Quadratic equations find their application in various real-world scenarios such as: sports, bridges, projectile motion, the curvature of bananas, and so on.
Here are three images representing real-world instances of quadratics:
Example 1: A cyclist travels along a parabolic trajectory to leap over obstacles.
Example 2: A person throws a basketball towards the hoop, moving in a gently upward path described by a quadratic curve.
Example 3: A football player kicks the ball upward, which follows a quadratic path as it travels a distance.
Utilizing the Law of Sines (sinA/a=sinB/b=sinC/c) and recognizing that the angles in a triangle add up to 180°.
The angle C calculates to 180-53-17=110°
Thus, we have 27/sin53=b/sin17=c/sin110
This leads to b=27sin17/sin53, c=27sin110/sin53
The perimeter is defined as a+b+c, so
p=27+27sin17/sin53+27sin110/sin53 units
p≈68.65 units (rounded to the nearest hundredth of a unit)
A.) P(t) = P0e^(kt)
P(20/60) = 40 e^(20k/60)
80 = 40 e^(k/3)
e^(k/3) = 80/40 = 2
k/3 = ln(2)
k = 3ln(2)
b.) P(8) = 40(2)^24 = 40(16777216) = 671088640 cells
d.) Rate of change = e^(8k) = e^(8(3ln(2))) = e^(24ln(2)) = e^(16.6355) = 16777216 cells/hour
e.) P(t) = 40(2)^(3t); t in hours
1,000,000 = 40(8)^t
25,000 = 8^t
ln(25,000) = t ln(8)
t = ln(25,000)/ln(8) = 4.87 hours
