f the distance the car traveled after applying the brakes equals 20 feet, what does that mean to the officer investigating the accident? (HINT: Let d = 20, bring 20 to the right so that the equation equals zero, identify the coefficients, A, B and C and then use the quadratic formula to solve mathematically.)
To find out what it means to the officer investigating the accident when the distance the car traveled after applying the brakes equals 20 feet, we need to apply the quadratic formula to solve the equation.
Let's assume that the equation representing the distance the car traveled after applying the brakes, when brought to the right side, equals zero, is of the form Ax^2 + Bx + C = 0.
Given that the distance traveled, d, is 20 feet, we can rewrite the equation as x^2 + Bx + C - 20 = 0.
To solve this equation mathematically, we need to identify the coefficients A, B, and C.
In this case, A = 1, B = B, and C = C - 20.
Applying the quadratic formula, x = (-B ± √(B^2 - 4AC)) / 2A, we can determine the possible values of x, which represent the possible solutions for the distance the car traveled after applying the brakes.
By determining the values for x, it would help the officer investigating the accident to understand how far the car traveled after applying the brakes and make inferences about the speed at which the car was traveling and the effectiveness of the braking system.
To understand what the distance the car traveled after applying the brakes means to the investigating officer, we need to analyze the given information mathematically.
First, let's set up the equation using the information given and rearrange it to make it equal to zero:
Let d = 20 (distance traveled after applying brakes)
The equation becomes: d - 20 = 0
Now, let's identify the coefficients in the equation:
A = 1 (coefficient of d^2 term, which is zero in this case)
B = 0 (coefficient of d term, which is zero in this case)
C = -20 (constant term)
Using the quadratic formula: x = (-B ± √(B^2 - 4AC)) / (2A)
Plugging in the values:
d = (-0 ± √(0^2 - 4(1)(-20))) / (2(1))
Simplifying:
d = (± √(0 + 80)) / 2
d = (± √80) / 2
d = (± 4√5) / 2
d = ± 2√5
Therefore, the possible solutions for d are +2√5 and -2√5.
In this scenario, if the car traveled 20 feet after applying the brakes, the investigating officer would conclude that the car either came to a stop in 20 feet (+2√5) or continued to move in reverse for 20 feet (-2√5).
It is important to note that the quadratic formula was used to solve for d mathematically. However, the investigating officer would likely rely on additional evidence, such as skid marks or witness statements, to determine the actual cause and circumstances of the accident.