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4 years ago

Find the 9th term in a geometric sequence whose common ration is 1/3 and first term is 6

Mathematics

1 answer:

sasho [114]4 years ago

7 0

Answer:

Therefore 9th term of the geometric sequence is $\frac{2}{2187}$

Step-by-step explanation:

Given first term(a) = 6

and common ratio = $\frac{1}{3}$

$T_n= ar^{n-1}$

$\therefore T_9=ar^{9-1}$

$\Leftrightarrow T_9=a r^8$

$\Leftrightarrow T_9=6\times ( \frac{1}{3}) ^8$

$\Leftrightarrow T_9=\frac{2}{2187}$

Therefore 9th term of the geometric sequence is $\frac{2}{2187}$

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Part A: Find the LCM of 8 and 9. Show your work. (3 points)

joja [24]

Answer:

part A: 72

part B=7

part C=7(5+9)

Step-by-step explanation:

A=the lowest common multiple found in both the 9 and 8 times table. 8s=8 16 24 32 40 48 56 64 72

9s=9 18 27 36 45 54 63 72

B=7 because 35=5×7 and if we break down 63,it

would be 9×7 or 3×3×7

C=7(5+9) because if we expand the brackets it would

be 7×5+7×9=35+63

Hope it helps?

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3 years ago

30 POINTS, BRAINLIEST, PLEASE HAALLPPP TT^TT

Licemer1 [7]

It's a pretty simple suvat linear projectile motion question, using the following equation and plugging in your values it's a pretty trivial calculation.

V^2=U^2+2*a*x

V=0 (as it is at max height)

U=30ms^-1 (initial speed)

a=-g /-9.8ms^-2 (as it is moving against gravity)

x is the variable you want to calculate (height)

0=30^2+2*(-9.8)*x

x=-30^2/2*-9.8

x=45.92m

With these questions it's best to just memorise the suvat equations and either draw or imagine the actions involved, that was you can tell what piece of given information translates to which variable. For example; I know that I am looking for max height, so when a ball is at its highest point, it can't be moving up anymore (thus V = 0). I also know that it is moving upwards against gravity, so gravity will be decelerating the ball (therefore a=-g). In a paper, it may as for assumptions with this question, a good answer would be no air resistance or movement due to any other external forces. I hope I helped :)

8 0

3 years ago

Im tired of brainly today i will sue you if you dont clean up your ways!

vagabundo [1.1K]

Answer:

Great speech!

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

K+3d=8c-8d<br><br> solve for d

FromTheMoon [43]

Move k to the other side to isolate d.

So we will get 3d = 8c - 8d - k

Now divide both sides by 3 to isolate d.

So d = 8/3c - 8/3d - k/3

5 0

3 years ago

Which is the graph of y= 2(x-3)^2 +2

WINSTONCH [101]

The graph of y = 2(x - 3)² + 2 can be seen in the attached picture. This problem can be solved through the concept of parabola and transformation.

<h3>Further explanation</h3>

<u>The Problem:</u>

Which is the graph of y = 2(x - 3)² + 2?

<u>Question-1:</u>

How to make a graph y = 2 (x - 3) ² + 2 through the concept of a parabola.

<u>The Process:</u>

The equation of a parabola is given by $\boxed{ \ y = a(x - h)^2 + k \ }$ .

Keep in mind the following points:

vertex point at (h, k)
axis of symmetry at x = h
a > 0 the parabola opens upward
a < 0 the parabola opens downward
the y-intercept is $\boxed{ \ y = ah^2 + k \ }$ at x = 0.

From our case it can be concluded as follows:

the graph of y = 2(x - 3)² + 2 opens upward
vertex point at (3, 2)
axis of symmetry at x = 3
the y-intercept is 2(3²) + 2 = 20 or in coordinates of (0, 20)

<u>Question-2:</u>

How to make the graph of y = 2(x - 3)² + 2 through the transformation.

<u>The Process:</u>

To plot the graph of y = 2(x - 3) ² + 2 we apply for the following transformation order:

Step-1: clearly, to obtain the graph of y = (x - 3)² we shift the graph of y = x² to the right 3 units.

Step-2: to obtain the graph of y = 2(x - 3)², we stretch the graph of y = (x - 3)² by a factor of 2 (in other words, multiply each y-coordinate by 2).

Step-3: finally, to obtain the graph of y = 2(x - 3)² + 2 we shift the graph of y = 2(x - 3)² upward 3 units.

Thus the construction of the graph y = 2 (x - 3) ² + 2 is completed.

The graph of y = 2(x - 3) ² + 2 is drawn by the combination of shifting the graph of y = x² to the right 3 units and upward 2 units, and also stretch by a factor of 2. Between vertical shift and stretch steps, it is the same whatever steps are taken first.

- - - - - - - - - -

Notes

The transformation of graphs is changing the shape and location of a graph.
There are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching/shrinking).
In this case, the transformation is shifting horizontally and vertically and also stretching vertically.

In general, given the graph of y = f(x) and v > 0, we obtain the graph of:

$\boxed{ \ y = f(x) + v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ upward v units.
$\boxed{ \ y = f(x) - v \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ downward v units.

That's the vertical shift, now the horizontal one. Given the graph of y = f(x) and h > 0, we obtain the graph of:

$\boxed{ \ y = f(x + h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the left h units.
$\boxed{ \ y = f(x - h) \ }$ by shifting the graph of $\boxed{ \ y = f(x) \ }$ to the right h units.

Hence, the combination of vertical and horizontal shifts is as follows:

$\boxed{ \ y = f(x \pm h) \pm v \ }$

The plus or minus sign follows the direction of the shift, i.e., up-down or left-right .

Notice the following definitions for stretch and shrink.

In general, given the graph of $\boxed{y = f(x)}$ , we obtain the graph of $\boxed{y = cf(x)}$ by stretching $\boxed{ \ c > 1 \ }$ or shrinking $\boxed{ \ 0 < c < 1 \ }$ the graph of $\boxed{y = f(x)}$ vertically by a factor of c.
In general, given the graph of $\boxed{y = f(x)}$ , we obtain the graph of $\boxed{y = f(cx)}$ by stretching $\boxed{ \ 0 < c < 1 \ }$ or shrinking $\boxed{ \ c > 1 \ }$ the graph of $\boxed{y = f(x)}$ horizontally by a factor of c.

<h3>Learn more </h3>

What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)? brainly.com/question/1332667
Transformations that change the graph of (f)x to the graph of g(x) brainly.com/question/2415963
Which statement correctly describes the graph brainly.com/question/10929552

8 0

3 years ago

Read 2 more answers