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5. Let g(x) = . a. Is this function one-to-one? How did you determine this?b. If it is one-to-one, find .16. Graph (Show scale. Use dashed line for asymptotes. Identify some points on the graph.)yxa. What is the domain of the function?b. What is the range of the function?c. Identify any asymptotes.22. At the end of an advertising campaign, the sales (in dollars) declined, with weekly sales given by the equation y = 40,000(3 ), where x is the number of weeks after the end of the campaign. In how many weeks will sales be half of the sales at the end of the ad campaign?24. Business partners want to purchase a restaurant that costs $750,000. They have $300,000 for a down payment, and they can get a 25-year business loan for the remaining funds at 8% per year on the unpaid balance, with quarterly payments.a. What will be the payments?b. What is the total amount that they will pay over the 25 year period?c. How much interest will they pay over the life of the loan?27. For the function a. List all possible rational zeros.b. Find all real zeros algebraically.c. Write the polynomial in factored form.28. For the polynomial a. Find the degree of the polynomial. b. Determine the end behavior. c. Find the y-intercept. d. Find the x-intercepts.29 . For the function a. Find the domain of the function.b. Find the x- and y-intercepts of the function if there are any.c. Find any vertical asymptotes.d. Find any horizontal or slant asymptotes.e. Graph using a calculator then sketch by hand. (Show scale. Use dashed line for asymptotes. Identify some points on the graph.)yx
A trough is to be made with an end of the dimensions shown. The length of the trough is to be 21ft long. Only the angle theta can be varied. What value of theta will maximize the trough's volume?
Use Euler's method with step size 0.5 to compute the approximate y-values y1,y2,y3, and y4 of the solution of the initial-value problem y'= -2 + 2x - 4y, y(0)= -3
in the liquid limit test, the moisture content corresponds to 20, 25, & 35. and the blows are 35%, 2% & 15%. what is the liquid limit if the soil?
At a certain time, the temp is maintained constant, the P=100ln/in^2 and is increasing at 4 lb/in ^2. At what rate is the volume changing when it is 60 in^3?
First give the integrand expressed in terms of h, the terms of the height in feet from the bottom of the trough.
Jack and Jill ran a 200 meter race. Jill ran the race in 25 seconds and won by 5 meters; that is Jack had run only 195 meters when Jill crossed the finish line.
Verify that 18^3 - 1^3 = 17* 7^3 and find a point on the curve x^3 + y^3 = 17 with rational coordinates.
Assume that 10% of the population is left-handed. If three people are chosen at random, what is the probability that at least one will be left-handed?
Finding the integral in a table of integrals is not sufficient justification- for correctly and clearly demonstrating why.
Use green's theorem to calculate the area of the region between the x-axis and one arch of the cycloid with parametric equations x = a(t - sin t), y = a(1 - cos t).
The Bluegrass Distillery produces custom-blended whiskey.
Commuting to work: On Monday, Roger drove to work in 45 minutes(.75h). On Tuesday, he averaged 12 miles per hour more, and it took him 9 minutes (.15h) less to get to work. How far does he travel to work?
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