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Rus_ich [418]
3 years ago
15

A packaging company is going to make open-topped boxes, with square bases, that hold 140 cubic centimeters. What are the dimensi

ons of the box that can be built with the least material? (Round your answers to the nearest hundredth.)
Mathematics
1 answer:
Kitty [74]3 years ago
8 0

Answer:

x = 6.54 cm

h = 3.27 cm

Step-by-step explanation:

Volume of open top box

V = 140 cm³

Dimensions of the box

It is a base square box then area of the base of side x is

A(b) = x²

And we will call h the height of the box then

V = 140   ⇒    140 = x²*h     ⇒   h = 140/ x²

We have to calculate the area of the 4 sides

Area of one side is  As = x*h        ⇒ total area of 4 sides = 4 x* 140/x²  

Ats  =  560/x

Then Total area of the box is

A(t)  =  Area of the base  +  Total area of sides

A(x)  =   x²  +   560/x

Taking derivatives on both sides of the equation we get:

A´(x)  =  2x   -  560/x²

A´(x)  =  0     ⇒    2x   -  560/x² = 0   ⇒   2x³  -  560  = 0

x³  =  280     ⇒    x  = 6.54 cm

And h      h  =  140/ (6.54)²    ⇒ h =  140/ 42.77    h  = 3.27 cm

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2 years ago
Write the fraction or mixed number as a decimal 4/10
katovenus [111]
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4 0
3 years ago
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6 0
2 years ago
Two planes start flying towards each other simultaneously from two different cities. The distance between the cities is 960 mile
ANTONII [103]

Answer:

257.5 mph

332.5 mph

Step-by-step explanation:

The initial distance between the two planes is 960 miles, while the final distance (after t=1.5 h) is 75 miles, so the total distance covered by the two planes in 1.5h is

d=960-75=885 miles

Calling v1 and v2 the velocities of the two planes, we have the following equations:

(1) v_1 = v_2 + 75 --> velocity of plane 1 exceeds velocity of plane 2 by 75 mph

(2) v_1 t+ v_2 t=885 --> the total distance covered by the two planes is 885 miles (t=1.5 h is the time, and the products v1 t and v2 t represent the distance covered by each plane)

Substituting t=1.5 h, the second equation becomes:

1.5 v_1+1.5 v_2=885\\v_1 + v_2 = 590

By substituting (1) into this last equation, we find:

(v_2+75)+v_2 = 590\\2v_2 + 75 = 590\\2v_2 = 515\\v_2=257.5

And substituting this back into eq.(1), we find

v_1 = 257.5 + 75=332.5

So, the speeds of the two planes are

257.5 mph

332.5 mph



3 0
3 years ago
Please answer all the questions if possible, due 2morrow... also, is what I did for the top answer right?
geniusboy [140]
1a. It does say y is "less than 8", which means 7, 6, 5, 4, etc. So it should be y < 8, with the arrow going from 8 to the the left. 
Everything else in 1 is correct. 

For 2, you're just picking out which of the given numbers satisfy the inequality, for example
a. 14, 15, 16 are solutions. 13 is not because it is less than 14.

3. Same thing as 1 
8 0
3 years ago
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