Suppose the lateral displacement of the center of a bridge may be modeled as a spring-and-mass system, with low friction and a high spring constant. Let z = r(t) be the lateral displacement of the center of the bridge, let m>0 be the mass, and let k> 0 be the spring constant. Neglect the effect of friction, and consider an external wind force w(t) acting on the center of the bridge. Then r(t) obeys the differential equation + kr = w(t) m dt2 Find a wind force function w = w(t) with ||w||x = max Jw(t)| < 1 that will definitely result in the bridge collapsing in time, and explain why the bridge will eventually collapse with this choice of w. tER

Question content area top Part 1 Substance A decomposes at a rate proportional to the amount of A present.   ​a) Write an equation that gives the amount A left of an initial amount Upper A 0A0 after time t. ​b) It is found that 1818 lb of A will reduce to 99 lb in 3.53.5 hr. After how long will there be only 1 lb​ left?       Question content area bottom Part 1 ​a) Choose the equation that gives A in terms of Upper A 0A0​, ​t, and​ k, where kgreater than>0.     A. ​A(t)equals=Upper A 0 e Superscript ktA0ekt   B. ​A(t)equals=Upper A 0 e Superscript negative ktA0e−kt Your answer is correct.   C. ​A(t)equals=Upper A 0 Superscript ktA0kt   D. ​A(t)equals=Upper A 0 Superscript negative ktA0−kt Part 2 ​b) There will be 1 lb left after enter your response here hr. ​(Do not round until the final answer. Then round to the nearest whole number as​ needed.)

2 6-y ·S. ye² dx dy -3 y² 2. (Section 16.2) Consider

Chapter 1, Section 1.5, Question 012 Is y directly proportional to x? y = 14x- 8x If so, give the constant of proportionality. If not, enter NA. Click if you would like to Show Work for this question: Open Show work