Let
x ----------> the height of the whole poster
y ----------> the width of the whole poster

We need to minimize the area A=x*y

we know that
(x-4)*(y-2)=722
(y-2)=722/(x-4)
(y)=[722/(x-4)]+2

so
A(x)=x*y--------->A(x)=x*{[722/(x-4)]+2}
Need to minimize this function over x > 4

find the derivative------> A1 (x)
A1(x)=2*[8x²-8x-1428]/[(x-4)²]

for A1(x)=0
8x²-8x-1428=0
using a graph tool
gives x=13.87 in

(y)=[722/(x-4)]+2

y=[2x+714]/[x-4]-----> y=[2*13.87+714]/[13.87-4]-----> y=75.15 in

the answer is
the dimensions of the poster will be
the height of the whole poster is 13.87 in
the width of the whole poster is 75.15 in

6 0

2 years ago

The moon is a sphere with radius of 959 km. Determine an equation for the ellipse if the distance of the satellite from the surf

Sergeeva-Olga [200]

Answer:

$\frac{x^2}{1316^2}+\frac{y^2}{1669^2}=1$

Step-by-step explanation:

An ellipse is the locus of a point such that its distances from two fixed points, called foci, have a sum that is equal to a positive constant.

The equation of an ellipse with a center at the origin and the x axis as the minor axis is given by:

$\frac{x^2}{b^2}+\frac{y^2}{a^2} =1 \\\\where\ a>b$

Since the distance of the satellite from the surface of the moon varies from 357 km to 710 km, hence:

b = 357 km + 959 km = 1316 km

a = 710 km + 959 km = 1669 km

Therefore the equation of the ellipse is:

$\frac{x^2}{1316^2}+\frac{y^2}{1669^2}=1$

5 0

2 years ago

Karen is waiting for a pot of soup to cool

Studentka2010 [4]

Answer:

It went down 5.5°C a minute.

Step-by-step explanation:

You have to look for the difference of 100 and 78, which is 22.

Divide the difference with the minutes (4), equalling 5.5.

4 0

2 years ago

Scott and Ariel want to make as much as snack mix as possible, but no more than 25 cups of mix. I they can use only full cups of

photoshop1234 [79]

Answer:

hello your question has some missing parts attached below is the missing information

answer : Scott will make 5 snack mix without going over

Step-by-step explanation:

Given that:

Scott makes a snack mix with ; 2 cups of Almonds and 3 cups of raisins

= 5cups per snacks mix

Ariel makes a snack mix with : 3 cups of almonds and 5 cups of sunflower seeds = 8 cups per snack mix

Now back to your question above

Given that : No more than 25 full cups is required to make a snack mix

For Scott

= 25 / 5 = 5 snack mix ( No make overs )

For Ariel

= 25 / 8 = 3.125 snack mix ( there is a makeover of 0.125 )

Hence it can be said that Scott will make the most mix without going over

8 0

2 years ago