Tutor profile: Kristie M.
If there are 250 bacteria in a dish and the the population doubles every 5 days, what is the population after 10 days?
(1) We will use the formula for exponential functions to get the final population. A = Ao (b) ^ t/c where: A = final population Ao = initial population b = growth factor t = time c = time for b to occur (2) Based on the given problem, Ao = 250 bacteria b = 2 (doubles) c = 5 ( doubles every 5 days) t = 10 days A = ??? Substitute and solve: A = Ao (b) ^ t/c A = 250 (2) ^ 10/5 A = 2000 Therefore, there will be 2000 bacterial population after 10 days.
If Lebron James has a vertical leap of 1.35 m, then what is his takeoff speed and his hang time?
(1) Given: a = -9.8 m/s^2 (constant acceleration) d = 1.35 m (distance) Vf = 0 m/s (final velocity Find: Vi = ??? (initial velocity, this will be his take off speed) t = ??? (double the time is his hang time) (2) Based on the given, we'll used the formula Vf^(2) = Vi^(2) + 2ad (3) Substitute and solve. Vf^(2) = Vi^(2) + 2ad ( 0 m/s)^(2) = Vi^(2) + 2 (-9.8 m/s^2) (1.35 m) 0 m^2/s^2 = Vi^(2) + 2 (-13.23 m^2/s^2) 0 m^2/s^2 = Vi^(2) - 26.46 m^2/s^2) 26.46 m^2/s^2) = Vi^(2) --- get the square root Vi = 5.14 m/s Therefore, James Lebron's takeoff speed is 5.14 m/s. To find hang time, find the time to the peak and then double it. Use the formula below to get the time: Vf = Vi + at 0 m/s = 5.14 m/s + (-9.8 m/s^2) t 0 m/s = 5.14 m/s - 9.8 m/s^2) t - 5.14 m/s = - 9.8 m/s^2) t (- 5.14 m/s) / (-9.8 m/s^2) = t t = 0.523 s --- multiply by 2 to get the hang time hang time = 1.05 s
Find the equation of the line that passes through points (2, 3) and (2, 5).
(1) Since 2 points were given, we'll use the formula for the slope (m), which is m = (y2 - y1) / (x2 - x1). (2) Assign the given points (2,3) and (2,5) x1 = 2 y1 = 3 x2 = 2 y2 = 5 (3) Substitute on the formula for slope, m = (5-3) / (2-2) m = 2/0 (4) The slope is undefined which means the line is perpendicular to the x-axis and its equation has the form x = constant. Since both parties have equal x coordinates 2, the equation is given by: x = 2
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