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A comet travels along a parabolic path around the Sun. The Sun is the focus of the path. When the comet is at the vertex of the

AlladinOne [14]

Remember that for a function of the form $y=a x^{2}$ , a parabola, the focus will be: $(0, \frac{1}{4a} )$ .
We know that the vertex of the parabola is (0,0), and the sun is the focus of the parabola; we also know that the focus is in the positive y-axis and when the comet is as its vertex, the distance between them is 60'000.000 km; therefore the focus of our parabola is (0, 60'000.000).
Now that we know the focus, we can find $a$ using the focus of the parabola:
$\frac{1}{4a} =60'000.000$
$1=(60'000.000)(4a)$
$1=240'000.000a$
$a= \frac{1}{240'000.000}$

Now, the only thing left is replacing the value of $a$ in our equation $y=a x^{2}$ :
$y=( \frac{1}{240'000.000)} ) x^{2}$
$y= \frac{ x^{2} }{240'000.000}$

We can conclude that the equation that represents the path of the comet is $y= \frac{ x^{2} }{240'000.000}$

5 0

3 years ago

A triangle has vertices of (-2, -1), (0, -5), and (3, 2). What are the vertices of the image after applying the translation

dimulka [17.4K]

Answer:

B. (1, -5), (3, -9), (6, -2)

Step-by-step explanation:

First vertex: -2 + 3 = 1, -1 - 4 = -5, so (1, -5)

Second vertex: 0 + 3 = 3, -5 - 4 = -9, so (3, -9)

Third vertex: 3 + 3 = 6, 2 - 4 = -2, so (6, -2)

(1, -5), (3, -9), (6, -2)

I hope this helps :))

5 0

4 years ago

What is x, if the volume of the cylinder is 768pi rcm3?

AVprozaik [17]

let's recall Cavalieri's Principle, <u>solids with equal altitudes and cross-sectional areas at each height have the same volume</u>, so even though this cylinder is slanted with a height = x and a radius = 8, the cross-sectional areas from the bottom to top are the same thickness and thus the same area, so its volume will be the same as a cylinder with the same height and radius that is not slanted.

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=8\\ h=x\\ V=768\pi \end{cases}\implies 768\pi =\pi (8)^2(x)\implies 768\pi =64\pi x \\\\\\ \cfrac{768\pi }{64\pi }=x\implies 12=x$

5 0

3 years ago

Solve the inequality and show on a number line<br><br> (picture included below)

aksik [14]

Step-by-step explanation:

I cant show a number line so i'll do my best to explain how its graphed.

15) x - 1 < 15

add 1 to both sides:

x < 16

Because it is less than, rather than less than or equal to, it's graphed with an open circle (not filled in) on 16, and everything less than 16 highlighted

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16) 2(y + 1) - 2 ≥ 12

distribute the 2:

2y + 2 - 2 ≥ 12

combine like terms

2y ≥ 12

isolate y:

y ≥ 6

This one is greater than or equal to, so it's graphed with a closed circle (filled in) and everything above 6 highlighted

6 0

4 years ago

Read 2 more answers

the average rainfall in Clearview is 38 inches . this year 29.777 inches fell . How much less rain fell this year than falls in

dexar [7]

38 (average) - 29.777 (this year) = 8.223 inches less this year than the average year.

6 0

4 years ago