The sketch of the parabola is attached below
We have the focus
The point
The directrix, c at
The steps to find the equation of the parabola are as follows
Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates;
and
.
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
Step 2
Find the distance between the point P to the directrix
. It is a vertical distance between y and c, expressed as
Step 3
The equation of parabola is then given as
=
⇒ substituting a, b and c
⇒Rearranging and making
the subject gives
No one ton is 1200lbs so 2 tons is 2400lbs so 1500lbs<2400lbs.
Find the smallest number that is divisible by 2, 3, 4, 5, 6 and add 1.
We need the least common multiple of 2, 3, 4, 5, 6.
2 = 2
3 = 3
4 = 2^2
5 = 5
6 = 2 * 3
LCM = product of common and not common prime factors with larger exponent.
LCM = 2^2 * 3 * 5 = 4 * 3 * 5 = 60
To always have a remainder of 1, you need of add 1 to 60.
The number is 61.
Check:
61/2 = 30 remainder 1
61/3 = 20 remainder 1
61/4 = 15 remainder 1
61/5 = 12 remainder 1
61/6 = 10 remainder 1
Answer:
x = 4
y = 13
Step-by-step explanation:
x + y = 17
y = 2x + 5
substitute for y:
x + (2x + 5) = 17
reduce:
3x + 5 = 17
subtract 5 from each side:
3x = 12
divide both sides by 3:
x = 4
y = 2(4) + 5
y = 13