Uppose r⃗ (t)=cos(πt)i+sin(πt)j+5tk represents the position of a particle on a helix, where z is the height of the particle. (a) what is t when the particle has height 15? t= 3 \displaystyle{3}3 (b) what is the velocity of the particle when its height is 15? v⃗ = < -pisin(3pi),picos(3pi),5> \displaystyle< -\pi{\sin{{\left({3}\pi\right)}}},\ pi{\cos{{\left({3}\pi\right)}}},{5} > < −πsin(3π),πcos(3π),5> (c) when the particle has height 15, it leaves the helix and moves along the tangent line at the constant velocity found in part (b). find a vector parametric equation for the position of the particle (in terms of the original parameter t) as it moves along this tangent line.

Find the zero function by factoring (try to show work) h(x)=-x^2-6x-9

Credit card a offers an introductory apr of 3.4% for the first three months and standard apr of 15.7% thereafter,

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.