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3 years ago

(1/8)^5*(1/8)^3 simplify this expression

Mathematics

1 answer:

matrenka [14]3 years ago

8 0

(x^m) times (x^n)=x^(m+n)
(1/8)^5 times (1/8)^3=(1/8)^(5+3)=(1/8)^8=1/(8^8)

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3 years ago

Find an equation with a solution of x = 2 of multiplicity 1 , and a solution of x = − 1 of multiplicity 2 .

luda_lava [24]

We want to find an equation for the given solutions and the multiplicity of each solution.

The equation is:

$0 = (x - 2)*(x + 1)^2$

First, assume that we have a given equation and we know that we have solutions {x₁, x₂, ..., xₙ}, each one with multiplicity {m₁, ..., mₙ}.

The equation, of a polynomial that meets these requirements, is given by:

$0 = A*(x - x_1)^{m_1}*...*(x - x_n)^{m_n}$

Where A is the leading coefficient and can be any real number.

Now that we know that, here we have the solutions:

x = 2 with multiplicity 2
x = -1 with multiplicity 2

We don't have information about the leading coefficient, so we assume it is equal to 1.

Then the equation is:

$0 = (x - 2)*(x + 1)^2$

If you want to learn more, you can read:

brainly.com/question/11536910

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3 years ago

If your going 70 mph how long does it take to get 70 mph

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3 years ago

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2 years ago

A machine at a bottling company fills water bottles. the number of bottles filled is proportional to the amount of time the mach

Whitepunk [10]

In the table shown below:

Let N be the number of bottles filled,

Let T be the time in hours.

Given that the number of bottles filled is proportional to the amount of time the machine runs, we have

$\begin{gathered} N\propto T \\ \text{Introducing a proportionality constant, we have } \\ N\text{ = kT} \\ \Rightarrow k\text{ = }\frac{N}{T} \\ \end{gathered}$

Let's evaluate the value of k for each day.

Thus, on monday,

$\begin{gathered} N\text{ = 9900} \\ T\text{ = 5.5} \\ \text{thus,} \\ k\text{ = }\frac{9900}{5.5} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Tuesday:

$\begin{gathered} N\text{ = }11160 \\ T\text{ = }6.2 \\ \text{thus,} \\ k\text{ = }\frac{11160}{6.2} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Wednesday:

$\begin{gathered} N\text{ = }12330 \\ T\text{ = }6.25 \\ \text{thus,} \\ k\text{ = }\frac{12330}{6.25} \\ \Rightarrow k\text{ = 1972.8} \end{gathered}$

Thursday:

$\begin{gathered} N\text{ = }10440 \\ T\text{ = }5.80 \\ \text{thus,} \\ k\text{ = }\frac{10440}{5.8} \\ \Rightarrow k=1800 \end{gathered}$

It is observed that all exept wednesday have the same value of k.

Thus, the amount of time required for the number of bottles filled on wednesday is evaluated as

$\begin{gathered} N\text{ = }12330 \\ k\text{ = 1800} \\ T\text{ = ?} \\ \text{but} \\ k\text{ = }\frac{N}{T} \\ 1800\text{ = }\frac{12330}{T} \\ \Rightarrow T\text{ = }\frac{\text{12330}}{1800} \\ T\text{ = 6.85} \end{gathered}$

Hence, the incorrect day is Wednesday. The amount of time for that many bottles should be 6.85 hours.

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1 year ago