2x +7x-15 x' -16 Use the function f(x) = for parts (a) - (e) below, show your work for cach part: (a) Find y-intercept. (b) Find x-intercepts. (c) Find vertical asymptotes, if any.
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- Radius of a Shock Wave An explosion produces a spherical shock wave whose radius R expands rapidly. The rate of expansion depends on the energy E of the explosion and the elapsed time t since the explosion. For many explosions, the relation is approximated closely by R=4.16E0.2t0.4. Here R is the radius in centimeters, E is the energy in ergs, and t is the elapsed time in seconds. The relation is valid only for very brief periods of time, perhaps a second or so in duration. a. An explosion of 50 pounds of TNT produces an energy of about 1015 ergs. See Figure 2.71. How long is required for the shock wave to reach a point 40 meters 4000 centimeters away? b. A nuclear explosion releases much more energy than conventional explosions. A small nuclear device of yield 1 kiloton releases approximately 91020 ergs. How long would it take for the shock wave from such an explosion to reach a point 40 meters away? c. The shock wave from a certain explosion reaches a point 50 meters away in 1.2 seconds. How much energy was released by the explosion? The values of E in parts a and b may help you set an appropriate window. Note: In 1947, the government released film of the first nuclear explosion in 1945, but the yield of the explosion remained classified. Sir Geoffrey Taylor used the film to determine the rate of expansion of the shock wave and so was able to publish a scientific paper concluding correctly that the yield was in the 20-kiloton range.Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?14. a) The x and y-intercepts. b) The orizontal and vertical asymptotes. c) The first and second derivatives.
- 1.Identify the kind of function. 2.Find the x- and y- intercepts and the vertical abs horizontal asymptotes. 3.Find the end behavior of the function (y,y)Horizontal asymptote is “y=1” but I keep getting “y=0” what step am I missing? Please and thank youvertical and horizontal asymptotes as equations for the function (y= x=)
- 1.Find the X-intercepts (x,y) and y-intercept (x,y) and the vertical and horizontal asymptotes. 2.Describe the end behavior of the function.y = -x^3+6x^2+63x-100 Find and show work - Local maxima = ? Local minima = ? Inflection Points = ?The function y = f(x) = (−1/x) + (1/x^2) on the domain 0 < x < ∞ Find the local maximum and minimum point (x and y coordinates) of the graph. B) Inflection point (both x and y coordinates). C) horizontal and vertical, asymptote of the graph?
- The cost of an appliance whose purchase price is $600 and annual hydro cost is $115 is given by the function C(n)=(600+115n)/n , where C is the annual cost, in dollars, and n is the number of years. Show all your work. Clearly label all cases (j, k, l…).a) Determine x-intercept(s) if it exists. (1) b) Determine y-intercept(s) if it exists. (1) c) Determine the equations of the horizontal asymptote if it exists. (2) d) Determine the equations of the vertical asymptote(s) if it exists. (2) e) State the domain of the entire function. (1) f) State the domain for the real-life situation. (1) g) State the range of the entire function. (1) h) State the range for the real-life situation. (1) i) Determine the number of years needed to reduce the annual cost to below $180. (2) j) Sketch a graph of C versus n for the entire function in a paper-pencil style. Clearly label the axes, scale on both axes, the asymptote(s), and the intercept(s). (9) k) How is the graph of the entire function different…4. Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing graphs (with a graphing device) that display the major features of the curve. Use these graphs to estimate the maximum and minimum values. (Round your answers to three decimal places.) f(x)=((2x+3)^2(x-2)^5)/(x^3(x-5)^2) 4a)find the two local minima pointsThe graph of a function crosses the y-axis at the point y = 2 and the x-intercept of the tangent line drawn at any point of the graph is 1 more than the x-coordinate of the point of tangency. What is the function? Is such function unique? Provide all the details of your solution.