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: 0.42 and 5 outcomes.
Step-by-step explanation:
i guess that carlos has a fair coin and a number cube.
the probability can be calculated as the number of outcomes that we want divided the total number of outcomes.
The coin has two possible outcomes, heads and tails, then the probability of getting heads is p1 =1/2
the number cube has 6 numbers, 5 of those 6 numbers are greater than 1, then the probability of getting a number greater than 1 is p2 =5/6
the joint probability is the product of those two:
P = 1/2*5/6 = 5/12 = 0.42
The combinations that include heads and number greater than 1 are 5 combinations:
Heads and 2
Heads and 3
Heads and 4
Heads and 5
Heads and 6.
A.rolling a number cube labeled 1 to 6, and landing on a 2 or 4
Answer:
pretty sure its 5
Step-by-step explanation:
Answer:
D. A = πr^2
Step-by-step explanation:
The formula of the area of a circle is <u>A = πr^2</u>.