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bogdanovich [222]
4 years ago
5

I have a square piece of cardboard that is 24 inches on each side. i want to cut out a square in each corner and the fold up the

sides to make an open box. how big should i make the squares that i cut out in order to make the box have the greatest volume?
Mathematics
1 answer:
Kobotan [32]4 years ago
5 0
A square of side 4 inch must be cut in order to get greatest volume.

after cutting a square of side x inch and folding it into a box, the length of each side of the box's base is (24-2x) inch and box's height is x inch.
∴volume, V= (24-2x)² × x 
differentiate V with respect to x and put dV/dx = 0
we get x =12 and x= 4 
x=12 is not possible so maximum volume is obtained when x=4 inch.
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Write the equation of the line which passes<br> through the points (4,2) and (-3, 1)
Finger [1]

Answer:

y = 1/3x + 4/7

Step-by-step explanation:

Slope Formula: m=\frac{y_2-y_1}{x_2-x_1}

Slope-Intercept Formula: y = mx + b

Step 1: Find slope <em>m</em>

m = (1 - 2)/(-3 - 4)

m = -1/-7

m = 1/7

y = 1/7x + b

Step 2: Find y-intercept <em>b</em>

1 = 1/7(3) + b

1 = 3/7 + b

b = 4/7

Step 3: Write linear equation

y = 1/3x + 4/7

4 0
3 years ago
The surface area of a rectangular prism is 10.4 in2. What is the surface area of a similar prism that is larger by a scale facto
gavmur [86]
The surface areas of similar solids is proportional to the square of their sides 
<span>since the ratio of sides is 1 : 3 </span>
<span>their surface areas have the ratio 1</span>²<span>: 3</span>²<span> or 1:9 </span>
<span>so the surface area is 9(10.4) or 93.6 </span>

<span>or </span>

<span>original width = x </span>
<span>original length = y </span>
<span>original heigt = z </span>
<span>original surface area = 2(xy) + 2(xz) + 2(yz) </span>
<span>= 2(xy + xz + yz) </span>

<span>new width = 3x </span>
<span>new length = 3y </span>
<span>new height = 3z </span>
<span>new surface area = 2(9xy) + 2(9xz) + 2(9yz) </span>
<span>= 18(xy + xz + yz) </span>

<span>ratio of new to old = 18(xy + xz + yz) : 2(xy + xz + yz) </span>
<span>= 9:1</span>
7 0
3 years ago
33. How will you check if your solution is correct?​
Vsevolod [243]

Answer:

you basically do the same things just backwards

Step-by-step explanation:

for example 9+9=18    well to double check your work all you do is flip to equation 18-9=9

5 0
2 years ago
Find the exact value of sec 795
sladkih [1.3K]
Evaluate the trigonometric expression using sum and difference formulas.

3 0
3 years ago
Read 2 more answers
Sally can paint the wall in 54 minutes. If Sally and Ethan work together, they can paint the wall in 36 minutes. How much time d
MAXImum [283]

Answer:

108\ minutes

Step-by-step explanation:

1) we know that

Sally can paint the wall in 54 minutes

so

The 100% of the wall ------> she can paint in 54 minutes

by proportion

calculate how much is the percent of the work in 36 minutes

\frac{100\%}{54} =\frac{x\%}{36}\\ \\x=36*100/54\\ \\x=66.67\%

That means

Sally in 36 minutes can paint the 66.67% of the wall

2) Sally and Ethan work together, they can paint the wall in 36 minutes

so

Ethan in 36 minutes can paint (100%-66.67%)=33.33%

by proportion

Calculate how much time does it take for Ethan to paint the wall by herself

\frac{33.33\%}{36} =\frac{100\%}{x}\\ \\x=36*100/33.33\\ \\x=108\ minutes

6 0
3 years ago
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