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3 years ago

How do you solve for n^3 + 3n^2 + n - 33 = 0?

Mathematics

1 answer:

Inga [223]3 years ago

4 0

Answer:

one real root: n ≈ 2.38450287889

Step-by-step explanation:

My favorite solution method for higher-degree polynomials is to use a graphing calculator.

Descartes' rule of signs tells you the one sign change among coefficients means there will be one positive real root. A graph shows you it is about 2.4, hence irrational (not a divisor of 33, so not rational).

You can use a cubic formula to find an explicit expression for the root, or you can find its value using any of several iteration methods. The attachment shows Newton's method iteration being used to refine the graph value of 2.385 to the more accurate 2.38450287889.

Factoring that root from the cubic results in a quadratic with irrational coefficients. Its vertex form is approximately ...

y = (n +2.692)² + 6.591

Hence, the complex roots will be near -2.692±i√6.591.

_____

There are formulas for the roots of a cubic. The formula tells you the real root for this cubic is ...

n = 2√(2/3)cosh(1/3·arccosh(24√(3/2))) -1 ≈ 2.38450287889

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Given the box plot, will the mean or the median provide a better description of the center? box plot with min at 11, Q1 at 22. 5

Slav-nsk [51]

The median, because the data distribution is skewed to the right.

Given that

The box plot with the following parameters:

Minimum value at 11,

First Quartile, Q1 at 22.5,

Median at 34.5,

Third Quartile, Q3 at 36,

Maximum value at 37.5.

According to the question

When a distribution has a longer tail to one of its sides, then it is said to be skewed.

Since the tail is longer to the left, it is said to be left-skewed.

The data distribution is skewed to the left because the median (34.5) is closer to the third quartile (36) than to the first quartile (22.5).

For skewed data, we always prefer the median because it is less affected by the outliers and if the mean is chosen, the value of the mean is biased towards the side that has larger values while the median does not get affected by it. So, we choose the median.

For skewed distributions, the median is the best measure of center.

Hence, the median, because the data distribution is skewed to the right.

To know more about Mean click the link given below.

brainly.com/question/2508120

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3 years ago

What is the 32nd term of the arithmetic sequence where a1 = 12 and a13 = -60

Olin [163]

Answer:

The 32nd term of Arithmetic sequence is -174

Step-by-step explanation:

Given: $a_1=12, a_{13}=-60$

We are given two term of the Arithmetic sequence.

Formula:

$a_n=a+(n-1)d$

For $a_1=12$

$a=12$

For $a_{13}=-60$

$a+12d=-60$

Using two equation solve for a and d

$12+12d=-60$

$1+d=-5$

$d=-6$

We need to find 32nd term

$a_{32}=a+31d$

$a_{32}=12+31(-6)$

$a_{32}=12-186$

$a_{32}=-174$

Hence, The 32nd term of Arithmetic sequence is -174

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zhannawk [14.2K]

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Find out more on graphing inequalities at brainly.com/question/11234618.

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