It takes 28 minutes for 7 people to paint 7 walls.

Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl

Vikki [24]

Answer:

Height: 3/2 inches

Length: 12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

The new length of the cardboard = 15 -2x (because we cut from 4 corners)
The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

<=> V = $4x^3 -44x^2 +105x$

To maximum volume, we use the first derivative of the volume

$\dfrac{dV}{dx} = 0$

<=> $12x^2-88x+105=0$

<=> $\left(2x-3\right)\left(6x-35\right) = 0$

<=> 2x -3 = 0 or 6x -35 = 0

<=> x = 3/2 or x = 35/6

To determine which value of x gives a maximum, we evaluate

$\dfrac{d^2V}{dx^2}$ = 24x -88

If x = 3/2, we have:

$\dfrac{d^2V}{dx^2}$ = 24(3/2) -88 = -52

If x = 35/6, we have:

$\dfrac{d^2V}{dx^2}$ = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

Height: 3/2 inches

Length: 15-2(3/2) = 12 inches

Width: 7 - 2(3/2) = 4 inches

5 0

3 years ago

X2 + y2 − 4x + 12y − 20 = 0

balu736 [363]

Answer:

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Step-by-step explanation:

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5 0

3 years ago

What is the rate of change in distance for the first 5 minutes of the race

antoniya [11.8K]

15 I may be wrong but If I am please provide more information.

4 0

3 years ago

28.4.2 Test (CST): Transformations, Congruence, and Similarities, Part 2

frez [133]

Answer:

R'(2,4)

Step-by-step explanation:

When doing translations you subtract or add within the coordinates like a normal problem.

If it helps you, write it as seperate equations like:

1-1 and 5-1

Hope that helps ✓

8 0

2 years ago

I need 1-5 and 8 and 9 solved

meriva

Answer:

1. A

2. H

3.B

4. H

5. A

Those are the answers

Step-by-step explanation:

1. 30 - 2(-8)= 46

2. BODMAS applied 6-7 =-1

3. 45/-5=-9

4. Sum is h +73

5.BODMAS applied 60 /6 = 10

8 0

3 years ago