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3 years ago

3x with a 2 as an exponent +8x=35

Mathematics

2 answers:

Alex3 years ago

8 0

Answer:

The roots are {-5, 7/3}.

Step-by-step explanation:

I am assuming you want to solve this for x.

3x^2 + 8x = 35

3x^2 + 8x - 35 = 0 Try factoring by the 'ac' method.

ac = 3 * -35 = - 105.

We need 2 numbers whose product is -105 and whose sum = + 8.

These are +15 and - 7, so we write:

3x^2 + 15x - 7x - 35 = 0 Now factor by grouping:

3x(x + 5) -7(x + 5) = 0 (x + 5) is common so:

(3x - 7)(x + 5) = 0

The roots are {-5, 7/3}.

masha68 [24]3 years ago

8 0

It is (-5)(7/3) that’s the answer

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3 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

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3 years ago