Suppose f(x, y, z) and g(x, y, z) are continuously differentiable functions with f(1, 2, 3) = 5 and g(1, 2, 3) = 7. assume that the surface f(x, y, z) = 5 and the surface g(x, y, z) = 7 have the same tangent plane at (1, 2, 3). evaluate ∇f(1, 2, 3)×∇g(1, 2, 3) (remember to give reasons).

In a certain pentagon, the interior angles are a,b,c,d,e where a,b,c,d,e are integers strictly less than 180. ("strictly less than 180" means they are "less than and not equal to" 180.) if the median of the interior angles is 61 and there is only one mode, then what are the degree measures of all five angles?

Acarnival sold tickets for $1.50 for adults and $1.00 for students. there were 54 tickets sold for a total of $70.50. write a system of equations to represent the number of adult tickets,x, and the number of student tickets,y. find the solution and explain what it means. i'll you if you me

Jabari is power washing houses for a summer job. for every job, he charges an initial fee plus $30 for each hour of work. his total fee for a 4 -hour job, for instance, is $170 . jabari's total fee,f, for a single job is a function of the number,t, of hours it takes him to complete the job. write the function's formula.