Math 180 Name _________________ Summer 2013 Homework #1 Due Wednesday, June 26 No late papers accepted! No excuses! 1. Solve each equation or inequality. a) 2 x − 3 ≥ 4 b) sin 3x ( ) = cos 3x ( ) 0, 2π [ ] c) 3 2 x− 1 = 5 x+2 d) log 2 x + log 2 x − 2 ( ) = 3
1. Solve each equation or inequality. a) 2x 3 4 b) sin 3x( ) =
cos 3x( ) 0,2[ ] c) 32 x1 = 5x+2 d) log2 x + log2 x 2( ) = 3
e) cos +1= sin 0,2[ ] f) 3xex + x2ex = 0
g) ex 12ex 1= 0 h) 5x3 x2 4x + 4 0
2. A wire 10 cm long is cut into two pieces, one of length x and
the other of length 10 x . One piece is bent into the shape of a
square and the other piece of wire is bent into the shape of a
circle. Find a function that models the total area enclosed. State
the domain of your function.
3. A rectangle is inscribed in a circle of radius 4. Find a
function that models the
area of the rectangle as a function of x.
4. Carol has 2400 feet of fencing to fence in three adjacent
rectangular pens. a) Find a function that models the total area of
the pens. b) Find the domain. c) Find the dimensions of the pens
that will maximize the area.
