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3 years ago

Nth term of the sequence 8,48,288

Mathematics

1 answer:

Kruka [31]3 years ago

8 0

Answer:

Step-by-step explanation:

$a_1=8\\a_2=48\\a_3=288\\\\288:48=6\\48:8=6\\\\ \dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}= 6$

Therefore it's geometric sequence with common ratio of 6

$a_n=a_1\cdot r^{n-1}\\\\a_1=8\\r=6\\\\a_n=8\cdot6^{n-1}$

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A water tank is 3/4 full.

guapka [62]

x/.75=x-56/0.4

0.4x=.75x-42

-0.35x=-42

x=120

I set up a proportion in which x=the tank when it is 3/4 full. When the tank is 3/4 full, solving the proportion tells us the x=120 litres. 120/3=40, and 120+40 is 160, showing that a tank completely full would indeed hold 160 litres.

Hope this helps!

3 0

3 years ago

Wind farm configuration is a significant issue as the upwind turbines generate maximal energy while creating wakes for downwind

lord [1]

Answer:

a) [24.114,29.2858]

b) Since 30 is not in the 95% confidence interval, there is a 95% probability that 30 is not the true mean WEP

Step-by-step explanation:

The 95% confidence interval is given by the interval

$\bf [ \bar x-z^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}]$

where

$\bf \bar x$ = 26.7 is the sample mean

s = 17.7 is the sample standard deviation

n = 180 is the sample size

Since the sample size is big enough, we can use the Normal N(0,1) to compute $\bf z^*$ and it would be 1.96(*) (a value such that the area under the Normal curve outside the interval [-z, z] is 5% (0.05))

and our 95% confidence interval is

$\bf [26.7-1.96*\frac{17.7}{\sqrt{180}}, 26.7+1.96*\frac{17.7}{\sqrt{180}}]=\boxed{[24.114,29.2858]}$

(*)

This value can be computed in Excel with

<em>NORMINV(1-0.025,0,1)</em>

and in OpenOffice Calc with

<em>NORMINV(1-0.025;0;1)</em>

Since 30 is not in the 95% confidence interval, there is a 95% probability that 30 is not the true mean WEP

7 0

3 years ago

How to isolate scalars from a matrix

I am Lyosha [343]

The technique of matrix isolation involves condensing the substance to be studied with a large excess of inert gas (usually argon or nitrogen) at low temperature to form a rigid solid (the matrix). The early development of matrix isolation spectroscopy was directed primarily to the study of unstable molecules and free radicals. The ability to stabilise reactive species by trapping them in a rigid cage, thus inhibiting intermolecular interaction, is an important feature of matrix isolation. The low temperatures (typically 4-20K) also prevent the occurrence of any process with an activation energy of more than a few kJ mol-1. Apart from the stabilisation of reactive species, matrix isolation affords a number of advantages over more conventional spectroscopic techniques. The isolation of monomelic solute molecules in an inert environment reduces intermolecular interactions, resulting in a sharpening of the solute absorption compared with other condensed phases. The effect is, of course, particularly dramatic for substances that engage in hydrogen bonding. Although the technique was developed to inhibit intermolecular interactions, it has also proved of great value in studying these interactions in molecular complexes formed in matrices at higher concentrations than those required for true isolation.

3 0

3 years ago

If y = kx, and x = 3 and y = 15, calculate k.

kenny6666 [7]

Answer:

k = 5

Step-by-step explanation:

Since the equation is y = kx and x equals 3 while y equals 15, in order to solve this equation we are going to have to substitute the variables with their answers:

x = 3

y = 15

15 = 3k

Now we divide 3 from both 3x and 15 to segregate the variable x:

15/3 = 3k/3

5 = k

Now to check our work we are going to substitute 5 for the variable k, 3 for the variable x and 15 for the variable y.

y = kx

15= (5)(3)

15 = 15

Tada, I hope this helps you!

6 0

3 years ago

Read 2 more answers

On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction. The numb

liberstina [14]

This is a very long question br0(3b)Y=

5 0

2 years ago