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3 years ago

The third mean of a GP of two numbers 27 and 1/27 is 1. Find the number of means.

Mathematics

2 answers:

Artyom0805 [142]3 years ago

3 0

Answer:

The mean is $\sqrt{3}.$

Step-by-step explanation:

olga2289 [7]3 years ago

3 0

Step-by-step explanation:

how unusual to call this that way.

I think you (and your teacher) mean the third term in a geometric sequence (or geometric progression, hence GP) between 27 and 1/27 is 1.

that means the sequence goes

27, a2, a3, 1, ..., 1/27

and so, "the number of means" is the number of terms between 27 and 1/27.

I happen to know that 27 is 3³. and that fits perfectly.

a2 = a1/3 = 27/3 = 9

a3 = a2/3 = 9/3 = 3

a4 = q = a3/3 = 3/3 = 1

correct. so, the common ratio is 1/3 (every new term of the sequence is created by multiplying the previous term by 1/3).

and then, if we continue, we get

a5 = a4/3 = 1/3

a6 = a5/3 = 1/3 / 3 = 1/9

a7 = a6/3 = 1/9 / 3 = 1/27

so the terms between 27 and 1/27 are a2, a3, a4, a5 and a6. that are 5 terms "in between" or 5 "means" between 27 and 1/27.

You might be interested in

Find the equation of the line that passes through the points (-5,7) and (2,3)

Olegator [25]

Answer:

$y=-\frac{4}{7}x+4\frac{1}{7}$

Step-by-step explanation:

So, in order to solve this problem, I started off by drawing it out. On my graph that I have attached below, I first started out by locating the points (-5,7) and (2,3). Now, this is an optional step, but I highly encourage practicing your graphing skills by solving this problem on graph paper as well. Next, I connected the two points that I just graphed. This is the line that passes through (-5,7) and (2,3).

Now, here is where the actual solving starts. If you haven't already been taught this yet, I will introduce it to you now. I am going to find the equation of this line by filling in what I know in the equation y=mx+b, where m= the slope of the line, and b= y intercept.

Slope of the line: m= $\frac{y_{1} - y_{2} }{x_{1} - x_{2} } = \frac{7-3}{-5-2} = \frac{4}{-7}= -\frac{4}{7}$

If you haven't been taught how to find the slope of a line I recommend you find out.

Substitute the slope into the equation.

$y=-\frac{4}{7} x+b\\$

Now, we will solve for the 'b,' or y intercept.

We already have x and y values to use: (-5,7) or (2,3). I'll use x=2 and y=3 to solve for the y intercept.

$y=-\frac{4}{7} x+b\\\\3=-\frac{4}{7} *2+b\\\\3=-\frac{8}{7} +b\\b=3+\frac{8}{7} \\b=\frac{21}{7}+\frac{8}{7}=\frac{29}{7} =4\frac{1}{7} \\b=4\frac{1}{7}$

Last step: substitute the slope and y intercept into y=mx+b.

$y=mx+b\\y=-\frac{4}{7}x+4\frac{1}{7}$

That is the answer to this problem.

I hope this helps.

3 0

3 years ago

PLEASE HELP!

emmainna [20.7K]

Use the given recursion and starting value of $x_0 = 2.4$ to find $x_1$ :

$x_1 = \dfrac{x_0 + \frac6{x_0}}2 = \dfrac{2.4 + \frac{6}{2.4}}2 = 2.45$

Do the same for $x_2$ and $x_3$ :

$x_2 = \dfrac{x_1 + \frac6{x_1}}2 = \dfrac{2.45 + \frac6{2.45}}2 \approx 2.44949$

$x_3 = \dfrac{x_2+\frac6{x_2}}2 \approx \dfrac{2.44949 + \frac6{2.44949}}2 \approx \boxed{2.44949}$

(That's not a mistake. This just tells you that the 2nd and 3rd iterates are very close together and have at least the same first 5 digits after the decimal.)

5 0

2 years ago

What is the domain of the function yx4

lutik1710 [3]

The domain of the function is [-4,∞).

Domain is the set of all the possible inputs for which the function is defined.

The given function is:

y = √x+4

It is a radical function. The function is defined if the expression inside the radical greater than or equal to zero.

x+4≥0

Subtract 4 from both the sides.

x+4-4 ≥ 0-4