From the problem, the vertex = (0, 0) and the focus = (0, 3)
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12
Source:
http://www.1728.org/quadr4.htm
Answer:
Boat traveled 553.24 feet towards the lighthouse.
Step-by-step explanation:
In the figure attached AB is the light house of height 200 feet.
Angle of depression of the boat from the top of a lighthouse = angle of elevation of the lighthouse from the boat = 14°52'
so 1' = 
degree
so angle of elevation at point C = 14 + 
So angle of elevation from C = (14 + 0.87) = 14.87°
Similarly, when boat arrives at point D angle of elevation = 45°10' = 45 + 
= 45.17°
Now we have to calculate the distance CD, traveled by the boat.
In ΔABC
tan14.87 = 
0.2655 =
BC = 
BC = 753.239 feet
Similarly in ΔABD
tan45.17 = 
1 =
BD = 200 feet
So distance CD = BC - BD
CD = 753.239 - 200
= 553.24 feet
Therefore, Boat traveled 553.24 feet towards the lighthouse.
We have to calculate speed for 1 lap for all of 'em.
Cutwright - 84/35 = 2.4 mins for 1 lap
Evans- 96.6/42 = 2.3 mins for 1 lap
Liza- 102.6/38 = 2.7 mins for 1 lap
So, EVANS drove fastest among them as he took less time...
Answer:
Considering all seven-digit numbers that can be created from the digits 0-9 I could deduce that you can make 100 , 700, 800 even infinite numbers
Answer:
The graph is shown below.
Step-by-step explanation:
Given:
The inequality of a line to graph is given as:
In order to graph it, we first make the 'inequality' sign to 'equal to' sign. This gives,
Now, we plot this line on a graph. The given line is of the form:
Where, 'm' is the slope and 'b' is the y-intercept.
So, for the line , 
The y-intercept is at (0, -3).
In order to draw the line correctly we find another point. Let the 'y' value be 0.
Now, 
So, the point is (3, 0).
Now, we mark these points and draw a line passing through these two points.
Now, consider the line inequality . The 'y' value is less than 
. So, the solution region will be region below the line and excluding all the points on the line. So, we draw a broken line and shade the region below it.
The graph is shown below.
