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Concept explainers
(a)
To calculate: The function that represents the situation for the position function
(b)
To graph: The position function
(c)
To calculate: The average rate of change of the function from
(d)
The slope of the secant line, if the given position function is
(e)
To calculate: The equation of the secant line from
(f)
To graph: The equation of the secant line
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Chapter 2 Solutions
EBK COLLEGE ALGEBRA
- Physics In Exercises 67-70, (a) use the position equation s=16t2+v0t+s0 to write a function that represents the situation, (b) use a graphing utility to graph the function, (c) find the average rate of change of the function from t1 to t2, (d) describe the slope of the secant line through t1 and t2, (e) find the equation of the secant line through t1 and t2, and (f ) graph the secant line in the same viewing window as your position function. An object is thrown upward from a height of 6 feet at a velocity of 64 feet per second. t1=0,t2=3arrow_forwardThe point-slope form of the equation of the line with slope 3 passing through the point 1, 2 is _.arrow_forwardTell whether it is a function or not a functionarrow_forward
- X+200p=10,000 X>0 P>0 express the revenue (price times units sold), R, as a function of p. R=arrow_forward1 The total rainfall, y, in inches that fell x hours past noon is given by y=x+3. (a) How much rainfall was there at noon? (b) At what rate was the rain falling in the afternoon? 1 (c) What is the y-intercept of y=x+3? What does it represent? 1 (d) What is the slope of y=x+3? What does it represent?arrow_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
- The graph below shows the velocity v in feet per second of a small rocket that was fired from the top of a tower at time t = 0 (t in seconds). The rocket accelerated with constant upward acceleration until its fuel was expended, then fell back to the ground at the foot of the tower. The entire flight lasted 14 seconds. 4. (4,96) t (seconds) (14,-224) (a) What was the acceleration of the rocket while its fueled lasted? (b) How long was the rocket rising? (c) What distance did the rocket travel during the time it was rising? (d) How high was the tower from which the rocket was fired? v (ft/sec)arrow_forwardA tractor has an initial price of $8000.00 and sells for $1100.00 after 23 years. Assume that the tractor's value depreciates linearly with the passing years. (a) Let V represent the tractor's value in dollars and let t represent the number of years since the tractor was purchased. Write a formula to express the tractor's value as a function of time: V(t) = ... ... (b) Horizontal intercept of the value function V(t): ... Vertical intercept of the value function V(t):arrow_forwardThe temperature at which water starts to boil is called its boiling point and is linearly related to the altitude. Water boils at 212°F at sea level and at 193.6°F at an altitude of 10,000 feet. (a) Find a relationship of the form T = mx + b where T is degrees Fahrenheit and x is altitude in thousands of feet. (b) Find the boiling point at an altitude of 4,300 feet. (c) Find the altitude if the boiling point is 197.5°F. (d) Graph T and illustrate the answers to (b) and (c) on the graph. (a) Choose the correct relationship below. O A. T = 1.84x+212 O B. T = 1.84x +212 O C. T = 1.84x-212 O D. T= 1.84x - 212arrow_forward
- Can you please do all of them. Thank you :)arrow_forward4) A typical cup of coffee contains 100 mg of caffeine. Every hour, approximately 16% of the amount of caffeine in the body is metabolized and eliminated. Let C represent the amount of caffeine in the body in mg and let t represent the number of hours since a typical cup of coffee was consumed. (a) Write an equation where C is a function of t for a typical cup of coffee. (b) How much caffeine is left in the body after 3 hours? (c) Suppose an individual cannot sleep unless she has less than 50 mg of caffeine in her blood. How many hours after drinking coffee must she wajt until she is able to fall asleep?arrow_forwardAn object is shot vertically upward from the ground with an initial velocity of 224 ft/sec. For vertical motion near the Earth's surface, acceleration due to gravity is -32 feet per second squared. (The negative means that acceleration is downward.) (a) Explain why the graph of velocity of the object against time is linear. O The graph of velocity is linear because the acceleration is decreasing at a constant rate. O The graph of velocity is linear because the velocity is increasing at a constant rate. O The graph of velocity is linear because the velocity is decreasing at a constant rate. The graph of velocity is linear because the velocity is constant. The graph of velocity is linear because the acceleration is increasing at a constant rate. (b) Using the starting velocity and your answer to part (b), find the time at which the object reaches the highest point. sec (c) Use your answer to part (c) to decide when the object hits the ground. sec (d) Graph the velocity against time. Mark…arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
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