The differential equation in Example 3 of Section 2.1 is a well-known population model. Suppose the DE is changed to dP = P(aP - b), dt where a andb are positive constants. Discuss what happens to the population P as time t increases. as t increases. If Po > b/a, then P(t) as t increases; if 0 < Po < b/a, then P(t) -? Consider the following autonomous first-order differential equation. + 2) = y In(y + Find the critical points and phase portrait of the given differential equation. oF OF 0F -1-

Arecipe calls for 2 2/4 cups of raisins, but julie only has a 1/4 measuring cup. how many 1/4 cups is needed to measure out 2 2/4 cups of raisins?

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

Consider the following geometry problems in 3-space enter t or f depending on whether the statement is true or false. (you must enter t or f -- true and false will not work.) f equation editorequation editor 1. a plane and a line either intersect or are parallel t equation editorequation editor 2. two planes parallel to a third plane are parallel f equation editorequation editor 3. two lines either intersect or are parallel f equation editorequation editor 4. two planes orthogonal to a third plane are parallel f equation editorequation editor 5. two planes orthogonal to a line are parallel f equation editorequation editor 6. two planes either intersect or are parallel f equation editorequation editor 7. two lines orthogonal to a third line are parallel t equation editorequation editor 8. two lines parallel to a third line are parallel t equation editorequation editor 9. two planes parallel to a line are parallel f equation editorequation editor 10. two lines parallel to a plane are parallel f equation editorequation editor 11. two lines orthogonal to a plane are parallel