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

Sasha has just gotten a new job in a nearby city. after comparison shopping, she found that renting a nice two-bedroom apartment would cost around $800 per month. her utilities would cost about $150 per month. sasha has enough money saved for a down payment, and she found that she can buy a three-bedroom house or condo with a mortgage payment of $1,000 per month, including taxes and homeowner's insurance. her utilities would cost about $200 per month. what is the advantage of buying the house over renting the apartment?