a) The solution to the simultaneous equations is x = -2.0, y = -1.0.
b) When x = 15, the values of y are y1 = 33 and y2 = -6.
The runner's speed increased steadily during the first three seconds of the race. The table provides the speed at half-second intervals. To estimate the distance traveled, we can calculate the lower and upper estimates.
According to the given table, the runner's speed is recorded at half-second intervals. We can calculate the distance traveled by the runner by approximating the area under the curve of the speed-time graph. Since the speed is given at half-second intervals, we can divide the time interval into six smaller intervals of half a second each.
To estimate the lower and upper bounds for the distance traveled, we can use the trapezoidal rule. The trapezoidal rule states that the area under a curve can be approximated by dividing it into trapezoids. The formula for calculating the area of a trapezoid is (1/2) × (base1 + base2) × height. In this case, the bases are the speeds at consecutive time intervals, and the height is the time interval of half a second.
Comparing the values of y, we notice that:
The values of y in each equation are different.
The values of y in each equation are not equal to the solution in part a).
The reason for this is that the lines intersect at a different point than the point where x = 15.
Part Value of y
Equation 1 33
Equation 2 -6
Solution -1.0