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taurus [48]
3 years ago
13

What is the common ratio of the geometric sequence 1, 4, 16, 64, ...?

Mathematics
2 answers:
krok68 [10]3 years ago
8 0
For Example;
1) \frac{4}{1} = 4
2) \frac{16}{4}  = 4

For this sequence the common ratio = 4
Vika [28.1K]3 years ago
6 0
A geometric sequence refers to a sequence where to get from one term to another you need to multiply by the same number each time. This number is called common ratio or factor. 

On the case are given the numbers 1,4,16,64 as part of the sequence.

From 1 to 4 multiply by 4
From 4 to 16 multiply by 4
From 16 to 64 multiply by 4
 
After the previous reasoning, you can conclude that the common factor or ratio of the geometric sequence is 4.
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There is a blizzard, and Matt notices that the snow is falling at a constant rate. Two hours after the beginning of the snowstor
MaRussiya [10]

Answer:

2 inches per hour, 5 inches, y=2x+5

Step-by-step explanation:

No, I don't think I will

8 0
3 years ago
the price per share of a stock decreased from $90 per share to $36 per share. by what percent did the price of the stock decreas
givi [52]

Answer:

60%

Step-by-step explanation:

we know that

the price per share of a stock decreased from $90 per share to $36 per share

In this problem

$90 represent the 100%

so

using proportion

Find out what percentage represent the difference of ($90-$36)

($90-$36)=$54

Let

x ----> the percentage of the difference

\frac{100\%}{\$90}=\frac{x}{\$54}\\\\x=54(100)/90\\\\x=60\%

8 0
3 years ago
I NEED YOUR HELP!!<br> What is 2 + 3x8
Gemiola [76]

Answer:

Don't need Help don't depend on others do you'r work by yourself why you came to this world for asking help from other not do your work by yourself.Today I am going to help but from tomorrow you have to do by yourself

Step-by-step explanation:

=2x+3x8

=add

=5x8

=x=5=8/2

=x=5/4 is your answer

4 0
3 years ago
Read 2 more answers
This is a "water tank" calculus problem that I've been working on and I would really appreciate it if someone could look at my w
Sedaia [141]
Part A

Everything looks good but line 4. You need to put all of the "2h" in parenthesis so the teacher will know you are squaring all of 2h. As you have it right now, you are saying "only square the h, not the 2". Be careful as silly mistakes like this will often cost you points. 

============================================================

Part B

It looks like you have the right answer. Though you'll need to use parenthesis to ensure that all of "75t/(2pi)" is under the cube root. I'm assuming you made a typo or forgot to put the parenthesis. 

dh/dt = (25)/(2pi*h^2)
2pi*h^2*dh = 25*dt
int[ 2pi*h^2*dh ] = int[ 25*dt ] ... applying integral to both sides
(2/3)pi*h^3 = 25t + C
2pi*h^3 = 3(25t + C)
h^3 = (3(25t + C))/(2pi)
h^3 = (75t + 3C)/(2pi)
h^3 = (75t + C)/(2pi)
h = [ (75t + C)/(2pi) ]^(1/3)

Plug in the initial conditions. If the volume is V = 0 then the height is h = 0 at time t = 0
0 = [ (75(0) + C)/(2pi) ]^(1/3)
0 = [ (0 + C)/(2pi) ]^(1/3)
0 = [ (C)/(2pi) ]^(1/3)
0^3 =  (C)/(2pi)
0 = C/(2pi)
C/(2pi) = 0
C = 0*2pi
C = 0 

Therefore the h(t) function is...
h(t) = [ (75t + C)/(2pi) ]^(1/3)
h(t) = [ (75t + 0)/(2pi) ]^(1/3)
h(t) = [ (75t)/(2pi) ]^(1/3)

Answer:
h(t) = [ (75t)/(2pi) ]^(1/3)

============================================================

Part C

Your answer is correct. 
Below is an alternative way to find the same answer

--------------------------------------

Plug in the given height; solve for t
h(t) = [ (75t)/(2pi) ]^(1/3)
8 = [ (75t)/(2pi) ]^(1/3)
8^3 = (75t)/(2pi)
512 = (75t)/(2pi)
(75t)/(2pi) = 512
75t = 512*2pi
75t = 1024pi
t = 1024pi/75
At this time value, the height of the water is 8 feet

Set up the radius r(t) function 
r = 2*h
r = 2*h(t)
r = 2*[ (75t)/(2pi) ]^(1/3) .... using the answer from part B

Differentiate that r(t) function with respect to t
r = 2*[ (75t)/(2pi) ]^(1/3)
dr/dt = 2*(1/3)*[ (75t)/(2pi) ]^(1/3-1)*d/dt[(75t)/(2pi)] 
dr/dt = (2/3)*[ (75t)/(2pi) ]^(-2/3)*(75/(2pi))
dr/dt = (2/3)*(75/(2pi))*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)

Plug in t = 1024pi/75 found earlier above
dr/dt = (25/pi)*[ (75t)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (75(1024pi/75))/(2pi) ]^(-2/3)
dr/dt = (25/pi)*[ (1024pi)/(2pi) ]^(-2/3)
dr/dt = (25/pi)*(1/64)
dr/dt = 25/(64pi)
getting the same answer as before

----------------------------

Thinking back as I finish up, your method is definitely shorter and more efficient. So I prefer your method, which is effectively this:
r = 2h, dr/dh = 2
dh/dt = (25)/(2pi*h^2) ... from part A
dr/dt = dr/dh*dh/dt ... chain rule
dr/dt = 2*((25)/(2pi*h^2))
dr/dt = ((25)/(pi*h^2))
dr/dt = ((25)/(pi*8^2)) ... plugging in h = 8
dr/dt = (25)/(64pi)
which is what you stated in your screenshot (though I added on the line dr/dt = dr/dh*dh/dt to show the chain rule in action)
8 0
3 years ago
Divide by 12 nd equal 14
ICE Princess25 [194]
170 dived by 12 is 14

7 0
3 years ago
Read 2 more answers
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