Sodium 24 has a half-life of approximately 15 hours. Consider a sample of 100 milligrams. a. Write an equation to determine the number of milligrams remaining after t days. Show all work. b. How many milligrams are remaining after 45 hours? Show all work. c. How long will it be until there are 5 milligrams remaining? Show all work. Math symbols Relations Geometry * Groups * Trigonometry Go to the Next Statistics GreekConsider the region bounded by 43; = 1:2 and 23; = 3:. a. Find the area bounded by the two curves. Show all work. b. Find the volume of the solid generated by revolving the region around the x-axis. Show all work. c. Find the volume of the solid generated by revolving the region around the y-axis. Show all work. For an indefinite integral, use the notation INT in place of the symbol. For example, I (a: + l)d:1: should be written as INT (:1: + 1] do. For a definite integral, use the notation INT (o, b]. For example, If (a: + 1) do: should be written as [NT (1, 2} (m + 1) dz. For a definite integral that has been 2 integrated, use the notation EVAL (a, b]. For example, (I; + m)' should be written as 1 (g + m) EVAL (1, 2). SEE I Math symbols I Fielations I Geometry I Groups I Trigonometry I Statistics I Gravel: Let f (ac) = 23 - 3x2 + 3. a. What are the domain and range of f? b. What are the relative extrema of f? Justify your answer. c. Are there any points of inflection? Justify your answer. d. Where is f increasing and decreasing? Justify your answer. * Math symbols Relations Geometry Groups Trigonometry Statistics GreekA man walks in a straight path away from a streetlight at a rate of 4 feet per second. The man is 6 feet tall and the streetlight is 15 feet tall. a. At what rate is the length of his shadow changing? b. At what rate is the distance from the top of the streetlight to the tip of his shadow changing when the man is 12 feet from the streetlight? *Math symbols Relations Geometry Groups Trigonometry Statistics Greek. . . . dy _ 4;: Consider the differential equation E =+3' a. Find the general solution in explicit form. b. Find the particular solution in explicit form, if y(2) = 1. c. Find the equation of the tangent line at (2, 1] to the particular solution. For an indefinite integral, use the notation INT in place of the symbol. For example, I (a: + 1} do should be written as INT (3: + 1] do. For a definite integral, use the notation INT (a, b]. For example, I12 (3 + 1) dz should be written as [NT (1, 2H1: + 1) d3. Fora definite integral that has been 2 integrated, use the notation EVAL (c, b]. For example, (I; + m)' should be written as 1 (g + m) EVAL {1, 2). WEE-l I In Math symbols l' Fielations Ir Geometryr I Groups I Trigonometry l Statistics h Gretel