6. sabrina is making an open box from a piece of cardboard that has a width of 12 inches and a length of 18 inches. she’ll form the box by making cuts at the corners and folding up the sides so that the flaps are square. if she wants the box to have a volume of 224 in3, how long should she make the cuts?

part i: given what you know about the box sabrina is making, write a polynomial to represent each dimension (width, length, and height) of the finished box. (3 points)
width =
length =
height =
part ii: the formula for volume is v = l • w • h. write an equation to represent the volume of the box. simplify on the right side by multiplying the polynomials and writing the answer in descending order. show your work.
hint: first multiply the binomials representing length and width. next, multiply the resulting trinomial by the expression representing height. (3 points)
v =

part iii: the length of each cut at the corners is represented by x. to make a box, x must fall in a certain range of values. for example, x cannot be 15 because that would make the flap longer than the width of the box. identify one reasonable value of x. why did you choose that value? (1 point)

part iv: complete the table of values for the polynomial equation you wrote in part ii. show your work. (5 points)
x v
0

1

2

3 216
4

5

6 0
part v: based on your table, what x-value creates a box with a volume of 224 in3? (1 point)

part vi: using the polynomials you wrote in part i, what are the dimensions of sabrina's completed box? (3 points)
width =

length =

height =

Abank gives 6.5% interest per year. what is the growth factor b in this situation?

Airplane speeds are measured in three different ways: (1) indicated speed, (2) true speed, and (3) ground speed. the indicated airspeed is the airspeed given by an instrument called an airspeed indicator. a plane’s indicated airspeed is different from its true airspeed because the indicator is affected by temperature changes and different altitudes of air pressure. the true airspeed is the speed of the airplane relative to the wind. ground speed is the speed of the airplane relative to the ground. for example, a plane flying at a true airspeed of 150 knots into a headwind of 25 knots will have a ground speed of 125 knots. the problems below refer to static and dynamic pressure. static pressure is used when a body is in motion or at rest at a constant speed and direction. dynamic pressure is used when a body in motion changes speed or direction or both. a gauge compares these pressures, giving pilots an indicated airspeed. in problem #s 1 and 2, use the following information. the indicated airspeed s (in knots) of an airplane is given by an airspeed indicator that measures the difference p (in inches of mercury) between the static and dynamic pressures. the relationship between s and p can be modeled by s=136.4p√+4.5. 1. find the differential pressure when the indicated airspeed is 157 knots. 2. find the change in the differential pressure of an airplane that was traveling at 218 knots and slowed down to195 knots. in problem #s 3 and 4, use the following information. the true airspeed t (in knots) of an airplane can be modeled by t=(1+a50,000) ⋅ s, where a is the altitude (in feet) and s is the indicated airspeed (in knots). 3. write the equation for true airspeed t in terms of altitude and differential pressure p. 4. a plane is flying with a true airspeed of 280 knots at an altitude of 20,000 feet. estimate the differential pressure. explain why you think your estimate is correct.

The lengths of all sides of a triangle are integers when measured in decimeters. one of the sides has length of 1 dm and another of 3 dm. find the perimeter of the triangle.'