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3 years ago

D. One holding pen uses 500 feet of fence

Mathematics

1 answer:

inn [45]3 years ago

7 0

9514 1404 393

Answer:

500 ft or 166 2/3 yards

Step-by-step explanation:

The tie wire is (100)/(100 +500) = 1/6 of the total length of wire used. If 1000 yards of wire is used, 1/6 of that amount can be expected to be tie wire. That is ...

(1000 yd)/6 = 166 2/3 yd = 500 ft

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Jane needs open-topped boxes to store her excess inventory at year's end. She purchases large

Debora [2.8K]

Answer:

x = 1,6 in ( the side of the corner squares )

V(max) = 67,58 in³

Step-by-step explanation:

The cardboard is:

L = 12 in w = 8 in

Let´s call "x" the side of the square from the corner:

Then the sides of the base of the open box are:

( L - 2*x ) and ( w - 2*x ) and x is the height

( 12 - 2*x ) and ( w - 2*x )

V(ob) = (L - 2*x ) * ( - 2*x ) * x

Wich is a function of x

V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x

V(x) = ( 96 - 24*x - 16*x + 4*x²) * x

V(x) = 96*x - 40*x² + 4*x³

Tacking derivatives on both sides of the equation

V´(x) = 12*x² - 80*x + 96

V´(x) = 0 12*x² - 80*x + 96 = 0

Solving for x

x₁,₂ = 80 ± √ 6400 - 4608 / 24

x₁,₂ = 80 ± 42,33 / 24

x₁ = 5,10 We dismiss this solution since 2*x becomes 2*5,10 = 10,20

ant this value is bigger than 8 inches

x₂ = 1,60 in

Therefore dimensions of the box

a = 12 - 2*x ; a = 12 - 3,20 ; a = 8,8 in

b = 8 - 2*x ; b = 8 - 3,20 ; b = 4,80 in

And the volume of the open box is:

V(max) = 8,8*4,8*1,6

V(max) = 67,58 in³

How do we Know that is the maximun value for V?

We find V´´(x) = 24*x - 80 for x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has a local maximun for a value of x = 1,6

3 0

3 years ago

4. The students in Mr. Michael’s art class are decorating a booth for Harvest Day. They have blue cloth that is 60 inches long,

MrRissso [65]

Length of blue cloth is 60 inches , length of gold cloth is 48 inches and length of white cloth is 72 inches.

a.

As, the length of all pieces are equal, so for getting the greatest possible length of the pieces, we need to find GCF(greatest common factor) of 60, 48 and 72.

First we will factor out all three numbers completely......

$60=2*2*3*5\\ \\ 48=2*2*2*2*3\\ \\ 72=2*2*2*3*3$