The top and bottom margins of a poster are 6 cm and the side margins are each 6 cm. If the area of printed material on the poster is fixed at 380 square centimeters, find the dimensions of the poster with the smallest area.

the solution to the problem is  

( a , b ) = ( 24 , 35.75 )

Step-by-step explanation:

Let a be the width of the poster and b the height.

Let A be the area of the poster to be minimized.

A = 380+ 2 ( a ⋅ 4 ) + 2 ( b ⋅ 6 ) − 4 ( 6 ⋅ 4 )

= 3840+ 8 a+ 12 b − 96

= 284+ 8 a + 12 b

A = a ⋅ b  

So let's get a in function of b:

284 + 8 a + 12 b = a b

284 + 12 b = a b − 8 a

284 + 12 b = a ( b − 8 )

 a =284+ 12 b/ b − 8

Now,  

A ( b )

will be the function in one single variable (b) that we will minimize:

A ( b ) = a ⋅ b

= ( 284 + 12 b b − 8 ) ⋅ b = 284 b + 12 b ^3/ b − 8

I have to find the first derivative of the function to minimize it:

A ' ( b ) = 12 b^ 2 − 16 b − 192/ ( b − 8 )^ 2

The minimum points satisfy the condition  

A ' ( b ) = 0

so:

b 2 − 16 b − 192 = 0

b = − 8  or  b = 24

But for obvious reason (b is the height of a poster), b must be positive, so only b=24 is a correct solution.

Now we have to find a:

a = 284+ 12 b/ b − 8 = 284+ 12 ⋅ 24 /24 − 8 = 35.75

So, the solution to the problem is  

( a , b ) = ( 24 , 35.75 )

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

b

step-by-step explanation:

u take $75 minus $60.the anwer/original($75)multiply by 100