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90. Pollution. The concentration of particulate matter (in parts per million) during a 24-hour period is given approximately by
where t is time in hours. Find the average concentration during the period from t = 0 to t = 24.
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- .Suppose that for a certain disease the cumulative number of deaths is given by 7.8 C(t) = , 1+0.001(s – 30)² ds (people) 0 corresponds to the first day of the outbreak. Find the death rate, as a function of days t where t R(t).arrow_forward1. The following data represents (time in s, distance traveled in meters) for a car: (0, 0), (2, 40), (4, 85), (6, 130), (8, 180), (10, 250). Use second order accurate formulas to approximate the speed at t = 0, t = 4 and t = 10. Also convert the values into km per hour.arrow_forwardThe population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 400,000 mosquitoes in the area initially, and predators (birds, bats, and so forth) eat 50,000 mosquitoes/day. Determine the population of mosquitoes in the area at any time. (Note that the variable t represents days.)arrow_forward
- 5. This box has a length x and a width that is 4 times its length. The volume is 500 cm³. Find a formula for the surface area as a function of x.arrow_forward1. The heat index (HI) is an estimate of the temperature felt by the human body based on the actual measured air temperature T (in °F') and relative humidity h,. It is given by HI = – 42 + 2T + 10h, – 0.227Th, – 1.997T²h,?. a. If the air temperature in your area is 1070F with a relative humidity of 8%, how hot does your body feel?arrow_forward... Question 9 of 10 > Worldwide, wind energy' generating capacity, W, was 236,733 megawatts at the end of 2011 and 371,374 megawatts at the end of 2014. (Generating capacity is the maximum rate at which energy can be produced, measured in this problem in megawatts.) NOTE: Round coefficients to two decimal places if needed. (a) Use the values given to write W, in megawatts, as a linear function of t, the number of years since 2011. Linear function: W (b) Use the values given to write W as an exponential function of t. Exponential function: W = (c) Select the figure which W (MW) correctly depicts the graphs of the functions you found in parts (a) and (b) on the same axes. Linear FEB 23 G Search or type URL %23 24 2 9. 8. 3. R M R.arrow_forward
- Derive the " Kuhn-Tucker" FoC conditions and find the max.arrow_forwardIn ΔXYZ, XY = 6.32, YZ = 5.83, and XZ = 11.05. m<y= (blank) 25.6 degrees 85.1 degrees 113.4 degrees 130.8 degreesarrow_forwardEmissions of sulfur dioxide by industry set off chemical changes in the atmosphere that result in "acid rain". The acidity of liquids is measured by pH on a scale of 00 to 14.14. Distilled water has pH 7.0,7.0, and lower pH values indicate acidity. Normal rain is somewhat acidic, so "acid rain" is sometimes defined as rainfall with a pH below 5.0.5.0. The pH of rain at one location varies among rainy days according to a Normal distribution with mean 5.43 and standard deviations 0.54. What proportion of rainy days have rainfall with pH below 5.0?5.0?arrow_forward
- A certain sport car can accelerate from a starting point to a speed of v(t) = -0.39t? + 13t where v is measured in metres per second. a. Find the distance that the car will travel in the first 4 seconds. Round to two decimal places if necessary b. Find the distance that the car will travel in the first 9 seconds. Round to two decimal places if necessaryarrow_forward3. In an experiment, the growth rate of a population of bacteria t hours after the bacteria are exposed to moist air is approximated by k√t, where P dP dt represents the population size and k is a constant. The population of bacteria is 1,000 before the bacteria are exposed to moist air and the population grows to 1,200 after 4 hours. Find the population bacteria after 9 hours. -arrow_forwardA person's Body Mass Index is I = 2, where W is the body weight (in kilograms) and H is the body height (in meters). W H² Estimate the change in height that will decrease I by 1 if (W, H) = (26, 1.3), assuming that W remains constant. (Use decimal notation. Give your answer to three decimal places.) AH≈arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage