All categories

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

You might be interested in

(Small sample confidence intervals for a population mean) suppose you are taking a sampling of 15 measurements. you find that x=

Luda [366]

Answer:

The 99% confidence interval is $71.67 < \mu < 78.33$

Step-by-step explanation:

From the question we are told that

The sample size is $n = 15$

The sample mean is $\= x = 75$

The standard deviation is $s = 5$

Given that confidence is 99% then the level of significance is mathematically represented as

$\alpha = 100 - 99$

$\alpha = 1\%$

$\alpha = 0.01$

Next we obtain the critical values of $\frac{ \alpha }{2}$ from the normal distribution table

The value is

$Z_{\frac{ \alpha }{2} } = 2.58$

Generally the margin for error is mathematically represented as

$E = Z_{\frac{ \alpha }{2} } * \frac{ s}{ \sqrt{n} }$

=> $E = 2.58 * \frac{ 5}{ \sqrt{15} }$

=> $E = 3.3307$

The 99% confidence interval is mathematically represented as

$\= x -E < \mu < \= x +E$

=> $75 - 3.3307 < \mu$

=> $71.67 < \mu < 78.33$

3 0

3 years ago

Help PLSSSSSSSSSSSSSSSSS

Charra [1.4K]

The answer for this question is
: 125

Hope this helps

7 0

3 years ago

Read 2 more answers

How can mental math help you find solutions to inequalities?

shepuryov [24]

Answer:

There are many examples the basics are also easy to remember.

Step-by-step explanation:

We can input these for the following equation.

x > 5

(x is greater than 5)

Then compare to - x < 5

(minus x is less than 5)

We try a sum

3x -2 ≤ 1

we can then balance subtract -2

3x ≤ -1

then divide by 3

x= -1 /3

We try another value

3x -2 ≤ 0

1 ≤ 3x

1/3 ≥ x

We can check that each equality fits and alter the number accordingly.

For the first one we are saying it is no greater than 1

For the second we say it is greater than zero.

We are able to prove both have the answer.

Just like when we look for negative percentages and count down we record this as we count in mental math.

7 0

3 years ago

the number is less than 190,000 and greater than 180,000, 5000 more than the number has 187 thousands, 200 less than the number

jarptica [38.1K]

187000-5000=182000
182400+200=182600
The number is 182,600

5 0

3 years ago

I need help on this ASAP please

Artist 52 [7]

Answer:

X= 1

(If correct please mark brainliest. :))

Step-by-step explanation:

5 0

3 years ago