HELP. Quadratic problems.

[leads]

Hi all,

My son came home from school with an assignment on quadratics.

He has no idea how to approach the problems. Unfortunately, I have tried to help but am really struggling.

Any help greatly appreciated!!!


1. A square has one side x and a circle has a radius y.

a) Write an expression for: the perimeter of the square
the perimeter of the circle.

b) The two shapes are made out of a piece of wire total length 8cm.

Find an expression for x in terms of y.

c) Show that the total area of the two shapes is given by
Ay
A=pi/4(pi+4)y^2-2piy+4

d) if the total area of the two shapes is the smallest possible, what percentage of the wire is used for the circle?

THANK YOU!!!

 

[stapel]

My son came home from school with an assignment on quadratics. He has no idea how to approach the problems. Unfortunately, I have tried to help but am really struggling.

From long experience, we've learned that attempting to converse through a "translator" who "doesn't speak the language" is doomed to failure. So please have your son reply with specifics.

1. A square has one side x and a circle has a radius y.

a) Write an expression for: the perimeter of the square
the perimeter of the circle.

These are simple formulas (here: these should be memorized). Plug the given variables into the appropriate formulas.

b) The two shapes are made out of a piece of wire total length 8cm.

Find an expression for x in terms of y.

Add the two "perimeter" expressions from the two relevant formulas. Set the sum equal to the given total value. Solve the resulting literal equation. (here)

c) Show that the total area of the two shapes is given by
Ay
A=pi/4(pi+4)y^2-2piy+4

The areas of the shapes are given by simple formulas. Plug the given variables into the given formulas. Add the two "area" expressions, and set equal to "A". Plug the result from part (c) into the "area" equation in place of every instance of "y". Simplify and confirm that you get the result they've provided.

d) if the total area of the two shapes is the smallest possible, what percentage of the wire is used for the circle?

You have a positive quadratic, which graphs as a parabola. (here) Which point on an upward-opening parabola is the lowest on the graph (that is, gives the smallest value of the quadratic)? How do you find this point?

Please be complete. Thank you!