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3 years ago

Find the 9th term of the geometric sequence 10, 40, 160, ...

Mathematics

1 answer:

HACTEHA [7]3 years ago

5 0

Answer:

2,560

Step-by-step explanation:

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Use the properties of logarithms to prove log, 1000 = log2 10.

Leto [7]

Given:

Consider the equation is:

$\log_81000=\log_210$

To prove:

$\log_81000=\log_210$ by using the properties of logarithms.

Solution:

We have,

$\log_81000=\log_210$

Taking left hand side (LHS), we get

$LHS=\log_81000$

$LHS=\dfrac{\log 1000}{\log 8}$ $\left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right]$

$LHS=\dfrac{\log (10)^3}{\log 2^3}$

$LHS=\dfrac{3\log 10}{3\log 2}$ $[\because \log x^n=n\log x]$

$LHS=\dfrac{\log 10}{\log 2}$

$LHS=\log_210$ $\left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right]$

$LHS=RHS$

Hence proved.

6 0

3 years ago

Can anyone solve this?

erastova [34]

It would be 76 degrees because it’s a vertical angle

4 0

3 years ago

Two other form of 0.326

DaniilM [7]

As a fraction it would be 163/500 and it is 326 thousand

3 0

3 years ago

Is the square root of 23 rational or irrational

skelet666 [1.2K]

It is irrational because it’s not terminating (please hit “thanks”

3 0

3 years ago

Read 2 more answers

Sara is a drummer in her school is marching band she wants to make a geometrically similar model of a snare drum for her stuffed

strojnjashka [21]

Answer:

Option B.

Step-by-step explanation:

Let the radius of the snare drum = r

and radius of the model = R

Ratio of the dimensions of the snare drum and the model = 1 : 4

So, $\frac{r}{R}=\frac{1}{4}$

Now as per question, dimensions of the snare drum is multiplied by a scale factor of $\frac{1}{2}$

Radius of the snare drum = $\frac{r}{2}$

Ratio of the radius of the snare drum and cylindrical model ,

$\frac{\frac{r}{2}}{R} =\frac{1}{4}$

$\frac{r}{2R}=\frac{1}{4}$

$\frac{r}{R}=\frac{1}{2}$

Therefore, the cylinder with Sara's dimensions will be geometrically similar but the scale factor will be 1 : 2

Option B is the answer.

6 0

3 years ago

Find the 9th term of the geometric sequence 10, 40, 160, ...​

Find the 9th term of the geometric sequence 10, 40, 160, ...