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ikadub [295]
2 years ago
8

Need the answers for 4-8

Mathematics
1 answer:
Fed [463]2 years ago
6 0

Answer:

hope this helps you out ask me if you need more help

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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
Anyone know how to do this?!!
iren2701 [21]

Answer:

slope is -1/4

Step-by-step explanation:

\frac{-4}{12}=\frac{-1}{4}

\frac{-2}{8}= \frac{-1}{4}

and so on...

formula: \frac{x}{y}

hope this helps!!!

6 0
2 years ago
The house Trevor's family lives in has 6 66 people (including Trevor) and 3 33 bathrooms. In the past month, each person showere
yKpoI14uk [10]

Answer:

The amount Trevor's family pay per minute on shower water is $0.005.

Step-by-step explanation:

The cost of water is,

Cost = $0.20/liter

Amount of water used over the entire month:

Amount of water used = 72 liters

Compute the total water cost as follows:

Total water cost = Amount of water used × Cost

                           = 72 × 0.20

                           = $14.4/liter

The average number of minutes each person showered is:

Average number of minutes = 480 minutes.

The number of people in Trevor's house:

N = 6

Compute the total amount of time the 6 person showered as follows:

Total amount of time = Average number of minutes × N

                                   = 480 × 6

                                   = 2880 minutes

Compute the pay per minute on shower water as follows:

Pay per minute on water = Total water cost ÷ Total amount of time

                                          = $14.4 ÷ 2880

                                          = $0.005

Thus, the amount Trevor's family pay per minute on shower water is $0.005.

4 0
3 years ago
; the boy to girl ratio is 10 to 8. If there are 16 girls in the class, how many boys are there?​
Zigmanuir [339]

Answer:

There are 20 boys

Step-by-step explanation:

4 0
2 years ago
During a nine-hour snowstorm, it snows at a rate of 2 inches per hour for the first 3 hours, at a rate of 3 inches per hour for
Softa [21]

Answer:

use f(x)=y=mx+b

let snow = S, time = t instead of y and x

S(t)=mt+b

The rate of inches per hour represents the slope of the graph, m.

The y-variable would be the amount of snow, S.

The x-variable would be the time, t, in hours.

The function has three pieces:

i) S(t)= 2t (slope = 2)

ii) S(t) = 3t (slope = 3)

iii) S(t) = 0.75t (slope = 0.75)

For the first piece, i), t=3, so the amount of snow is 6 inches.

For the second piece, ii) t=5, so the amount of snow is 15 inches.

For the third piece, iii) t=1, so the amount of snow is 0.75 inch.

In total, it snowed 21.75 inches.

total snow

4 0
3 years ago
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