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Physics In Exercises 67-70, (a) use the position equation
An object is thrown upward from a height of
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- 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_forwardHelp me pleasearrow_forward
- Oil imports Crude oil and petroleum products areimported continuously by the United States. Thetable shows the billions of dollars of net expendituresfor the imports of these products for several years.a. Write a linear function that models this data, withx equal to the number of years after 2015 and yequal to the billions of dollars of expenditures.Report the model with two decimal places.b. Is the model an exact fit for the data? c. What does the model predict the billions of dollars of net expenditures will be for the imports in2023?d. When does the model predict the billions of dollars of net expenditures for the imports will be208.2 $billion?arrow_forwardPopulationThe resident population of Wisconsin (in thousands) was 5655 in 2009 and 5743 in 2013. Assume that the relationship between the population y and the year t is linear. Let t = 0 represent 2000. (Source: U.S. Census Bureau) (a) Write a linear model for the data. What is the slope and what does it tell you about the population? (b) Use the model to estimate the population in 2011. (c) Use your school’s library, the Internet, or some other reference source to find the actual population in 2011. How close was your estimate? (d) Do you think your model could be used to predict the population in 2018? Explainarrow_forwardGasoline mileage Suppose the cost of driving an automo- bile is a linear function of the number x of miles driven and that gasoline costs $3 per gallon. A certain automobile presently gets 20 mi/gal, and a tune-up that will improve gasoline mileage by 10% costs $120. (a) Express the cost C, of driving without a tune-up in terms of x. (b) Express the cost C, of driving with a tune-up in terms of x. (c) How many miles must the automobile be driven after a tune-up to make the cost of the tune-up worthwhile?arrow_forward
- Ohm's law states that the voltage drop Vacross an ideal resistor is linearly proportional to the current i flowing through the resistor as V= iR. Where R is the resistance. However, real resistors may not always obey Ohm's law. Suppose that you perform some very precise experiments to measure the voltage drop and the corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohm's law. i -1 - 0.5 - 0.25 0.25 0.5 1 V -637 -96.5 -20.25 20.5 96.5 637 Instead of the typical linear regression method for analyzing such experimental data, fit a curve to the data to quantify the relationship. Compute V for i = 0.1 using Polynomial Interpolation.arrow_forwardOhm's law states that the voltage drop Vacross an ideal resistor is linearly proportional to the current i flowing through the resistor as V= iR. Where R is the resistance. However, real resistors may not always obey Ohm's law. Suppose that you perform some very precise experiments to measure the voltage drop and the corresponding current for a resistor. The following results suggest a curvilinear relationship rather than the straight line represented by Ohm's law. i -1 - 0.5 - 0.25 0.25 0.5 1 V -637 -96.5 -20.25 20.5 96.5 637 Instead of the typical linear regression method for analyzing such experimental data, fit a curve to the data to quantify the relationship. Compute V for i = 0.1 using Newton's Divided Difference Method.arrow_forwardWorld grain production was 1,241 million tons in 1975 and 2,048 million tons in 2005, and has been increasing at an approximately constant rate. (a) Find a linear function for world grain production, P, in million tons, as a function of t, the number of years since 1975.arrow_forward
- helparrow_forwardDefine the term linear functions?arrow_forwardTwo cars start at the same time and travel in the same direction along a straight road. The figure below gives the velocity, v, of each car as a function of time, t. (a) Which car attains the larger maximum velocity, and how do you know? (b) Which car travels farther, and how do you know? (c) Which car stops first, and how do you know?arrow_forward
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