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1 year ago

Write the quadratic equation that has roots -1-rt2/3 and -1+rt2/3 if its coefficient with x^2 is equal to 1

Mathematics

1 answer:

weeeeeb [17]1 year ago

7 0

The equation of the quadratic function is f(x) = x²+ 2/3x - 1/9

<h3>How to determine the quadratic equation?</h3>

From the question, the given parameters are:

Roots = (-1 - √2)/3 and (-1 + √2)/3

The quadratic equation is then calculated as

f(x) = The products of (x - roots)

Substitute the known values in the above equation

So, we have the following equation

$f(x) = (x - \frac{-1-\sqrt{2}}{3})(x - \frac{-1+\sqrt{2}}{3})$

This gives

$f(x) = (x + \frac{1+\sqrt{2}}{3})(x + \frac{1-\sqrt{2}}{3})$

Evaluate the products

$f(x) = (x^2 + \frac{1+\sqrt{2}}{3}x + \frac{1-\sqrt{2}}{3}x + (\frac{1-\sqrt{2}}{3})(\frac{1+\sqrt{2}}{3})$

Evaluate the like terms

$f(x) = x^2 + \frac{2}{3}x - \frac{1}{9}$

So, we have

f(x) = x²+ 2/3x - 1/9

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brainly.com/question/1214333

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Find the coordinates of the point which divides the line segment joining the points (4, -3) and (8,5) in the ratio 3:1 internall

Inessa05 [86]

Answer:

The coordinates of the point that divides the line internally in the given ratio is (7,3)

Step-by-step explanation:

To find this coordinates, we use the in renal division formula

we have this as;

(x,y) =( nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)

(x1,y1) = (4,-3)

(x2,y2) = (8,5)

(m,n) = (3,1)

So, substituting these values, we have ;

(x,y) = (1(4) + 3)8))/(3 + 1) , (1(-3) + 3)5)/(1 + 3)

(x,y) = (28)/4, (12/4)

(x,y) = (7,3)

7 0

3 years ago

Write the Taylor Series for f(x) = sin(x)center

tangare [24]

Answer:

Taylor series of sin(x) centered at x = 0.

Step-by-step explanation:

Taylor series expansion:

$\sum_{n=0}^N f^n(a)\displaystyle\frac{(x-a)^n}{n!}$

Here, f(x) = sin (x) and a = 0

$f(x) = \sin x, f(0) = 0\\f'(x) = \cos x, f'(0) = 1\\f''(x) = -\sin x, f''(0) = 0\\f'''(x) = -\cos x, f'''(0) = -1\\f^4(x) = \sin x, f^4(0) = 0\\f^5(x) = \cos x, f^5(0) = 0$

Putting all the values and expanding, we get,

$f(x) = f(a) + \displaystyle\frac{f'(a)(x-a)}{1!} + \displaystyle\frac{f''(a)(x-a)^2}{2!} + \displaystyle\frac{f'''(a)(x-a)^3}{3!} + \displaystyle\frac{f^4(a)(x-a)^4}{4!} + \displaystyle\frac{f^5(a)(x-a)^5}{5!} + ...\\\\= \sin 0 + \displaystyle\frac{x}{1!} + \displaystyle\frac{(0)x^2}{2!} + \displaystyle\frac{(-1)x^3}{3!} + \displaystyle\frac{(0)x^4}{4!} + \displaystyle\frac{(1)x^5}{5!} + ...$

Solving, we get

$\sin x = x - \displaystyle\frac{x^3}{3!} + \displaystyle\frac{x^5}{5!} - \displaystyle\frac{x^7}{7!} + ...\\\\\sin x = x - \displaystyle\frac{x^3}{6} + \displaystyle\frac{x^5}{120} - \displaystyle\frac{x^7}{5040} + ...$

3 0

3 years ago

If your starting salary is 40,000 and you receive a 3% increase at the end of every year, what is the total amount, in dollars,

liberstina [14]

$\bf \qquad \textit{Amount for Exponential Growth}\\\\
A=I(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\to &40,000\\
r=rate\to 3\%\to \frac{3}{100}\to &0.03\\
t=\textit{elapsed time}\to &16\\
\end{cases}
\\\\\\
A=40000(1+0.03)^{16}\implies A=40000(1.03)^{16}$

5 0

3 years ago

Read 2 more answers

Triangle abc is represented. points d and f are marked on side ab and points e and g are marked on side ac. segments de and fg a

Ghella [55]

If points d and f are on side ab and points e ang g are on side ac then line segment de and fg are parallel.

Given There is a triangle abc.

Parallel lines are those lines that do not meet at any point. If we draw a triangle abc and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle.

Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.

Learn more about parallel lines here brainly.com/question/16742265

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2 years ago

What’s the slope of the following graph?

nadezda [96]

The slope of a straight line which is parallel to X axis is always equal to 0 (zero).

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2 years ago