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3 years ago

Simplify √(x^2-10x+25) if -5≤x<5

Mathematics

1 answer:

romanna [79]3 years ago

8 0

$\qquad\qquad\huge\underline{{\sf Answer}}$

Let's simplify ~

$\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 10x + 25 }$

$\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 5x - 5x + 25 }$

$\qquad \sf \dashrightarrow \: \sqrt{ {x}^{} (x- 5) - 5(x - 5) }$

$\qquad \sf \dashrightarrow \: \sqrt{ (x- 5) (x - 5) }$

$\qquad \sf \dashrightarrow \: \sqrt{ (x- 5) {}^{2} }$

$\qquad \sf \dashrightarrow \: (x- 5)$

value x lies between :

$\qquad \sf \dashrightarrow \: - 5 \leqslant x \leqslant 5$

if the value of x is taken -5

$\qquad \sf \dashrightarrow \: - 5 - 5$

$\qquad \sf \dashrightarrow \: - 10$

if value of x is taken as 5

$\qquad \sf \dashrightarrow \:5 - 5$

$\qquad \sf \dashrightarrow \:0$

So, the possible values of the required expression lies between ~

$\qquad \sf \dashrightarrow \: - 10 \leqslant \sqrt{ {x}^{2} - 10x + 25 } < 0$

I hope you understood the whole procedure. let me know if you have any doubts in given steps ~

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Answer:

The unit vectors are:

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Step-by-step explanation:

Unit vectors that are a parallel to the tangent line have the same slope than the tangent line, thus we can find the slope of the tangent line, find directional vectors and then their corresponding unit vectors.

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Thus we have slope m = 4, then the parallel unit vector has slope m = 4/1

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From the slope m = 4/1, we can write it as a direction vector with x =1 and y = 4. Notice also that x = -1 and y = -4 would have given as as well slope m = 4 too.

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$\hat u =\cfrac{\vec u}{|\vec u|}$

So finding the magnitude we get

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$\vec u_1 = \left$

And the second unit vector is

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Answer:

x = 3/2 - ((y + 4)²)/2

Step-by-step explanation:

The coordinates of the focus of the parabola = (1, -4)

The directrix of the parabola is the line, x = 2 (parallel to the y-axis)

The general form of a parabola having a directrix parallel to the y-axis is presented as follows;

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The line representing the directrix is x = h - p

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From the directrix, we have;

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Answer:

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