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oksano4ka [1.4K]

3 years ago

9

PLZ PLZ PLZ HELP ME!!! AND QUICKLY TOO!!! (15 POINTS)

1 answer:

Orlov [11]3 years ago

8 0

The answer would be:

A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin

See attached picture:

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Dada la ecuacion 25x2 + 4y2 = 100, determina las coordenadas de los vertices, focos, las longitudes de los respectivos ejes mayo

Likurg_2 [28]

Answer:

The given equation is

$25x^{2} +4y^{2}=100$

Which represents an elipse.

To find its elements, we need to divide the equation by 100

$\frac{25x^{2} +4y^{2} }{100} =\frac{100}{100} \\\frac{x^{2} }{4} +\frac{y^{2} }{25} =1$

Where $a^{2} =25$ and $b^{2}=4$ . Remember that the greatest denominator is $a$ , and the least is $b$ . So, we extract the square root on each equation.

$a=5$ and $b=2$ .

In a elipse, we have a major axis and a minor axis. In this case, the major axis is vertical and the minor axis is horizontal, that means this is a vertical elipse.

The length of the major axis is $2a=2(5)=10$ .

The length of the minor axis is $2b=2(2)=4$ .

The vertices are $(0,5);(0,-5)$ and $(2,0);(-2,0)$ .

Now, the main parameters of an elipse are related by

$a^{2}=b^{2} +c^{2}$ , which we are gonna use to find $c$ , the parameter of the focus.

$c=\sqrt{a^{2}-b^{2} }=\sqrt{25-4}=\sqrt{21}$

So, the coordinates of each focus are $(0,\sqrt{21})$ and $(0,-\sqrt{21})$

The eccentricity of a elipse is defined

$e=\frac{c}{a}=\frac{\sqrt{21} }{5} \approx 0.92$

The latus rectum is defined

$L=\frac{2b^{2} }{a}=\frac{2(4)}{5} =\frac{8}{5} \approx 1.6$

Finally, the graph of the elipse is attached.

7 0

3 years ago

Raegan needs 2 boards to make a shelf one board is 1 1/2 m long and the other is 3 1/2 m long what is the total length of the sh

ollegr [7]

Answer:

5 m

Step-by-step explanation:

Find the total length of the shelf by adding together the lengths of the two boards:

1 1/2 + 3 1/2

= 5

So, the total length of the shelf is 5 m

6 0

3 years ago

What is the equation of a circle with center (2,-8) and radius 9?

leonid [27]

Answer:

9^2= (x+2)^2+(y+8)^2

Step-by-step explanation:

The equation is r^2=(x+h)^2+(y-k)^2

4 0

4 years ago

Read 2 more answers

Which pair of numbers are equidistant from -28 on a number line

nasty-shy [4]

Positive 28 I think.

6 0

4 years ago

Is this correct? (B)

sergiy2304 [10]

Yes you are correct. Nice work.

(h,k) = (10,-4) is the center; r = 2 is the radius

(x-h)^2 + (y-k)^2 = r^2

(x-10)^2 + (y-(-4))^2 = 2^2

<h3>(x-10)^2 + (y+4)^2 = 4</h3>

5 0

3 years ago