Concept explainers
Free-Falling Object In Exercises 37 and 38. use the position function
When will the object hit the ground? At what velocity will the object impact the ground?
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Calculus
- If you travel 300 miles on the first day and then drive v miles per hour for t hours on the second day, then the total distance traveled over the teo-day period is given by d=300+vt miles. Use a formula to express v as a function of d and t for this two-day event.arrow_forwardEarthquake the graph shows the vertical acceleration of the Ground from the 1994 Northridge earthquake in Los Angles, as measured by a seismograph. (Here t represents the time in seconds.) (a) At what time t did the earthquake first make noticeable movement of the Earth? (b) At what time t did the earthquakes seem to end? (c) At what time t was the maximum intensity of the earthquake list reachedarrow_forwardCeramics When the temperature of a pot in a kiln is 1200, an artist turns off the heat and leaves the pot to cool at a controlled rate of 18 per hour. Express the temperature of the pot in degrees Celsius as a function of the time t in hours since the kiln was turned off.arrow_forward
- Flood Control A river is 8 feet above its flood stage. The water is receding at a rate of 3 inches per hour. Write a mathematical model that shows the number of feet above flood stage after t hours. Assuming the water continually recedes at this rate, when will the river be 1 foot above its flood stage?arrow_forwardA and B are points on the graphs of functions y1 and y2, respec-tively. Find the corresponding point on the graph of y = y1 + y2. A = (pi , - 0.5), B = (pi,-1)arrow_forwardDistance between cars At noon, car A is 10 feet to the right and 20 feet ahead of car B, as shown in the figure. If car A continues at 88 ft/sec (or 60 mi/hr) while car B continues at 66 f/sec (or 45 mi/hr), express the distance d between the cars as a function of t, where t denotes the number of sec- onds after noon. Exercise 78arrow_forward
- Use the model given to answer the questions about the object or process being modeled. Arizonans use an average of 50 gal of water per person each day. The number of gallons W of water used by x Arizonans each day is modeled by W = 50x. (a) Make a table that gives the number of gallons of water used for each 1000-person change in population, from 0 to 5000. Population Water use (gal) 0 0 1000 2000 3000 4000 5000arrow_forwardMath.arrow_forwardFind the first derivative ____, where a, b, c, m and n, are constants. A clear step by step solving of this question would be much appreciated. Thank you!arrow_forward
- (UT) When you board a Ferris wheel moving counter- clockwise at a constant rate, your feet are 4 feet off the ground. At the highest point of the ride, your feet are 88 feet above the ground. It takes 220 seconds for the ride to complete one full revolution. Circle the correct values to create the correct function to model this situation, where t is time elapsed in seconds and h is height above the ground in feet. h (t) = c±a cos(bt) c = [ Select ] rt ±= [Select] a = [ Select ] b = [Select ]arrow_forwardA mass of 2 kg stretches a spring 0.07 m. The mass is in a medium that exerts a viscous resistance of 23 N when the mass has a velocity of 2 The viscous resistance is proportional to the speed of the object. m - S Suppose the object is displaced an additional 0.03 m and released. m Find an function to express the object's displacement from the spring's natural position, in m after t seconds. Let positive displacements indicate a stretched spring, and use 9.8 gravity. as the acceleration due to $2 u(t) = Submit Questionarrow_forwardc) Graph each of the two functions for a 2-min rided) Find the derivative of f(t) and g(t). Based on the graphs, what is the maximum height reached be the rider? When does this occur?e) Find the acceleration function for f(t) and g(t). Based on those derivative functions, what is the maximum vertical speed of the rider?arrow_forward
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