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gayaneshka [121]

3 years ago

7

What are the roots of x in -10x^2+12x-9=0

1 answer:

Alekssandra [29.7K]3 years ago

6 0

$- 10 {x}^{2} + 12x - 9 = 0 \\ \Leftrightarrow {x}^{2} - \frac{6}{5} x + \frac{9}{10 } = 0 \\ \Leftrightarrow {x}^{2} - \frac{6}{5}x + \frac{9}{25} = - \frac{9}{10} + \frac{9}{25} \\ \Leftrightarrow \underbrace{ {(x - \frac{3}{5} )}^{2} }_{ \geqslant 0} = - \frac{27}{50} \\ \Leftrightarrow x\in\emptyset \\ \Rightarrow Roots: None$

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A function, f(x) = 4x + 5, has a domain 0 < x < 50. What is its range?

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Find a closed-form solution to the integral equation y(x) = 3 + Z x e dt ty(t) , x > 0. In other words, express y(x) as a fun

MrMuchimi

Answer:

$y{x} = \sqrt{7+2Inx}$

Step-by-step explanation:

$y(x)= 3 + \int\limits^x_e {dx}/ \, ty(t) , x>0}$

Let say; By y(x)= y(e)

we have;

$y(e)= 3 + \int\limits^e_e {dt}/ \, ty= 3+0$

Using Fundamental Theorem of Calculus and differentiating by Lebiniz Rule:

$y^{1} (x) = 0 + 1/ xy$

$y^{1} = 1/xy$

dy/dx = 1/xy

$\int\limits {y} \, dxy = \int\limits \, dx/x$

$y^{2}/2 Inx + C$

RECALL: y(e) = 3

$(3)^{2} / 2 = In (e) + C$

$\frac{9}{2} =In(e)+C$

$\frac{9}{2} - 1 = C$

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$y^{2} / 2 = In x +C$

$y^{2} / 2 = In x +7/2$

MULTIPLYING BOTH SIDE BY 2 , TO ELIMINATE THE DENOMINATOR, WE HAVE;

$y^{2} = {7+2Inx}$

$y{x} = \sqrt{7+2Inx}$

8 0

3 years ago