Suppose you need to know an equation of the tangent plane at a surface s at the point p(3, 1, 4). you don't have an equation for s but you know the following curves both lie on s. r1(t) = < 3 + 3t, 1 - t2, 4 - 5t + t2> r2(u) = < 2 + u2, 2u3 - 1, 2u + 2> find an equation of the tangent plane at p.

(a) (8%) compute the probability of an even integer among the 100 integers 1! , 2! , 3! , until 100! (here n! is n factorial or n*(n-1)*(n-2) *… 1) (b) (16%) compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, …., 1+2+3+… + 99, and 1+2+3+… + 100

Which triangle congruence postulate or theorem justifies my claim that the steps i made using construction paper and scissors produce an isosceles triangle? was it sss, sas, asa, aas, or hl?

Michelle and julie work at a catering company. they need to bake 264 cookies for a birthday party that starts in a little over an hour and a half. each tube of cookie dough claims to make 36 cookies, but michelle eats about 1/5 of every tube and julie makes cookies that are 1.5 times as large as the recommended cookie size.it takes about 8 minutes to bake a container of cookies, but since julie's cookies are larger, they take 12 minutes to bake. a. how many tubes should each girl plan to bake? how long does each girl use the oven? b. explain your solution process what did you make? c. what assumptions did you make?