Show that the area of an isosceles triangle with equal sides of length x is A =1/2x^2sin(theta) , where theta is the angle formed by the two equal sides.

Graph red beads cost $1 an ounce and gold beads cost $3 an ounce. juanita wants to purchase a 12-ounce mixture of red and gold beads that she can sell for $2 an ounce. the solution of the system shows the number of beads needed for juanita to break even. x + y = 12, x + 3y = 24 how many ounces of red beads will juanita buy to break even? how many ounces of gold beads will she buy?

Find the values of y: 3y^3(y^2+ 2/3y)=0

Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. how fast is the height of the pile increasing when the pile is 14 ft high? (round your answer to two decimal places.) ft/min