Use the linear approximation to approximate a suitable function f(x, y, z) and thereby estimate (3.99)2 + (4.02)2 + (1.98)2. 1. Compute the tangent vector to the given path.
c(t) = (2t sin(t), 5t)
2. Let f(x, y) = 6ex -y. Find the equation for the tangent plane to the graph offat the point (5, 5).

How are sas and sss used to show that two triangles are congruent?

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

You dug a hole that was 8 feet deep. after taking a short break, you dug down 3 more feet in the same hole. when finished digging, a tractor accidentally filled the hole with 4 feet of dirt. how deep is your hole now?