Essential Calculus
2nd Edition
ISBN: 9781285209067
Author: Stewart
Publisher: Cengage
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An electric current can be represented by the function y=2cos(2π(x−0.02)), with time in x seconds. How many times does the current reach a value of 1 on the interval 0<x<5?
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Studies have shown that the number of accidents a driver has varies with the age of the driver, and is highest for very young and very old drivers. The number of serious accidents for drivers of age x during a recent year was approximately f(x) = 0.013x2 − 1.46x + 48 for 16 ≤ x ≤ 85.
Find the age that has the least accidents, rounding your answer to the nearest year.
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Find the value of x for which the line tangent to the graph of f(x)=7/2x^2−5x+1 is parallel to the line y=−3x−4 Write your answer as a fraction
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- What is the composition of two functions, fg ?arrow_forwardThe height h of a projectile is a function of the time t it is in die air. The height in feet for t seconds is given by the function h(t)=-16t2+96t . What is the domain of die function? What does the domain mean in the context of die problem?arrow_forwardThe function D(p) gives the number of items that will be demanded when the price is p. The production cost C(x) is the cost of producing x items. To determine the cost of production when the price is $6, you would do which of die following? a. Evaluate D(C(6)) . b. Evaluate C(D(6)) . c. Solve D(C(x))=6 . d.Solve C(D(p))=6 .arrow_forward
- Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.arrow_forwardThe number N of beavers in a given area after x years can be approximated by N=5.5100.23x,0x10. Use the model to approximate how many years it will take for the beaver population to reach 78.arrow_forwardSuppose that the function y = f(x) is decreasing on the interval [ - 2, 7].(a) Over what interval is the graph of y = f(x + 2) decreasing?(b) Over what interval is the graph of y = f(x - 5) decreasing?(c) What can be said about the graph of y = - f(x)?(d) What can be said about the graph of y = f( - x)?arrow_forward
- The total world wide box office receipts for a long running blockbuster movie are approximated by the function T(x) = (120x2)/(x2 + 4) where T(x) is measured in millions of dollars ans x is the number of months since the movie’s released. What are the total box office receipts after the first month? The second? The third? What will be the movie’s gross in the long run?arrow_forwardSuppose it has been determined that the sales at the gallery decline after the end of advertising campaign, with daily sales given by s=7000(-2^-0.1x) Where S is In dollars an ex is the number of days after the complaint ends. What are the daily sales 50 days after the end of the campaign?arrow_forwardHow is your=h/b x isn’t it supposed to be -h/b xarrow_forward
- Studies have shown that the number of accidents a driver has varies with the age of the driver, and is highest for very young and very old drivers. The number of serious accidents for drivers of age x during a recent year was approximately f(x) = 0.013x2 − 1.48x + 48 for 16 ≤ x ≤ 85. Find the age that has the least accidents, rounding your answer to the nearest year.arrow_forwardWomen in the Workforce Using data starting with 1950 and projected to 2050,the number of women (in millions) in the workforce is given by the function P=0.79x+20.86, Where x equals the number of years after 1950. (a)Find the Value of P when x=70 .Explain what it means. (b) What value of x represent 2030? Use the model to find the number of women in the worforce in 2020.arrow_forwardUse the Maximum Revenue information above to answer this question. Since price cannot be negative, we have X ≤_________. Use the Maximum Revenue information above to answer this question. A negative value of X would result in a price increase. Since the problem is stated in terms of price reductions, we must restrict X so that X≥ _____.arrow_forward
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