A garden center has 150 fruit trees to sell.
2 answers:
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Answer:
Oook, quick setup: pick a cartesian plane, be the position of the helicopter as time passes, and
your position as you start running. In my horrible sketch, the green line is the distance when you start running, the red line is the distance you need, in general what you want is to move one end of the segment up, the other right, and stretch it.
That distance is easily found with the formula for the distance between two points in the plane, or (playing a bit with the squares). At this point we need to write down expressions for both
and find at what value of t we need to evaluate our distance.
For the sake of semplicity, let's start measuring times the moment you start running. Since speed is constant, both expressions will be of the form
The equation for the runner becomes simply , since you haven't moved until the heli is high enough.
The equation of the helicopter is since the heli is 30ft above ground when you start running.
Finally, we need to know how many seconds have passed when the heli is at 60 ft above ground. that happens when . in this time, you are at
from the origin.
Plugging it in the distance formula you get:
Answer:
<em>The zeros of the polynomial are -1 and 5</em>
Step-by-step explanation:
<u>Quadratic Equation Solving</u>
The standard representation of a quadratic equation is:
where a,b, and c are constants.
Solving with the quadratic formula:
We have the following equation to solve:
Before attempting to solve it, we must simplify the equation.
Collecting like terms and reordering:
Here: a=1, b=-4, c=-5
The discriminant of this quadratic equation is:
Given d is positive, the equation has two roots, and since d is a perfect square, both roots are rational.
Applying the formula:
Dividing by 2:
Separating both roots:
x = 2 + 3 = 5
x = 2 - 3 = -1
The zeros of the polynomial are -1 and 5