All categories

3 years ago

Find the first six terms of the sequence.

Mathematics

1 answer:

Yuliya22 [10]3 years ago

8 0

Answer:

6, 12, 24, 48, 96, 192

Step-by-step explanation:

The first term a1 = 6 and the common ratio is 2.

So it is 6, 6*2, 6*2^2 ....

You might be interested in

jason and his family travels 160 miles in 3.2 hours. if they continue at this constant speed, how long will it take them to trav

Misha Larkins [42]

Set up a proportion
160 mi/ 3.2 hrs ≈ 300 mi/x hrs
cross multiply and solve for x and you get x≈6
It will take them 6 hours

3 0

3 years ago

How to prove this???

swat32

$\cos^3 2A + 3 \cos 2A \\
\Rightarrow \cos 2A (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (1 - \sin^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - \sin^2 2A) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - (2\sin A \cos A)(2\sin A \cos A)) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - 4\sin^2 A \cos^2 A) \\ 
\Rightarrow 4(\cos^2 A - \sin^2 A) (1 - \sin^2 A \cos^2 A) 
$

go to right side now

$4( \cos^6 A - \sin^6 A)\\
\Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A)$

use $x^3 - y^3 = (x-y)(x^2 + xy + y^2)$ and $x^3 + y^3 = x^2 - xy + y^2$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A) \\
\Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\
~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A)$

so $\sin^2 A + \cos^2 A = 1$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\ ~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 + \cos A \sin A )(1- \cos A \sin A ) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \cos^2 A \sin^2 A )\\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \sin^2 A \cos^2 A ) \\
 \Rightarrow Left hand side$

4 0

2 years ago

B 5 3 a 4 What is the length of the hypotenuse of this triangle? 3 units 5 units 4 units

Lunna [17]

Answer:

5 units

Step-by-step explanation:

The hypotenuse is always the longest segment on a triangle. If the lengths of the sides of this triangle are 3 units, 4 units, and 5 units, the hypotenuse will be 5 units. You can use the pythagorean theorem to check.

a^2+b^2=c^2

If you substitute the variable with the lengths of the legs in ascending order, you will get 3^2+4^2=5^2. Simplifying the equation, you will get 9+16=25, or 25=25. Thus, proving the equation.

Hope this helped! :)

6 0

3 years ago

pls answer Sylvia read that the height of the Empire State Building is 443.2 m and wants to build a scale model of the building

uysha [10]

Answer:

Step-by-step explanation:

converting 8 ft to inches

8 * 12 = 96inches

if 96 inches = 443.2 m

1 inch = (443.2 * 1)/96 = 4.6m

which is closest to option c

8 0

3 years ago

A basketball team has 10 players. Before each game, the coach picks 2 of those players to carry the team's

labwork [276]

The different group of 2 players that the coach can pick is 45 groups.

<h3>Selection of groups</h3>

The selection of groups of 2 player can be done using the method of combination.

<h3>Different groups of 2 players</h3>

The different group of 2 players that the coach can pick from the 10 players is calculated as follows;

n = 10C2

$n = \frac{10!}{(10-2)! 2!} = \frac{10 \times 9\times 8!}{8! \times 2} = 45$

Thus, the different group of 2 players that the coach can pick is 45 groups.

Learn more about combinations here: brainly.com/question/25821700

6 0

2 years ago