Find a basis for the following plane in R 3 x − 3 y − z = 0 First, solve the system, then assign parameters s and t to the free variables (in this order), and write the solution in vector form as s u + t v . Below, enter the components of the vectors u = [ u 1 , u 2 , u 3 ] T and v = [ v 1 , v 2 , v 3 ] T .

There is a line with slope 1/a going through the point (a, a²). find the equation of the line perpendicular to this line at this point. (don’t let this problem intimidate you! solve the problem as you would if i’d given you specific values. just use variables instead.)

Can you me find the missing length. i attached an image.

Acoffee shop orders at most $3,500 worth of coffee and tea. the shop needs to make a profit of at least $1,900 on the order. the possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea: 6c + 13t ≤ 3,500 3.50c + 4t ≥ 1,900 which graph's shaded region represents the possible combinations of coffee and tea for this order?