If two objects travel through space along two different curves, it's often important to know whether they will collide. (will a missile hit its moving target? will two aircraft collide? ) the curves might intersect, but we need to know whether the objects are in the same position at the same time. suppose the trajectories of two particles are given by the vector functions r1(t) = t2, 6t − 5, t2 r2(t) = 9t − 20, t2, 11t − 30 for t ≥ 0. find the values of t at which the particles collide. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.)

Arecipe uses 2 cups of sugar to make 32 brownies. how many cups of sugar are needed to make 72 brownies?

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

David estimated he had about 20 fish in his pond. a year later, there were about 1.5 times as many fish. the year after that, the number of fish increased by a factor of 1.5 again. the number of fish is modeled by f(x)=20(1.5)^x. create a question you could ask that could be answered only by graphing or using a logarithm.