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2 years ago

PLEASE HELP!!!!!!!!

Mathematics

1 answer:

Korolek [52]2 years ago

7 0

Answer:

2π - 4√5

(= -2.66 to nearest hundredth).

Step-by-step explanation:

√(2π - 4√5)^2

= 2π - 4√5 (by the definition of a square root)

If you want an approximate value it is

-2.66 to the nearest hundredth

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3 years ago

Which values are possible rational roots of 4x3+9x2−x+10=0 according to the rational root theorem? Select each correct answer. ±

navik [9.2K]

ANSWER

The possible rational roots are:

$\pm\frac{1}{2},\pm2,\pm \frac{5}{2}$

EXPLANATION

According to the rational root theorem, the possible rational roots of the polynomial,

$4x^3+9x^2-x+10=0$

are all the possible factors of the constant term divided by all the possible factors of the coefficient of the highest degree of the polynomial.

Therefore we examine the numerator and denominator of the options provided to see if they are factors of 10 and 4 respectively.

For

$\pm\frac{1}{2}$ , we can see that 1 is a factor of 10 and 2 is a factor of 4, hence it is a possible rational root.

The same thing applies to $\pm2,\pm \frac{5}{2}$ also.

As for

$\pm \frac{2}{5}$ , 2 is a factor of 10 but 5 is not a factor of 2, hence it is not a possible rational root.

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3 years ago

The number of Apple iPods sold in 2009 was 54.13 million. That number decreased approximately linearly to 26.38 million iPods so

AleksandrR [38]

Answer:

$A(t) = -6.9375t + 81.88$ is the amount, in millions, for the number of Apple iPods sold in t years after 2005.

Step-by-step explanation:

Linear function:

A linear function has the following function:

$y = mx + b$

In which m is the slope(the value that y changes by when x changes by 1) and b is the y-intercept(the initial value of the output).

Finding the value in 2005:

This is b.

The number of Apple iPods sold in 2009 was 54.13 million. That number decreased approximately linearly to 26.38 million iPods sold in 2013.

So in 4 years, it decreased from 54.13 - 26.38 = 27.75 million.

So the value in 2005 should also be 27.75 million more than in 2009, that is 54.13 + 27.75 = 81.88. So

$y = mx + 81.88$

Using A for y and t for x

$A(t) = mt + 81.88$

Finding the slope:

When we have two points, the slope is given by the change in the output divided by the change in the input.

In 4 years, the amount decrease by 27.75 million. So

$m = -\frac{27.75}{4} = -6.9375$

$A(t) = -6.9375t + 81.88$ is the amount, in millions, for the number of Apple iPods sold in t years after 2005.

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3 years ago