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dlinn [17]
2 years ago
6

Answer this question please ASAP!!!

Mathematics
1 answer:
Ymorist [56]2 years ago
7 0
17.4%

If helped mark me the brainiest!!
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An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out squares of equal size from the fou
Burka [1]

Answer:

Maximum volume of the box will be 7.41 cubic feet.

Step-by-step explanation:

Open box has been made from a metal sheet measuring 3 ft and 8 ft.

Let four square pieces were removed from the four corners with one side measurement x ft.

Volume of the open box = Length × width × height

Length of the box = (3 - 2x) ft

Width of the box = (8 - 2x) ft

Height of the box = x ft

Volume of the box = (3 - 2x)(8 - 2x)x

V = (24 - 6x - 16x + 4x²)x

V = 24x - 22x² + 4x³

Now we take the derivative of V with respect to x and equate the derivative to zero,

\frac{d}{dx}(V)=\frac{d}{dx}(24x - 22x^{2}+4x^{3})

V' = 24 - 44x + 12x²

V' = 0

12x² - 44x + 24 = 0

3x² - 11x + 6 = 0

3x² - 9x - 2x + 6 = 0

3x(x - 3) - 2(x - 3) = 0

(3x - 2)(x - 3) = 0

(3x - 2) = 0

and (x - 3) = 0

Therefore, x = 3, \frac{2}{3}

For x = 0.67

Length of the box = (3 - 2x) = 3 - 1.34

                              = 1.66 ft

Width of the box = (8 - 2x) = 8 - 1.34

                            = 6.66 ft

Volume of the box = 0.67 × 1.66 × 6.66

V = 7.41 cubic feet.

Similarly, for x = 3,

Length of the box = (3 - 2\times 3) = -3

which is negative but the length of the box can not be negative.

Therefore, maximum volume of the box will be 7.41 cubic feet.

6 0
3 years ago
On average and adult rest of it breathes in and out 12 times per minute about how many breaths will an adult take in a day?
Firlakuza [10]
Ques 1: 1min->12 breathsl
24*60=1440->12*24*60=17280breaths
answer : 17280 breaths
ques 2: 2 weeks(6*2=12days) -> 2808
1 day->2808/12=234 miles
answer :234 miles
8 0
3 years ago
Enter the number that makes the equation true.<br><br> 0.26 - 41/100 = blank/100 - 41/100
Lerok [7]
Note that you are subtracting the same number from both sides. Thus, blank/100 must equal .26. Convert .26 to a fraction by placing it over 100 and removing the decimal point: 26/100. blank = 26
5 0
3 years ago
A bus eats 4 people in a row and there are 12 rows how would fit on 2 buses?
BARSIC [14]

Answer:

4 \times 12 \times 2 = 96

96 people in total.

BTW its seats and I think you meant "how many"

6 0
3 years ago
Cristina has completed .4 of his test. The test has 40 questions total. if he completes 12 more how many more will he have left?
bixtya [17]

24 because she already completed four and if she completes twelve more that that will be 24 hope that helps


5 0
3 years ago
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