Suppose the vector-valued function r(t) = < f(t) ,g(t) ,h (t) > is smooth on an interval containing the point < f(t0) ,g(t0) ,h(t0) > . the line tangent to r(t) at t = t0 is the line parallel to the tangent vector r'(t0) that passes through < f(t0),g(t0),h(t0)> . find the line tangent to the curve at t = t0. r(t)=(2t-1,9t+5,t^2), t0= 1 the tangent line is < , , > .

Aswimming pool has an input pump for filling the pool and an output pump for emptying the pool. the input pump can fill the pool in 3 hours, and the output pump can drain the pool in 5 hours. as you go to bed, the pool is full, but a neighbor’s kid turns on the output pump. at midnight, you awake to find the pool half empty. immediately, you turn on the input pump, but you are sleepy and forget to turn off the output pump. at what time will the pool become full?

Jamie went to home depot.she bought 25 bags of soil that cost $9 per bag.she bought 15 pots at $8 each,and she bought 23 bags of pebbles at $15 each.she used a coupon that gave her $5 off for every 100 dollars she spent.how much did jame pay at the end?

Two florida panthers were weighed. one weighs 6x+21 pounds and the two together weigh 14x+11 pounds how much does he other panther weigh alone