Concept explainers
Determining Solutions In Exercises 3-6, determine whether each x-value is a solution (or an approximate solution) of the equation.
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College Algebra
- Galileo was the first person to study the motion of a pendulum, around the year 1600. He found that the time it takes a pendulum to complete a full swing depends only on the length of the pendulum. Galileo found that the period of a pendulum is proportional to the square root of its lengthT=2/L where T is the time in seconds it takes for the pendulum to complete 1 period and L is the length of the pendulum measured in meters. Definition of a Period: The time it takes a pendulum to complete one full back-and-forth swing. Below is a video of a pendulum on the UCF campus. If you watch the video, you'll notice that it takes approximately 8.5 seconds to complete a full period. Using this information, determine the length of the pendulum in meters.arrow_forwardSolve equation for x. e-x = 1arrow_forwardSolve the equation for x. ln x2 = 9arrow_forward
- ANSWER ALL THE QU A 200g sample of radioactive polonium-210 has a half-life of 138 days. This means that every 138 days, the amount of polonium left in the sample is half of the original amount. a) Write an equation that models the amount of Polonium b) What mass of Polonium-210 is left after 2 years? c) Determine how long it will take for the sample to reduce to 150g The University of McMaster undergraduate program is growing at a rate of 3% each year. The current enrollment is 12400. Determine when the enrollment will reach 13250. You have found an investment at the bank that pays 2.4% interest per year for 10 years. How much should you invest now so that you have $2000 at the end of the 10 years?arrow_forwardSolve the equation for x. ln 3x = ln 5arrow_forwardEliminating pollution If the pollution of Lake Erie were stopped suddenly, it has been estimated that the level y of pollutants would decrease according to the formula y = yoe-0.3821, where t is the time in years and y, is the pol- lutant level at which further pollution ceased. How many years would it take to clear 50% of the pollutants?arrow_forward
- Solve the equation for x. ln(ln 3x) = 0arrow_forwardln(w+5)=ln(5c+3) Solve the equation for carrow_forwardIn 2013, a certain company's annual revenue was 74 billion dollars and growing at the rate of 3.4x + 17.6 billion dollars per year, where x is the number of years since 2013. Find a formula to predict this company's annual revenue at any time x. I(x) = Use your formula to predict their revenue in 2022. (Round your answer to one decimal place.) $ billion Need Help? Read Itarrow_forward
- ELIMINATE THE ARBITRARY CONSTANT/S IN THE EQUATION. complete solution in paperarrow_forwardt In 2 Half-Life uses the formula N (t) = Noe h No Initial Amount t = time h = length of half-life. The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated coffee in the morning. How long will it take for only 60% of the caffeine to remain in his body? 5 -(3) 2 t = t = t = t= 3 In- 5 In 2 In 5 3 In 2 3 In 5 In 2 co (4.8) (18) (18) (4.8)arrow_forwardThe half-life of carbon-14 is 5730 years. How long does it take for 3.4 grams of carbon-14 to be reduced to 0.1 grams of carbon-14 by radioactive decay? ... years (Do not round until the final answer. Then round to the nearest hundredth as needed.) Help Me Solve This View an Example Get More Help -arrow_forward
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