Various dilutions of square a are shown which square was obtained by dilating square a by a scale factor of 3

What is the equation of the directrix of the parabola given by the equation y2 = -24x?

valentina_108 [34]

Hello!

The directrix of a parabola is a fixed line used in describing a curve or surface.

The standard form a parabola is 4p(x - h) = (y - k)². In this equation, h, k is the vertex, and p is the focal point.

To find the standard form, first, we would find p.

Since the equation given, y² = -24x, has a vertex at (0, 0), h, k would be zero. In this case, we can find p now.

4p = -24 (divide both sides by 4)

p = -6

4(-6)(x - 0) = (y - 0)² which can be simplified to: 4(-6)(x) = y².

Looking at the graph of the parabola, it is symmetric around the x-axis, so therefore, the directrix is a line parallel to the y-axis. To find the directrix, use the formula: x = 0 - p, and we know that p = -6.

x = 0 - (-6)

x = 6

Therefore, the directrix of the parabola is choice D, x = 6.

3 0

4 years ago

The dimensions of a closed rectangular box are measured as 60 centimeters, 50 centimeters, and 70 centimeters, with an error in

Studentka2010 [4]

Answer:

The maximum error in calculating the surface area of the box is 72 square centimeters.

Step-by-step explanation:

From Geometry, the surface area of the closed rectangular box ( $A_{s}$ ), in square centimeters, is represented by the following formula:

$A_{s} = w\cdot l + (w + l)\cdot h$ (1)

Where:

$w$ - Width, in centimeters.

$l$ - Length, in centimeters.

$h$ - Height, in centimeters.

And the maximum error in calculating the surface area ( $\Delta A_{s}$ ), in square centimeters, is determined by the concept of total differentials, used in Multivariate Calculus:

$\Delta A_{s} = \left(l+h\right)\cdot \Delta w + \left(w+h\right)\cdot \Delta l + (w+l)\cdot \Delta h$ (2)

Where:

$\Delta w$ - Measurement error in width, in centimeters.

$\Delta l$ - Measurement error in length, in centimeters.

$\Delta h$ - Measurement error in height, in centimeters.

If we know that $\Delta w = \Delta h = \Delta l = 0.2\,cm$ , $w = 60\,cm$ , $l = 50\,cm$ and $h = 70\,cm$ , then the maximum error in calculating the surface area is: