After an hour the level had dropped to 0.010 %. In one study, BAC in a fasting person rose to about 0.018 % after a single drink. Studies of the metabolism of alcohol consistently show that blood alcohol content (BAC) declines linearly, after rising rapidly after initial ingestion. Therefore, if 10 pairs of flip flops were purchased, there would be money left over to buy 12 baseball caps. To calculate how many hats could be bought if 10 pairs of flip flops were purchased, substitute 10 in for f, and solve for h: Using your equation from (a), determine the number of baseball hats that can be bought if 10 flip flops were purchased.If f represents the number of flip-flops and b represents the number of baseball hats, write a function to represent the number of flip-flops purchased as a function of unspent monies from baseball hats.To express this information as a function, remember that the question specified that there was $100 to spend, and that any money not spent on hats (at $5 ea) was spent on flip-flops (at $4 ea). The class wants to buy a number of $4.00 flip-flops and $5.00 baseball hats, and has a total of $100 to spend. The Arlington Freshmen class wants to have a fundraiser. This means that the ball reaches the ground in just under 3 seconds. The parabola has two x-intercepts, and other functions may have more.) Using the ZERO function, you should find that the x-intercept is approximately 2.93. (Note that the calculator works this way because it is asking you to identify which x-intercept to calculate. Like the MAX function, you need to input a left bound, a right bound, and a guess, although the guess is optional – just press ENTER. Press 2 nd TRACE to get the CALC menu, and choose option 2, ZERO. If we want to determine the exact value, or at least a good approximation of the x-intercept, we can use the ZERO function. If you return to the GRAPH screen, you should see that the x-intercept is around 3. Graphically, we are looking for the x-intercept of the parabola. Now, to answer the second part of the question, we need to determine when the height of the ball is 0. This means that 1.25 seconds after the ball is thrown into the air, it reaches a maximum height of 45 feet. If you use the MAX function, you should find that the coordinates of the vertex are (1.25, 45). Remember that the calculator will ask you to input a left bound, a right bound, and a guess for the maximum. To identify the coordinates of the vertex, you can use the MAX function in the CALC menu. Once you have set the window, press GRAPH. Ymax should be no less than 44, though you may want to make it larger, such as 50 or more, just to be sure that you can see the vertex. Then set Ymin = 0 (or a little less, if you want to see the y-axis). Press WINDOW, and set xmin = 0, xmax = 3. The maximum value is most likely somewhere near x = 1. Using the “ask” capability of the calculator, if you input x values of 1, 2, and 3, you will see that the function goes up to 44 at x = 1. It is often useful to look at a table of values. This fact should lead you to think that we need to look at y-values well above 20. Think about what kind of function this is: a parabola, facing downwards. In this case, the y-intercept is (0, 20). One way to start to determine a good window is to take into account the y-intercept of the function. If you graph this equation on your calculator, you will need to determine a good viewing window. To answer the first question, we need to examine the graph of the function. Using the general form of the equation given above, we can write the function h(t) = -16t 2 + 40t + 20, where h(t) represents the height above the ground. How high will the ball go, and when will it reach its maximum height? When will the ball hit the ground?įirst we need to write a function to model the situation. You toss a ball into the air with an initial vertical velocity of 40 ft/sec, so that it will land on the ground, not on the roof. You are standing on the roof of a building that is 20 feet above the ground.
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