1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Arlecino [84]
3 years ago
6

The boundary of the lawn in front of a building is represented by the parabola . The parabola is represented on the coordinate p

lane. The building's entrance is located at the parabola's focus, which has the coordinates . The lawn's gate is located at the parabola's vertex, which has the coordinates . The building’s front wall is located along the directrix of the parabolic lawn area. The directrix of the parabola is . NextReset
Mathematics
1 answer:
Colt1911 [192]3 years ago
4 0
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   

 


You might be interested in
10 POINTS PLS ANSWER
Marina CMI [18]

Answer:

x=15

Step-by-step explanation:

x+165degrees=180degrees

x=180-165

x=15

6 0
3 years ago
The probability density function of the time it takes a hematology cell counter to complete a test on a blood sample is f(x)=0.0
uysha [10]

Answer:

a) 20%

b) 40%

c) Mean = 62.5 seconds; Variance = 52.083 seconds

Step-by-step explanation:

The time it takes a hematology cell counter to complete a test on a blood sample is continuously distributed over the period of 50 to 75 seconds with probability f(x) = 0.04.

a) The percentage of tests require more than 70 seconds is:

P(X>70) = 1- \frac{70-50}{75-50} \\P(X>70) =0.2 = 20\%

b)The percentage of tests that require less than one minute (60 seconds) is:

P(X70) =0.4 = 40\%

c) The mean and variance of a continuous distribution are determined by:

M=\frac{A+B}{2}=\frac{50+75}{2}\\ M= 62.5\ seconds\\\\V=\frac{(B-A)^2}{12}=\frac{(75-50)^2}{12}\\  V= 52.083\ seconds

Mean = 62.5 seconds.

Variance = 52.083 seconds.

3 0
3 years ago
What is the measure of angle 5 if the measure of angle 2 is 37 degrees and the measure of angle 3 is 72 degrees
ahrayia [7]

Answer:

160 is a whole angle so 37+72=109                             160-109=51

51 is your answer

Step-by-step explanation:

7 0
2 years ago
Just wondering is 71 a PRIME number? ≡≡≡
Sergeu [11.5K]
Yes 71 is a Prime Number
7 0
3 years ago
Read 2 more answers
Which of following sets is equivalent to (a,b,c,d,e)
borishaifa [10]

Answer:

I don't see what your trying too explain to me

I only see the question itself

Step-by-step:

sorry I can't help you

8 0
2 years ago
Other questions:
  • Carlos purchased an antique chair for $15 he later so this year for $27 to an antique dealer what was the percent markup of the
    15·2 answers
  • In a class of 147 students, 95 are taking math(m), 75 are taking science (s), 52 are taking both math and science. What is the p
    14·1 answer
  • Five less than twice a number is seven
    15·2 answers
  • Circle the number that are solutions to the inequalities
    10·1 answer
  • A plane took a Navy Seal to a height of 10,000 feet above sea level. The Navy Seal jumped out of the plane and parachuted into t
    12·2 answers
  • Multiply (x-4) (2x + 3) using the distributive property. Select the answer
    9·1 answer
  • What is the difference in the rule of reflection for a point reflected across y=x and a point reflected across y=-x
    10·1 answer
  • A man enters a tall tower, needing to know its height. he notes that a long pendulum extends from the ceiling almost to the floo
    15·1 answer
  • Write an equation to represent the following:
    13·2 answers
  • Is everyone answering so we can ask more questions lol
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!