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3 years ago

10

The area of a rectangular garden is 38 square meters. The width of

2 answers:

const2013 [10]3 years ago

5 0

Answer:

<h2>Length = 9.5 m</h2><h2 />

Step-by-step explanation:

area of garden = 38 m²

width = 4 m

find Length

area = L x W

38 = L (4)

L = 38 / 4

L = 9.5 m

telo118 [61]3 years ago

4 0

38/4=9.5

9.5x4=9.5

9.5

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RideAnS [48]

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2 years ago

Given the parabola below, find the endpoints of the latus rectum. (x-2)^2=-20(y+2)

Shtirlitz [24]

Answer:

The endpoints of the latus rectum are $(12, -7)$ and $(-8, -7)$ .

Step-by-step explanation:

A parabola with vertex at point $C(x, y) = (h,k)$ and whose axis of symmetry is parallel to the y-axis is defined by the following formula:

$(x-h)^{2} = 4\cdot p \cdot (y-k)$ (1)

Where:

$y$ - Independent variable.

$x$ - Dependent variable.

$p$ - Distance from vertex to the focus.

$h$ , $k$ - Coordinates of the vertex.

The coordinates of the focus are represented by:

$F(x,y) = (h, k+p)$ (2)

The <em>latus rectum</em> is a line segment parallel to the x-axis which contains the focus. If we know that $h = 2$ , $k = -2$ and $p = -5$ , then the latus rectum is between the following endpoints:

By (2):

$F(x,y) = (2, -2-5)$

$F(x,y) = (2,-7)$

By (1):

$(x-2)^{2} = -20\cdot (-7+2)$

$(x-2)^{2} = 100$

$x - 2 = \pm 10$

There are two solutions:

$x_{1} = 2 + 10$

$x_{1} = 12$

$x_{2} = 2-10$

$x_{2} = -8$

Hence, the endpoints of the latus rectum are $(12, -7)$ and $(-8, -7)$ .

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