Part of a cross-country skier's path can be described with the vector function r = < 2 + 6t + 2 cos(t), (15 − t)(1 − sin(t))> for 0 ≤ t ≤ 15 minutes, with x and y measured in meters. the derivatives of these functions are given by x′(t) = 6 − 2sin(t) and y′(t) = −15cos(t) + tcos(t) − 1 + sin(t).1. find the slope of the path at time t = 4. show the computations that lead to your answer.2. find the time when the skier's horizontal position is x = 60.3. find the acceleration vector of the skier when the skier's horizontal position is x = 60.4. find the speed of the skier when he is at his maximum height and find his speed in meters/min.5. find the total distance in meters that the skier travels from t = 0 to t = 15 minutes.

Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5: 2: 3. chapter reference how much punch can she make if she has only 6 cups of plum juice?

If t8 = 4 and t12 = −2, find the first three terms of the arithmetic sequence.

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality