Thomas buys a cardboard sheet that is 12 by 8 inches. Create an equation for this situation, find the zeros, and sketch the function. What is the size of the cutout he needs to make so that he can fit the maximum amount of food in the box? If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be? What would be the dimensions of this box? Using complete sentences, explain the connection between the cutout and the volume of the box. Design an equation that would work for any cardboard sheet length, q, and width, p.

QUESTION POSTED AT 19/02/2020 - 01:10 PM

Answered by admin AT 19/02/2020 - 01:10 PM

For the answer to the question above,

1. If we let x as the side of the square cut-out, the formula for the capacity (volume) of the food dish is:
V = (12 - 2x)(8 - 2x)(x)
V = 96x - 40x^2 + 4x^3
To find the zeros, we equate the equation to 0, so, the values of x that would result to zero would be:
x = 0, 6, 4

2. To get the value of x to obtain the maximum capacity, we differentiate the equation, equate it to zero, and solve for x.
dV/dx = 96 - 80x + 12x^2 = 0
x = 5.10, 1.57
The value of x that would give the maximum capacity is x = 1.57

3. If the volume of the box is 12, then the value of x can be solved using:
12 = 96x - 40x^2 + 4x^3
x = 0.13, 6.22, 3.65
The permissible value of x is 0.13 and 3.65

4. Increasing the cutout of the box increases the volume until its dimension reaches 1.57. After that, the value of the volume decreases it reaches 4.

5. V = (q -2x) (p - 2x) (x)
Post your answer

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QUESTION POSTED AT 28/03/2020 - 12:59 PM

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QUESTION POSTED AT 28/03/2020 - 12:59 PM

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QUESTION POSTED AT 28/03/2020 - 12:57 PM

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QUESTION POSTED AT 28/03/2020 - 12:56 PM

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ANSWERED AT 28/03/2020 - 12:56 PM


QUESTION POSTED AT 28/03/2020 - 12:56 PM

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Plug into the above with A(4,5) and B(-4,11).

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ANSWERED AT 28/03/2020 - 12:55 PM


QUESTION POSTED AT 28/03/2020 - 12:55 PM

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QUESTION POSTED AT 28/03/2020 - 12:52 PM

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QUESTION POSTED AT 28/03/2020 - 12:52 PM

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Answer:

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Step-by-step explanation:

Since, if y = f(x) is a function,

Then y = a f(x) gives a vertical stretch if a > 1 and gives a vertical compression if 0 < a < 1.

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ANSWERED AT 28/03/2020 - 12:51 PM


QUESTION POSTED AT 28/03/2020 - 12:51 PM

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QUESTION POSTED AT 28/03/2020 - 12:49 PM

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ANSWERED AT 28/03/2020 - 12:48 PM


QUESTION POSTED AT 28/03/2020 - 12:48 PM

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ANSWERED AT 28/03/2020 - 12:48 PM


QUESTION POSTED AT 28/03/2020 - 12:48 PM

What are the intercepts of 6x + 8y = 24? a.(4, 0) and (0, 1) b.(12, 0) and (0, 1) c.(3, 0) and (0, 4) d.(4, 0) and (0, 3)

6x + 8y = 24

x intercept is the value when y =0 & y intercept is the value when x=0


for y=0 ==> 6x+0 =24 ==> x=4 for x=0==> 0+8y =24 ==> y=3

(4,0) & (0,3) (ANSWER d)

ANSWERED AT 28/03/2020 - 12:46 PM


QUESTION POSTED AT 28/03/2020 - 12:46 PM

Ιғ a cιrcle нaѕ a radιυѕ oғ 12 cм and a ѕecтor deғιned вy a 120 degree arc, wнaт ιѕ тнe area oғ тнe ѕecтor

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ANSWERED AT 28/03/2020 - 12:46 PM


QUESTION POSTED AT 28/03/2020 - 12:46 PM

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Answer:

The length of the longest metal rod that can be sent is 12 inches.

Step-by-step explanation:

As given, the only boxes available for shipping are 7-inch cubes. As Jorge needs to ship a thin metal rod to a metalworking shop, he will put the rods diagonally or space diagonally in the box.

The space diagonal of a cube can be found by the formula :

D=\sqrt{x^{2}+x^{2}+x^{2} }

= \sqrt{3} x

Here, x is 7 inches.

So, Diagonal is = \sqrt{3} \times7

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Rounding this to nearest whole number we get 12.

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ANSWERED AT 28/03/2020 - 12:44 PM


QUESTION POSTED AT 28/03/2020 - 12:44 PM

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ANSWERED AT 28/03/2020 - 12:44 PM


QUESTION POSTED AT 28/03/2020 - 12:44 PM