El doble de un numero al cubo menos el triple de otro al cuadrado, esta expresión a cual corresponde?

The product of the slopes of two perpendicular lines is -1
That means if the slope of one of them is m, then the slope of the other is $-\frac{1}{m}$
You reciprocal the slope of one and change its sign to find the slope of the other

The mid point of a segment whose endpoints are $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

The perpendicular bisector of a line is the line that intersect it in its mid-point and formed 4 right angles

∵ The end point of a given line are (9 , -3) and (-5 , -7)

∴ $x_{1}=9$ and $x_{2}=-5$

∴ $y_{1}=-3$ and $y_{2}=-7$

- Find the slope of the line by using the rule of the slope $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ $m=\frac{-7-(-3)}{-5-9}=\frac{-7+3}{-14}=\frac{-4}{-14}=\frac{2}{7}$

∴ The slope of the given line is $\frac{2}{7}$

To find the slope of the perpendicular bisector of it reciprocal it and change its sign

∴ The slope of the perpendicular bisector = $-\frac{7}{2}$

∵ The form of the linear equation is y = mx + b, where m is the

slope and b is the y-intercept

- Substitute the value of m in the equation

∴ The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + b

To find b substitute x and y in the equation by a point on the line

∵ The perpendicular bisector of the given line intersect it at

its midpoint

- Find the mid-point of the given line busing the rule above

∵ $x_{1}=9$ and $x_{2}=-5$

∵ $y_{1}=-3$ and $y_{2}=-7$

∴ The mid-point of the given line = $(\frac{9+(-5)}{2},\frac{-3+(-7)}{2})=(\frac{4}{2},\frac{-10}{2})=(2,-5)$

Point (2 , -5) is also lies on the perpendicular line

∴ x = 2 and y = -5

- Substitute them in the equation

∵ -5 = $-\frac{7}{2}$ (2) + b

∴ -5 = -7 + b

- Add 7 to both sides

∴ 2 = b

- Substitute the value of b in the equation

∴ The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + 2

The equation of the perpendicular bisector is y = $-\frac{7}{2}$ x + 2

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8 0

3 years ago

If xy + y² = 6, then the value of dy/dx at x= -1 is<br>

mylen [45]

Hi there!

$\large\boxed{\text{At (-1, -2), }\frac{dy}{dx} = -\frac{2}{5}}}$

$\large\boxed{\text{At (-1, 3), }\frac{dy}{dx} = -\frac{3}{5}}}$

We can calculate dy/dx using implicit differentiation:

xy + y² = 6

Differentiate both sides. Remember to use the Product Rule for the "xy" term:

(1)y + x(dy/dx) + 2y(dy/dx) = 0

Move y to the opposite side:

x(dy/dx) + 2y(dy/dx) = -y

Factor out dy/dx:

dy/dx(x + 2y) = -y

Divide both sides by x + 2y:

dy/dx = -y/x + 2y

We need both x and y to find dy/dx, so plug in the given value of x into the original equation:

-1(y) + y² = 6

-y + y² = 6

y² - y - 6 = 0

(y - 3)(y + 2) = 0

Thus, y = -2 and 3.

We can calculate dy/dx at each point:

At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.

At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.

5 0

3 years ago

Determine the range of the following graph:

uysha [10]

Answer:

-4 ≤ y ≤ 2 or [-4 , 2]

Step-by-step explanation:

The maximum of the function is +2 while the minimum is -4, the range is

-4 ≤ y ≤ 2 or [-4 , 2]

4 0

3 years ago