The inequality graphed in blue is y<-3x-2
The answer is 2268 now you have to regroup it
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
Step 1: Assign variable for the unknown that you need to find.
Step 2: List the given details
Distance between you and your friend is 12 miles. It means the total distance traveled by you by walk and your friend using bicycle when both travel towards each other to meet in 't' hours
Equation 1:
Your Walking rate and your friends Cycling rate is given below:
Step 3: Set up an equation using the relationship between distance, time and rate.
Substituting the above in equation 1
Distance traveled by you by walking from home and distance travelled by your friend in cycle in 0.8 hours is given below:
The answer is 79 because 9/10 divided by 71.1 is 79. And if you want to check, you can multiply 9/10 by 79, which will give you 71.1. I hope this helped :)
