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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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Determine the domain and range of the function . f(x)=2 3√ 108^2x {x| all real numbers}; {y| y > 0} {x| all real numbers}; {y

Gala2k [10]

Answer:

Domain : {x | all real numbers} ; Range: {y | y > 0}

Step-by-step explanation:

The function can be written as :

$f(x)=\sqrt[\frac{2}{3}]{108^{2\cdot x}}\\\\\implies f(x)=(108)^{(\frac{3}{2})^{2\cdot x}}$

Now, since x is exponent so it can take any real values. So, its domain of f(x) is all real numbers

But value of f(x) can not be less than 1 because for x = 0 the value of f(x) is 1 and also for any values of x, the value of f(x) can never be less than 1

So, Range of f(x) is all real numbers greater than 0

Hence, Domain and Range of f(x) is given by :

Domain : {x | all real numbers} ;

Range: {y | y > 0}

4 0

4 years ago

Read 2 more answers

Find the distance between the two points to the nearest tenth (if necessary) (0,-8) and (-5,4)

Luden [163]

Answer:

Step-by-step explanation:

7 0

3 years ago

The perimeter of a rectangle is 96 feet, and the width is 22 feet. What is the length

timama [110]

Answer:

Step-by-step explanation:

22+22= 44

96-44=52

52 devided by 2=26

Hope that helps:)

3 0

3 years ago

To prepare for a bicycling event, you warm up each day at a moderate pace then you ride hard for a number of miles. one day you

vovangra [49]

Answer:

The total distance covered is 15.6 miles.

Step-by-step explanation:

One day you warm up for 15 minutes at a pace of 0.1 miles per 25 seconds.

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. If the relationship between the magnitudes is direct, like in this case, the direct rule of three can be applied as follow:

a ⇒ b

c ⇒ x

Then $x=\frac{c*b}{a}$

First, the simple rule of three can be applied in the following way: if 1 minute equals 60 seconds, 15 minutes equals how many seconds?

$seconds=\frac{15 minutes*60 seconds}{1 minute}$

seconds= 900

So now you can apply the following rule of three: if in 25 seconds you travel 0.1 miles, in 900 seconds how many miles do you travel?

$distance=\frac{900 seconds*0.1 miles }{25 seconds}$

distance= 3.6 miles

If you then ride hard for 12 miles, the total distance traveled will be the sum of both:

3.6 miles + 12 miles = 15.6 miles

<u><em>The total distance covered is 15.6 miles.</em></u>

6 0

3 years ago

4. In slope-intercept form, what is the equation of a line perpendicular toy - 2x + 7 that passes

Phoenix [80]

Answer:

y = (-1/2)x + 21/2

Step-by-step explanation:

Given equation:

y - 2x + 7

Coordinates = (5,8)

Find:

Perpendicular equation

Computation:

y = mx + c

y - 2x + 7

y = 2x - 7

So,

m = 2

The negative reciprocal of 2 is -1/2

So,

For,

Coordinates = (5,8)

y = mx + c

8 = (-1/2)(5) + c

8 = -5/2 + c

c = 8 + 5/2

c = 21 /2

So,

y = mx + c

y = (-1/2)x + 21/2

7 0

3 years ago