A Boeing 747 jet takes off from Boston's Logan Airport, which is at sea level, and climbs to a cruising altitude of 27,000 ft at a constant rate of 1400ft/min.
A.) write a linear equation for the height of the plane in terms of the time after takeoff.
B.) use your equation to find the height of the plane 14 min after takeoff.
height = 1400t , for 0 ≤ t ≤ 19.29
b)
when t - 14
height = 1400(14) = 19600
A.) To write a linear equation for the height of the plane in terms of the time after takeoff, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, "y" represents the height of the plane, "x" represents the time after takeoff, "m" represents the rate of change (or slope), and "b" represents the initial height (or y-intercept).
Since the plane climbs at a constant rate of 1400 ft/min, the rate of change (slope) is 1400. The initial height (y-intercept) is at sea level, so it is 0. Therefore, the linear equation representing the height of the plane in terms of the time after takeoff is:
y = 1400x + 0
= 1400x
B.) To find the height of the plane 14 minutes after takeoff, we can substitute "x" with 14 in the equation:
y = 1400(14)
= 19600 ft
Therefore, the height of the plane 14 minutes after takeoff is 19,600 ft.
A.) To write a linear equation for the height of the plane in terms of the time after takeoff, we can use the slope-intercept form of a linear equation, which is given by y = mx + b, where y represents the height of the plane, x represents the time after takeoff, m represents the rate of change (slope), and b represents the initial height of the plane.
In this case, we are given that the plane climbs to a cruising altitude of 27,000 ft, starting from sea level (0 ft), at a constant rate of 1400 ft/min. This means that the slope of our linear equation will be 1400 ft/min.
Since the plane starts from sea level (0 ft), the initial height (intercept) is 0.
Therefore, the linear equation representing the height of the plane in terms of the time after takeoff is:
y = 1400x
B.) To find the height of the plane 14 minutes after takeoff using the equation y = 1400x, we substitute x = 14 into the equation and solve for y.
y = 1400(14)
= 19,600 ft
Thus, the height of the plane 14 minutes after takeoff is 19,600 ft.