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3 years ago

Find the product: ( x-1/x ) ( x+1/x ) ( x2+1/x2 ) ( x4+1/x4 )

Mathematics

1 answer:

erma4kov [3.2K]3 years ago

3 0

Use the difference of 2 squares (a - b)(a + b) = a^2 - b^2:-

(x - 1/x)(x + 1/x) = x^2 - (1/x)^2

= x^2 - 1/x^2

(x ^2 - 1/x^2)(x^2 + 1 /x^2)

= x^4 - 1/x^4

(x^4 - 1/x^4)(x^4 + 1/x^4)

= x^8 - 1 /x^8 Answer

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Tickets for a school play are $9 per person at the door. However, Devon can save $3 per ticket if he buys his tickets ahead of t

DaniilM [7]

Answer:

3n=72

Step-by-step explanation:

3 0

3 years ago

Determine what type of model best fits the given situation:

lyudmila [28]

Let value intially be = P

Then it is decreased by 20 %.

So 20% of P = $\frac{20}{100} \times P = 0.2P$

So after 1 year value is decreased by 0.2P

so value after 1 year will be = P - 0.2P (as its decreased so we will subtract 0.2P from original value P) = 0.8P-------------------------------------(1)

Similarly for 2nd year, this value 0.8P will again be decreased by 20 %

so 20% of 0.8P = $\frac{20}{100} \times 0.8P = (0.2)(0.8P)$

So after 2 years value is decreased by (0.2)(0.8P)

so value after 2 years will be = 0.8P - 0.2(0.8P)

taking 0.8P common out we get 0.8P(1-0.2)

= 0.8P(0.8)

$=P(0.8)^{2}$ -------------------------(2)

Similarly after 3 years, this value $P(0.8)^{2}$ will again be decreased by 20 %

so 20% of $P(0.8)^{2} \frac{20}{100} \times P(0.8)^{2} = (0.2)P(0.8)^{2}$

So after 3 years value is decreased by $(0.2)P(0.8)^{2}$

so value after 3 years will be = $P(0.8)^{2} - (0.2)P(0.8)^{2}$

taking $P(0.8)^{2}$ common out we get $P(0.8)^{2}(1-0.2)$

$P(0.8)^{2}(0.8)$

$P(0.8)^{3}$ -----------------------(3)

so from (1), (2), (3) we can see the following pattern

value after 1 year is P(0.8) or $P(0.8)^{1}$

value after 2 years is $P(0.8)^{2}$

value after 3 years is $P(0.8)^{3}$

so value after x years will be $P(0.8)^{x}$ ( whatever is the year, that is raised to power on 0.8)

So function is best described by exponential model

$y = P(0.8)^{x}$ where y is the value after x years

so thats the final answer

3 0

3 years ago

A weather plane took to the skies to measure the speed of the jet stream. The plane flew 1920 km with the jet stream as a tail w

Alex

For this case, the first thing we must do is define variables:
p: plane speed
w: wind speed
With the wind in favor, the speed is:
$p + w = 1920/2
$
With the wind against the speed is:
$p - w = 1920 / 3.2
$
Rewriting both equations, we have the following system of equations:
$p + w = 960

p - w = 600$
Then, solving the system of equations (graphically for example), we have the solution is:
$p = 780

w = 180$
Therefore, jet stream's speed:
$w = 180 km / h
$
Answer:
A) p + w = 960; p - w = 600; jet stream's speed = 180 km / h

7 0

3 years ago

Find the value of x such that the data set has a mean of 103.<br><br> 99,122,103,113,109,x

Mashcka [7]

That means the average of all data point equal:

(99+122+103+113+109+x)/6 = 103
===> (546+x)/6 = 103===> 546+x=618 & x=618-546=72, so x =72

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3 years ago

Which set is a function?

Llana [10]

Choice B.
how you can determine is to look at the x coordinates. If you see two x coordinates, and they have different corresponding y values, then the set is not a function.

7 0

3 years ago

Read 2 more answers