A famous fractal called the Sierpinski Triangle starts with one black triangle.  The triangle is then cut into four equal pieces, and the three outer triangles are coloured black and the inner triangle is white.  Each of the three black triangles is again divided into four equal triangles, and the three outer triangles are shaded black. a. Suppose the area of the first triangle is 100 cm2.  Determine the black shaded area in the second triangle.  Do the same for the third triangle. b. Write the general term describing the shaded area of the nth Sierpinski Triangle. c. Suppose the diagram continued on.  What total area would be shaded in the first ten Sierpinski Triangles?  Round to the nearest whole number. d. Suppose the fractal continued forever.  Determine the total area shaded in all the

if r > 0 and s >0, then the solution to the inequality 3(x-r)² >s will cover more of the number line when 

a. r is increased

b. r is decreased

c. s is increased

d. s is decreased

Adrianne is playing soccer, and kicks the ball at the goal.  The ball follows the path of a quadratic function.  When she kicks the ball, she is 20 feet away from the goal, and the ball hits a maximum height of 10 feet when it is 5 feet away from the goal line.  If the net is 8 feet tall, does she make a goal (assuming the goalie does not stop the ball)? a. Draw a diagram of the situation, including known values. 

Determine the first term of the arithmetic sequence in which the 16th term is 110 and the common difference is 7

Solve inequality x^2-15x+40 less than or equal to 10-4x. Use number line. 

Modern metal cans, like the one shown, are usually made of steel, and then covered with a thin layer of tin. 

A. Write an inequality representing the amount of sheet metal that can be used to make a can that is 10cm tall. 

B. Graph the inequality.

C. Explain how the graph can be used to determine the minimum amount of metal required for cans of various radii. 

a patient takes a pill that holds 50 mg of medicine in it.The pill is metabolized or used up, at a rate of 55% every hour.

a.Calculate how much of the pill is left after one hour.

b.rounded to the nearest hundredth, how much of the pill has been used by the body after four hours.

c.if the patient does not take another pill, how much of the pill will the patient use after an infinite amount of time?(nearest hundredth)

Use the diagram below to answer the question. 

The solution to (x-A)(x-B) less than or equal to 0 is 

a. A is less than or equal to x less than or equal to B, xER

b. B is less than or equal to x less than or equal to A, xER

c. x is greater than or equal to A or x is less than or equal to B, xER

d. x is greater than or equal to B or x is less than or equal to A, xER

Modern metal cans, like the one shown, are usually made of steel, and then covered with a thin layer of tin. 

A. Write an inequality representing the amount of sheet metal that can be used to make a can that is 10cm tall. 

B. Graph the inequality.

C. Explain how the graph can be used to determine the minimum amount of metal required for cans of various radii.

d. explain a factor that the surface area of a cylinder does not account for. 

e. suggest a change to a surface area of a cylinder inequality that would make it more accurately represent the amount of metal required to make a tin can like the one shown. 

if (3,6) lies on the boundry of the inequality y is greater than f(x), the point that must be a solution to teh inequality is 

a. (0,6)

b. (3,3)

c. (3,9)

d. (6,6)