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Maksim231197 [3]
3 years ago
13

Derive the equation of the parabola with a focus at (-5, 5) and a directrix of y = -1. (2 points) Please help

Mathematics
1 answer:
Svetlanka [38]3 years ago
4 0
We see that the the parabola opens up since directix is below the focus

for an parabolla opening up/down with vetex at (h,k) and the distance from teh vertex to the focus is p
(x-h)^2=4p(y-k)
the distance from vertex to directex is the same as from focus to directix

from (-5,5) and y=-1
that is  a vertical distance of 6
vertex is in the middle
6/2=3
5-3=2
the vertex is at (-5,2)
the distance is 3
(x-(-5))^2=4(3)(y-(2))
(x+5)^2=12(y-2)
y=\frac{1}{12}(x+5)^2+2

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Can a rational number be subtracted by a irrational number an equal a rational number?
vladimir2022 [97]

Answer:

No

Step-by-step explanation:

The sum of a rational number and an irrational number is irrational.

4 0
3 years ago
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Answer:

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Step-by-step explanation:

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6 0
2 years ago
Could a polyhedron exist with the given number of faces, vertices, and edges? Drag yes or no to each combination
DanielleElmas [232]

Answer:

(a) No

(b) No

(c) No

Step-by-step explanation:

Given

See attachment

Required

Select Yes or No for each

To do this, we make use of Euler's formula

F + V - E = 2

Where

F \to Faces; V \to Vertices; E \to Edges

(a):\ Faces = 8; Vertices = 12; Edges = 6

Using: F + V - E = 2

8 + 12 - 6 = 2

14 = 2

<em>The above equality is false. Hence, (a) does not exist</em>

(b):\ Faces = 6; Vertices = 6; Edges = 4

Using: F + V - E = 2

6 + 6 - 4 = 2

8 = 2

<em>The above equality is false. Hence, (b) does not exist</em>

<em />

<em />(c):\ Faces = 20; Vertices = 30; Edges = 12<em />

Using: F + V - E = 2

20 + 30 - 12 = 2

38 = 2

<em>The above equality is false. Hence, (c) does not exist</em>

5 0
3 years ago
Read 2 more answers
When Lila conducted an experiment on citywide pond water, all of her samples came from the pond in her uncle's backyard. Explain
liq [111]

Her area of study is too narrow. There are other sources of water in the city that she is not considering. So her sample is too biased leaning toward the Uncle's pond water, and that leaves out every other source. We say that the Uncle's source of water is over-represented while the other sources are completely under-represented.

Let's put it this way: We have a hypothetical city that has 100 acres of pond water either in or surrounding the city limits. If the Uncle's pond only represents 1% of this, then she's ignoring the other 99% of the ponds.

What Lila needs to do to to fix this error is to draw up a map of each major pond and mark those ponds with numbers 001,002,...998,999. In this example, there are 999 ponds. Then she needs to either use a random number table or computer software to help randomly generate values to help select the ponds. Doing so will ensure that she spans a good portion of the city and not stay focused on just the narrow area of her Uncle's backyard.

The reason why she needs to enlarge her area of study is because the results of her Uncle's pond study may lead to the wrong conclusion of the city overall. Let's say his pond is contaminated somehow, and it's only his pond that's the unfortunate one. She would likely see the pond is contaminated and conclude that the whole city's water is ruined as well, which isn't the case. Or we could have nearly the entire city's pond water in trouble, but her Uncle's pond is one of the lucky ponds not to get contaminated. We can see that Lila would likely conclude that no action needs to be taken to clean up the city's water sources, which is also not the case.

If Lila only cared about her Uncle's pond, then that pond (and perhaps immediate close surrounding area) would be her population of study. However, her study is about citywide pond water which is why she needs to extend to other places in the city or in the outer surrounding areas.

8 0
2 years ago
I need helpppppppppp
Savatey [412]
Units. cause square units are for area and cubic units are for volume.
6 0
3 years ago
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