Write the letter of the item that corresponds to the best response. What is the average value of the function f(x) = sin³xcos²x on the interval [-7,7]? 4 а. 15T IT 6. C. 12 d. 0 е. b.
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- Assume the bucket is leaking.It starts with 5 liters of water (5 kg) and leaks at a constant rate.It finishes draining just as it reaches the top. How much workwas spent lifting the water alone? (Hint: Do not include therope and bucket, and find the proportion of water left at elevationx m.)Which do you think will be larger, the average value of f(x,y)=xy over the square 0≤x≤13, 0≤y≤13, or the average value of f over the quarter circle x2+y2≤169 in the first quadrant? Calculate them to find out. Answer the two questions linked average value of F over square and quarter circleFind the average rate of change of the given function on the interval [4,5]. h(x)=5x2+7x−4 Enter your answer as a reduced improper fraction, if necessary.
- It is often difficult to evaluate the quality of products that undergo a ripening or maturation process. Researchers have successfully used ultrasonic velocity to determine the maturation time of a certain type of cheese. The age can be determined by Upper M left parenthesis v right parenthesis equals 0.0293216 v squared minus 102.12 v plus 80 comma 162, vgreater than or equals1742, where M(v) is the estimated age of the cheese (in days) for a velocity v (m per second). Complete part (b) below. (a) If this certain cheese ripens in 156 days, determine the velocity of the ultrasound that one would expect to measure. (Hint: Set M(v)equals156 and solve for v.) The velocity would be 22.992.5917422293 2293 m per second. (already solved) (Do not round until the final answer. Then round to the nearest whole number as needed.) (b) Determine the derivative of this function when vequals1800 m per second and interpret. Start by finding the derivative of M(v) =0.0293216v2 - 102.12v +…Suppose that a function F has a positive average rate of change from 1 to 4. Is it correct to assume that function f only increases on the interval (1,4)? Explain.The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated by the model V = 0.1729t + 0.1522t2 − 0.0374t3 , where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle.
- the side of a sqaure is 10 cm. find the approximately, by using differential, the increase in the area if the side is increased by 0.02 cm.The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using data obtained by Charles David Keeling, professor at Scripps Institution of Oceanography, the average amount of CO2 in the atmosphere from 1958 through 2016 is approximated by A(t) = 0.012414t2 + 0.7485t + 313.9 (1 ≤ t ≤ 59) where A(t) is measured in parts per million volume (ppmv) and t in years, with t = 1 corresponding to 1958.† Find the average amount of CO2 in the atmosphere from 1958 through 2016. (Round your answer to two decimal places.) ______ ppmv/yrThe increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using data obtained by Charles David Keeling, professor at Scripps Institution of Oceanography, the average amount of CO2 in the atmosphere from 1958 through 2016 is approximated by A(t) = 0.012414t2 + 0.7485t + 313.9 (1 ≤ t ≤ 59) where A(t) is measured in parts per million volume (ppmv) and t in years, with t = 1 corresponding to 1958.† Find the average rate of increase of the average amount of CO2 in the atmosphere from 1958 through 2016. (Round your answer to two decimal places.)