1 2 3 v(t) 30 50 40 60 The table above gives the velocity v(t), in miles per hour, of a truck at selected times, t, in hours. Using a trapezoidal sum with the three subintervals indicated by the table, what is the approximate distance, in miles, the truck traveled from time t = 0 to t = 3?
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- A ball is thrown vertically upward from a height of 8 feet with an initial velocity of 48 feet per second. The ball’s height, s(t), in feet, after t seconds is given by s(t) = -16t2 + 48t + 8. After how many seconds does the ball reach its maximum height? What is the maximum height?A ball is thrown from an initial height of 6 feet with an initial upward velocity of 27ft/s the balls height h in feet after t seconds is given by the following h= 6+27t-16t2 find all values of t for which the balls height is 16The number (n) of members of an AFL football club increases over time (t weeks) according to the rule n = -3t(t - 30), . a Find the average rate of increase in membership in the third week, i.e. from t = 2 to t = 3. b If the club sells 10 memberships on the first day of the fourth week, estimate the rate of change of the club’s membership at the end of the third week.
- An object is propelled vertically upward with an initial velocity of 20 meters per second. The distance s (in meters) of the object from the ground after t seconds is s = - 4.9t2 + 20t. (a) When will the object be 15 meters above the ground?(b) When will it strike the ground?(c) Will the object reach a height of 100 meters?A ball is thrown vertically upward from the top of a building 160 ft tall with an initial velocity of 48 feet per second. The distance d (in feet) of the ball from the ground after t seconds is d(t)= 160+48t - 16t2 a) After how many seconds does the ball strike the ground? b)When will the ball reach its maximum height? What is the maximum height of the ball?A stone is thrown with an initial velocity of 33ft/s from the edge of a bridge that is 49ft above the ground. The height of this stone above the ground t seconds after it is thrown is f(t)=-16t2+33t+49. If a second stone is thrown from the ground, then its height above the ground after t seconds is given by g(t)=-16t2+v0t, where v0 is the initial velocity of the second stone. Determine the value of v0 such that the two stones reach the same high point.
- Juaquim's starting salary at a company is $42,000 per year. On average, employees receive a 6.5% increase in salary every year. Which equation shows what his salary will be in x years? A) s=(1+0.065)xs=(1+0.065)x A), s is equal to open paren 1 plus 0 point 0 6 5 close paren to the x th power B) s=42000(1+0.065)xs=42000(1+0.065)x B), s is equal to 42000 times open paren 1 plus 0 point 0 6 5 close paren to the x th power C) s=42000(0.065)xs=42000(0.065)x C), s is equal to 42000 times 0 point 0 6 5 to the x th power D) s=42000(1−0.065)xA ball is thrown vertically upward with an initial velocity of 96 feet per second.The distance s (in feet) of the ball from the ground after t seconds is s(t)=96t-16t2. (a) At what time t will the ball strike the ground? (b) For what time t is the ball more than 128 feet above the ground?The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 285 − 16t2. (a) Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time. (i) 0.1 seconds (ii)0.05 seconds (iii)0.01 seconds (b) Estimate the instantaneous velocity (in ft/s) of the pebble after 2 seconds.
- Two balloons, one red and one green are released from a platform at t=0. Each balloon goes up for a while, then comes down. The height (in meters) of the red balloon from the platform after tt minutes is given by R(t)=−10t2+400tR(t)=−10t2+400t The height (in meters) of the green balloon from the platform after tt minutes is given by G(t)=−16t2+120tG(t)=−16t2+120t How long is the interval of time in which the red balloon is rising and the green balloon is falling? ANSWER: ____________ minutes Do not include units in the answer blank. Just a number. If rounding is necessary, round to two digits after the decimal.A stone is thrown with an initial velocity of 35 ft/s from the edge of a bridge that is 43 fr above the ground. The height of this stone above the ground t seconds after it is thrown is f(t)=-16t2+35t+43. If a second stone is thrown from the ground, then its height above the ground after t seconds is given g(t)=-16t2+v0t, where v0 is the initial velocity of the second stone. Determine the value of v0 such that the two stones reach the same high point