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3 years ago

What substitution should be used to rewrite 4x^4-21x^2+20=0 as a quadratic function?

Mathematics

2 answers:

pogonyaev3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

Let u = x² ( choice of variable is flexible ), then

4u² - 21u + 20 = 0 ← expressed as a quadratic

This can now be solved for u and converted back into terms of x

Ipatiy [6.2K]3 years ago

3 0

Answer:

refer the explanation

Step-by-step explanation:

this question can be written as

X^2=y

so,x^4=y^2

so it will be 4y^2-21y+20=0

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Y = (x)^(1/9)*Find f(x) when x=(1/2)Round your answer to the nearest thousandth.

Verizon [17]

We are given a function f ( x ) defined as follows:

$y=f(x)=x^{\frac{1}{9}}$

We are to determine the value of f ( x ) when,

$\times\text{ = }\frac{1}{2}$

In such cases, we plug in/substitue the given value of x into the expressed function f ( x ) as follows:

$y\text{ = f ( }\frac{1}{2}\text{ ) = (}\frac{1}{2})^{\frac{1}{9}}$

We will apply the power on both numerator and denominator as follows:

$f(\frac{1}{2})=\frac{1^{\frac{1}{9}}}{2^{\frac{1}{9}}}\text{ = }\frac{1}{2^{\frac{1}{9}}}$

Now we evaluate ( 2 ) raised to the power of ( 1 / 9 ).

$f\text{ ( }\frac{1}{2}\text{ ) = }\frac{1}{1.08005}$

Next apply the division operation as follows:

$f\text{ ( }\frac{1}{2})\text{ = }0.92587$

Once, we have evaluated the answer in decimal form ( 5 decimal places ). We will round off the answer to nearest thousandths.

Rounding off to nearest thousandth means we consider the thousandth decimal place ( 3rd ). Then we have the choice of either truncating the decimal places ( 4th and onwards ). The truncation only occurs when (4th decimal place) is < 5.

However, since the (4th decimal place) = 8 > 5. Then we add ( 1 ) to the 3rd decimal place and truncate the rest of the decimal places i.e ( 4th and onwards ).

The answer to f ( 1 / 2 ) to the nearest thousandth would be:

$\textcolor{#FF7968}{f}\text{\textcolor{#FF7968}{ ( }}\textcolor{#FF7968}{\frac{1}{2})}\text{\textcolor{#FF7968}{ = 0.926}}$

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The table shows the distance Randy drove on one day of her vacation

horsena [70]

Given the table showing the distance Randy drove on one day of her vacation as follows:

$\begin{tabular}
{|c|c|c|c|c|c|}
Time (h)&1&2&3&4&5\\[1ex]
Distance (mi)&55&110&165&220&275
\end{tabular}$

The rate at which she travels is given by

$rate= \frac{distance}{time} \\ \\ = \frac{55}{1} =55mi/h$

If Randy has driven for one more hour at the same rate, the number of hours she must have droven is 6 hrs and the total distance is given by

distance = 55 x 6 = 330 miles.

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svet-max [94.6K]

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Step-by-step explanation:

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