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Leokris [45]
2 years ago
13

Please Help! I have provided the screen shot

Mathematics
1 answer:
Alex_Xolod [135]2 years ago
7 0
(3,-4)
is your answer
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The boundary of the lawn in front of a building is represented by the parabola . The parabola is represented on the coordinate p
Colt1911 [192]
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   

 


4 0
3 years ago
Find the area of the shaded region. (Plz show work)
Kamila [148]

Answer:

Area of shaded region ≈ 192.42

Step-by-step explanation:

21/2 = radius

radius = 10.5 m

A = πr squared

Area of shaded region≈346.36

10.5 - 3.5 = 7

Area of unshaded region ≈ 153.94

346.36 - 153.94 = 192.42

8 0
3 years ago
Observa las ilustraciones y escribe la fracción que corresponde a cada giro
frosja888 [35]

Answer:

1: 7/12 2:1/3 3:1/2 4:1/3 5:5/8 6:1/2 7:6/10 8:1/1 9:1/4

Step-by-step explanation:

lo saque de otro trabajo igual.

6 0
2 years ago
What is 6(x+3)=2(2x+5)
koban [17]

Answer:

x = -4 ;

Step-by-step explanation:

6(x+3)=2(2x+5)

Distribution

6x+18 = 4x + 10

Subtract 4x on both sides

2x+18 = 10

Subtract 18 on both sides

2x = -8

Divided by 2

x = -4

Now if we have to substitute the value of X

6(-4+3)=2(-8+5)

Parenthesis first

6(-1) = 2(-3)

-6 = -6

7 0
3 years ago
Suppose a normal distribution has a mean of 266 and a standard deviation of
Elis [28]

Answer:

I think the answer is P(x>178)

Step-by-step explanation:

5 0
3 years ago
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