Suppose that the acceleration vector of a particle is given by a(t)=⟨−16cos(4t),−16sin(4t),−4t⟩, the paricle's initial velocity is v(0)=⟨1,0,1⟩, and the particle's initial position vector is r(0)=⟨1,1,1⟩. compute the following: a. the velocity vector of the particle at time t: v(t)= -4sin(4t)+1 i+ 4cos(4t)-4 j+ 4t^2/2-1 k b. the position vector of the particle at time t: r(t)= cos(4t)+t i+ sin4t-t+1 j+ 1 k

Jason is a body builder. despite being more fit, he weighs more than his brother ryan, who is the same height. which is a possible reason? a. jason has more muscle mass than ryan does. b. jason has more body fat than ryan does. c. jason has more muscle mass and body fat than ryan does d. jason has less body fat than ryan does.

You are a sales representative for a company that makes a new alternate fuel for vehicles. you have prepared a presentation for the environmental engineers to sell your new product. what question do you expect the audience to ask regarding whether the new fuel will cause less damage to the environment? a. do we have to change any parts of the vehicle to use this alternate fuel? b. will the vehicles get better fuel mileage with the alternate fuel? c. how much greenhouse gas does your fuel produce compared with current fuel sources? d. is the alternate fuel more expensive than fossil fuel?

The temperature at a point (x, y) is t(x, y), measured in degrees celsius. a bug crawls so that its position after t seconds is given by x = 6 + t , y = 8 + 1 3 t, where x and y are measured in centimeters. the temperature function satisfies tx(3, 9) = 5 and ty(3, 9) = 4. how fast is the temperature rising on the bug's path after 3 seconds? (round your answer to two decimal places.)