Aposter is to have a total area of
180cm2 with 1-cm margins at the bottom and sides and a 2
cmmargin at the top. what dimensions will give the largest
printedarea?

Dimensions of printed area

w = 8.95 cm

h = 13.44 cm

A(max) = 120.28 cm²

Step-by-step explanation:

Lets call  " x "  and  "y" dimensions of the poster area  ( wide and height respectively) . Then

A(t)  =  180 cm²  = x*y      y  =  180/ x

And the dimensions of printed area is

A(p) = ( x - 2 ) * ( y - 3 ) then  as y  = 180/x we make A function of x only so

A(x)  =  ( x - 2 ) * ( 180/x  - 3 )     ⇒  A(x)  = 180 - 3x - 360/x +6

A(x)  = - 3x  - 360 /x + 186

Taking derivatives on both sides of the equation we get:

A´(x)  = -3  + 360/ x²  

A´(x)  = 0    -3  + 360/ x²  = 0     -3x²  +  360  = 0

x²  = 120       ⇒   x = √120       x  =  10.95 cm

And  y  =  180 / 10.95 ⇒         y  =  16.44 cm

Then x and y are the dimensions of the poster then according to problem statement

w of printed area is    x - 2  =  10.95 - 2   =  8.95 cm

and  h  of printed area is  y - 3  = 16.44 - 3  = 13.44 cm

And the largest printed area is  w * h  = ( 8.95)*(13.44)

A(max) = 120.28 cm²

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)

the clb she uses is a driver, so its a 2/5 chance she hits a 180-189 yard shot

step-by-step explanation: