [436]3 years ago

3 0

Answer: 78m^2

Step-by-step explanation:

multiply coefficients and variables

m13 x m6 = 78m^2

kotykmax [81]3 years ago

3 0

Answer:

78m

Step-by-step explanation:

Since the variables are alike, you would just multiply them as you would do a normal multiplication problem! I used to have so much trouble with this omg. Anyway, 13x6=78 so the answer would be 78m

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Find the general term of {a_n}

Assoli18 [71]

From the given recurrence, it follows that

$a_{n+1} = 2a_n + 1 \\\\ a_{n+1} = 2(2a_{n-1} + 1) = 2^2a_{n-1} + 1 + 2 \\\\ a_{n+1} = 2^2(2a_{n-2}+1) + 1 + 2 = 2^3a_{n-2} + 1 + 2 + 2^2 \\\\ a_{n+1} = 2^3(2a_{n-3} + 1) + 1 + 2 + 2^2 = 2^4a_{n-3} + 1 + 2 + 2^2 + 2^3$

and so on down to the first term,

$a_{n+1} = 2^na_1 + \displaystyle \sum_{k=0}^{n-1}2^k$

(Notice how the exponent on the 2 and the subscript of <em>a</em> in the first term add up to <em>n</em> + 1.)

Denote the remaining sum by <em>S</em> ; then

$S = 1 + 2 + 2^2 + \cdots + 2^{n-1}$

Multiply both sides by 2 :

$2S = 2 + 2^2 + 2^3 + \cdots + 2^n$

Subtract 2<em>S</em> from <em>S</em> to get

$S - 2S = 1 - 2^n \implies S = 2^n - 1$

So, we end up with

$a_{n+1} = 4\cdot2^n + S \\\\ a_{n+1} = 2^2\cdot2^n + 2^n-1 \\\\ a_{n+1} = 2^{n+2} + 2^n - 1 \\\\\implies \boxed{a_n = 2^{n+1} + 2^{n-1} - 1}$

5 0

2 years ago

A cubical box without a top is 4 cm on each edge.it contains 64 identical 1cm cubes that exactly fill the box. How many of these

Len [333]

Answer:

52

Step-by-step explanation:

A cubical box without a top is 4 cm on each edge containing 64 identical 1 cm cubes.

We have to find the number of small cubes that actually touch the box.

Now, there are 4 layers of 16 cubes from bottom to top.

In the bottom-most layer, all the 16 small cubes will touch the bottom of the large cube.

Again, from the top three layers, only the outer small cubes will touch the sides of the large cube.

So, there are 12 small cubes in each top three layers that will touch the large cube.

Hence, in total there will be (16 + 12 ×3) = 52 small cubes that actually touch the large cube box. (Answer)

8 0

3 years ago

Help me please!!!<br> Sad face sad sad sad please helpppp

Romashka-Z-Leto [24]

It is Parallelograms !!

6 0

3 years ago

A container full of water weighs 15.5 lbs. When ¼ of the water is poured out, the container now weighs 12 ½ lbs. How much does t

posledela

Answer:

3.5 lbs.

Step-by-step explanation:

1/4 of the water is dumped, meaning that is 3 lbs. 1/4 is 3 lbs. 3x4 is 12. 15.5 - 12 = 3

5 0

2 years ago

Which expressions are equivalent to 4b ?

aivan3 [116]

Answer:

They are b and c.

Step-by-step explanation:

Let's simplify each expression:

a. b+2 (b+2b)

= b + 2b + 4b = 7b.

b. 3b + b = 4b.

c. 2(2b) = 2 * 2b = 4b.

5 0

3 years ago

Read 2 more answers