)for each vector field vector f(x, y,z), compute the curl of vector f and, if possible, find a function f(x, y, z) so that vector f = delta f. if no such function exists, enter none. suppose f vector (x, y, z) = (3yze^3xyz + 3z^2cos(xz^2))i vector + (3xze^3xyz)j vector + (3xye^ 3xyz + 6xz cos(xz^2))k vector. suppose vector f (x, y, z) = vector i /x + vector j / y + vector k / z. suppose vector f(x, y, z) = < -2y, 3x,7z> .

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