The top and bottom margins of a poster are 2 cm and the side margins are each 8 cm. if the area of printed material on the poster is fixed at 386 square centimeters, find the dimensions of the poster with the smallest area.

Answer :

39.294 cm × 9.823 cm

Explanation :

Let x be the length ( in cm ) of the printed material and y be the width ( in cm ) of the printed material,

So, the area of the printed material,

According to the question,

A = 386 cm²,

Since, the printed area is obtained in the margin of 2 cm from both top and bottom and margin of 8 cm in sides,

Thus, length of the poster = (x + 16) cm and width = (y + 4)

So, the area of the poster,

Differentiating with respect to x,

Again differentiating with respect to x,

For maxima or minima,

Sides can not be negative,

Also, at x = 39.294,

i.e. is minimum at x = 39.294,

∵ y = = 9.823

Hence, the dimensions of the poster with the smallest area,

39.294 cm × 9.823 cm

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!

step-by-step explanation: