A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 450 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.03 cents per square centimeter. The top will be made of glued paper, costing 0.06 cents per square centimeter. Find the dimensions for the package that will minimize production cost. Helpful information:h: height of cylinder, r: radius of cylinderVolume of a cylinder: V=πr²hArea of the sides: A= 2πrhArea of the top/bottom: A=πr²

r = 3.628 cm

h = 10.88 cm

cost = 11.16 cents

Step-by-step explanation:

we know the total volume = 450 cc

then pi * r ^ 2 * h = 450

solved for h:

h = 450 / (pi * r ^ 2)

h = 143.31 / r ^ 2

now the total cost of packing = 2 * 3.14 * r * h * 0.03 + 3.14 * r ^ 2 * 0.03 + 3.14 * r ^ 2 * 0.06

= 0.1884 * r * h + 0.0942 * r ^ 2 + 0.1884 * r ^ 2

= 0.1884 * r * h + 0.2826 * r ^ 2

putting the value of h in the previous equation we obtain

total cost = 27 / r + 0.2826 * r ^ 2

we have to minimize this to differentiate it and equate it with 0 :

-27 / r ^ 2 + 0.5652 * r = 0

r ^ 3 = 27 / 0.5652

r ^ 3 = 47.77

r = 3,628 cm

replacing:

we get h = 450 / (3.14 * 3,628 ^ 2) = 10.88 cm

the total cost can be calculated for the equation

we get the total cost = 27 / 3,628 + 0.2827 * 3,628 ^ 2 = 11.16 cents

answer: 0+0=0

step-by-step explanation:

that is the only answer that can make 0

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.