The boundary of the lawn in front of a building is represented by the parabola
y = (x^2) /16 + x - 2
And you have three questions which require to find the focus, the vertex and the directrix of the parabola.
Note that it is a regular parabola (its symmetry axis is paralell to the y-axis).
1) Focus:
It is a point on the symmetry axis => x = the x-component of the vertex) at a distance equal to the distance between the directrix and the vertex).
In a regular parabola, the y - coordinate of the focus is p units from the y-coordinate of the focus, and p is equal to 1/(4a), where a is the coefficient that appears in this form of the parabola's equation: y = a(x - h)^2 + k (this is called the vertex form)
Then we will rearrange the standard form, (x^2)/16 + x - 2 fo find the vertex form y = a(x-h)^2 + k
What we need is to complete a square. You can follow these steps.
1) Extract common factor 1/16 => (1/16) [ (x^2) + 16x - 32]
2) Add (and subtract) the square of the half value of the coefficent ot the term on x =>
16/2 = 8 => add and subtract 8^2 => (1/16) [ (x^2) + 16 x + 8^2 - 32 - 8^2]
3) The three first terms inside the square brackets are a perfect square trinomial: =>
(1/16) [ (x+8)^2 - 32 - 64] = (1/16) [ (x+8)^2 - 96] =>
(1/16) [(x+8)^2 ] - 96/16 =>
(1/16) (x +8)^2 - 6
Which is now in the form a(x - h)^2 + k, where:
a = 1/16 , h = - 8, and k = -6
(h,k) is the vertex: h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.
=> a = 1/16 => p =1/4a = 16/4 = 4
y-componente of the focus = -6 + 4 = -2
x-component of the focus = h = - 8
=> focus = (-8, -2)
2) Vertex
We found it above, vertex = (h,k) = (-8,-6)
3) Directrix
It is the line y = p units below the vertex = > y = -6 - 4 = -10
y = -10
Answer:
<u>Regular Polygon:</u>
<em>C, E </em>(All sides and angles are equal)
<u>Irregular Polygon:</u>
<em>A, B, </em>(Not all sides or angles are equal)
<u>Not a Polygon</u>
<em>E, F </em>(There are curves and not a closed shape)
Hope this helps! Comment if you have any questions :)
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Answer:
depende de el tamaño de la botella . puede llegar a tardar mucho tiempo si es grande , si es peña puede tardar menos
Answer:
Check Explanation and the attached image.
Step-by-step explanation:
The histogram of the set of data presented is presented in the attached image to.this solution
The histogram represents data by indicating the frequency of distribution on the y-axis and the sets of variables indicated on the x-axis.
With the constellations named numbers 0 to 6, the frequency of each constellation, that is, the number of stars in each constellation corresponds to the height of the bar representing each constellation.
Hope this Helps!!!
the answer is 13/7 and here is the correct question
the answer is 13/7 and here is the correct questionwhen a customer wants pie for dessert you cut a whole pies into 7 equal slices...at the end of your shift 3/7 of. a cherry pie.2/7. of an apple pie.3/7 of a peach pie.and 5/7 of a blueberry pie remain...How much pie remains as a fraction of. a whole pie...
Answer:
13/7
Step-by-step explanation:
From the question, we have
3/7 of cherry pie
2/7 of apple pie
3/7 of peach pie
5/7 of blueberry pie
Now we have to add up all of these in order to get the total amount of pie
3/7 + 2/7 +3/7 +5/7
= (3+2+3+5)/7
=13/7
If expressed as a mixed fraction
= 1 6/7
In conclusion, 13/7 pie remains as a fraction of a whole.
