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1 year ago

HALP!!! PLEASE!! I PROMISE YOU WILL BE MARKED BRAINLIEST!!!

Mathematics

1 answer:

elixir [45]1 year ago

5 0

The sum of the inverses of the solutions of the quadratic equation is equal to 2.75.

<h3>How to find the solutions of the quadratic equation?</h3>

Here we the quadratic equation:

0 = 5x^2 - 11x + 4

The solutions are given by Bhaskara's formula:

$x = \frac{11 \pm \sqrt{(-11)^2 - 4*4*5} }{2*5} \\\\x = \frac{11 \pm \sqrt{41} }{10}\\\\$

So the two solutions are:

$a = \frac{11 + \sqrt{41} }{10}\\\\\\b = \frac{11 - \sqrt{41} }{10}$

Then we have:

$\frac{1}{a} + \frac{1}{b} = \frac{10}{11 + \sqrt{41} } + \frac{10}{11 - \sqrt{41} } \\\\= \frac{10*(11 + \sqrt{41} + 11 - \sqrt{41}) }{(11 + \sqrt{41})*(11 - \sqrt{41})} \\\\= \frac{10*(11 + 11 ) }{(11 + \sqrt{41})*(11 - \sqrt{41})}\\\\= \frac{220}{80} = 2.75$

If you want to learn more about parabolas:

brainly.com/question/4061870

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What is the sum of the arithmetic series

docker41 [41]

Answer:

$S_ {12} = 192$

Step-by-step explanation:

The nth term of the given arithmetic sequence is

$U_n = 3 + 2n$

The first term of this series is:

$U_1 = 3 + 2(1) = 5$

The last term of this series is when

$n = 12$

$U_ {12}= 3 + 2(12)$

$U_ {12}= 3 + 24 = 27$

The sum of the first n terms of an arithmetic series when the first an last term is known is given by:

$S_n = \frac{n}{2}(a + l)$

Where a=5 is the first term and l=27 is the last term.

$S_ {12} = \frac{12}{2}(5 + 27)$

$S_ {12} =6(32) =19 2$

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3 years ago

Use Gaussian elimination to write each system in triangular form

Feliz [49]

Answer:

To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is $x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

Swapping two rows
Multiplying a row by a nonzero number
Adding a multiple of one row to another row

To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

$\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right]$

For this matrix we need to perform the following row operations:

$R_2 - 1 R_1 \rightarrow R_2$ (multiply 1 row by 1 and subtract it from 2 row)
$R_3 + 1 R_1 \rightarrow R_3$ (multiply 1 row by 1 and add it to 3 row)
$R_4 - 1 R_1 \rightarrow R_4$ (multiply 1 row by 1 and subtract it from 4 row)

$R_2 \leftrightarrow R_3$ (interchange the 2 and 3 rows)

$R_2 / 2 \rightarrow R_2$ (divide the 2 row by 2)
$R_1 - 1 R_2 \rightarrow R_1$ (multiply 2 row by 1 and subtract it from 1 row)
$R_4 - 1 R_2 \rightarrow R_4$ (multiply 2 row by 1 and subtract it from 4 row)
$R_3 \cdot ( -1) \rightarrow R_3$ (multiply the 3 row by -1)
$R_2 - 1 R_3 \rightarrow R_2$ (multiply 3 row by 1 and subtract it from 2 row)
$R_4 + 3 R_3 \rightarrow R_4$ (multiply 3 row by 3 and add it to 4 row)
$R_4 / 4.5 \rightarrow R_4$ (divide the 4 row by 4.5)

After this step, the system has an upper triangular form

The triangular matrix looks like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5 \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 & 2 \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

If you later perform the following operations you can find the solution to the system.

$R_1 + 0.5 R_4 \rightarrow R_1$ (multiply 4 row by 0.5 and add it to 1 row)
$R_2 + 0.5 R_4 \rightarrow R_2$ (multiply 4 row by 0.5 and add it to 2 row)
$R_3 - 2 R_4 \rightarrow R_3$ (multiply 4 row by 2 and subtract it from 3 row)

After this operations, the matrix should look like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & 0 & -\frac{1}{9} \\0 & 1 & 0 & 0 & -\frac{1}{9}\\0 & 0 & 1 & 0 & \frac{4}{9} \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

Thus, the solution is:

$x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

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3 years ago

What is the slope of the line represented by the equation y=2

skelet666 [1.2K]

Remember y=mx+b

Since y=2 that means it is a horizontal line at 2 on the y axis which means it does not have a slope. The slope would be zero.

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2 years ago

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Answer: 288pi in3

Step-by-step explanation:

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V=4/3pir^3

V=4/3pi(6^3)

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2 years ago

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