Aprinter needs to make a poster that will have a total of 500 cm2 that will have 3 cm margins on the sides and 2 cm margins on the top and bottom. what dimensions of the poser will give the largest printed area?

The largest printed area is 381.43 cm^2 .

Step-by-step explanation:

The width of the full poster = 500/x

Length of the printed area = l =x - 4

Width of the printed area = w = (500/x) - 2

Area of the printed space = (x - 4) × ((500/x) - 2)

Now, take derivative of the area

A' = (x - 4)×(-500/x^2) + ((500/x) - 2)

A' = (2000/x^2) - 2

A' = (2000-2x^2) / x^2

put derivative equal to zero like A' = 0

(2000-2x^2) / x^2 = 0

2000 = 2x^2

x^2 = 1000

x = 31.62

So, the length of the original poster is = x = 31.62 cm

The width of the full poster = 500/x = 15.81 cm

l = x - 4 = 27.62

w = 500/x - 2 = 13.81

Therefore, The area of space available for printing is = l × w

= 27.62 × 13.81 = 381.43 cm^2 .

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

2

step-by-step explanation: