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A: Topic:- application of derivatives
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A: Integration is area under the curve so simply calculate the area under the curve with proper sign.
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Q: B. The position of a particle moving along a horizontal line is given by r(t) = t-6t²+9t, where t20…
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- The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?Near the surface of the moon, the distance that an object falls is a function of time. It is given by d(t)=2.6667t2 , where t is in seconds and d(t) is in feet. If an object is dropped from a certain height, find the average velocity of die object from t=1tot=2 .The position function of a particle is given below. s(t) = t3 + 3t2 - 4t, t 0 When does the particle reach a velocity of 5 m/s?t=
- The position function of a particle is given below. s(t) = t3 + 6t2 − 32t, t ≥ 0 When does the particle reach a velocity of 4 m/s?t = ? sThe position function of a particle is given below. s(t) = t3 + 1.5t2 - 16t, t 0 When does the particle reach a velocity of 2 m/s?t = second(s)The position function of a particle is given by s = t3 - 4.5t2 - 7t, t > 0.(a) Find the velocity and acceleration of the particle.(b) When does the particle reach a velocity of 5 mys?(c) When is the acceleration 0? What is the significance of this value of t?
- The position function of a particle is given bys = t3 -4.5t2 -7t t≥0(a) When does the particle reach a velocity of 5m/s ?(b) When is the acceleration 0? What is the significanceof this value of ?The position function of a particle is given below. s(t) = t3 + 6t2 − 59t, t ≥ 0 When does the particle reach a velocity of 4 m/sThe position function of a particle is given by s = t3 + t2 − 15t + 500. 3 a) Find the velocity 2 pointsb) Find the acceleration 2 pointsc) Find the acceleration when the speed is 0. 1 point
- The position function of a particle is given by s(t)=t^3−4t^2−8t, t≥0 where s is measured in meters and t in seconds. When does the particle reach a velocity of 9 m/s?The position function of a particle moving along the x−axis is given by x(t)=t3−4t2+5t−2, t≥0. Find the open t−intervals when the particle is moving to the left.At time t=0, a driver jumps from a diving board that is 25 feet high. Because the drivers initial velocity is 15 feet per second, her position function is h=-16t^2+15t+25. a) when does the diver hit the water? b) what is the divers velocity at impact?