Let h(t) and V(t) be the height and volume of water in a tank at time t. If water drains through a hole with area a at the bottom of the tank, then Torricelli’s Law says that
where g is the acceleration due to gravity. So the rate at which water flows from the tank is proportional to
the square root of the water height.
Part 1
Suppose the tank is cylindrical with height 6 feet and radius 2 feet and the hole is circular with radius 1 inch. If
we take , show that h satisfies the differential equation
You are going to want to start with the formula for volume of a cylinder then use the equation given above for
Torricelli’s Law to substitute in. Your work should start with the volume formula and end with the differential
equation above.

Use the expression below.–4b + 8c + 12 – 8b – 2c + 6part asimplify the expression. enter your answers in the boxes. b + c + part bfactor the simplified expression using the gcf. a. 2(–2b + c + 3) b. 3(–2b + c + 3) c. 4(–2b + c + 3) d. 6(–2b + c + 3)part cwhat is the value of the expression when b = 2 and c = –3? enter your answer in the box.

(50 ) mrs. julien’s and mrs. castillejo’s classes are selling cookie dough for a school fundraiser. customers can buy packages of macadamia nut chip cookie dough and packages of triple chocolate cookie dough. mrs. julien’s class sold 25 packages of macadamia nut chip cookie dough and 30 packages of triple chocolate cookie dough for a total of $221.25. mrs. castillejo’s class sold 5 packages of macadamia nut chip cookie dough and 45 packages of triple chocolate cookie dough for a total of $191.25. (a) write the system of equations that model the problem. be sure to explain which equation represents which situation. (b) find the cost of each type of cookie. show your work. (c) explain which method you used to solve the system and why you chose that method.

David is standing on the sixth rung of a ladder while painting his house. which expressions represent a change in david’s position of 2 rungs on the ladder? choose exactly two answers that are correct. a. 6+2 b. 6-2 c. 2x6 d. 6/2