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Lady bird [3.3K]
2 years ago
14

Hi please help !!! asap

Mathematics
1 answer:
Taya2010 [7]2 years ago
7 0
Ayurveda is the traditional Hindu system of medicine, which is based on the idea of balance in bodily systems and uses diet, herbal treatment, and yogic breathing
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Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl
Vikki [24]

Answer:

Height: 3/2 inches

Length:  12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

  • The new length of the cardboard = 15 -2x (because we cut from 4 corners)
  • The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

<=> V = 4x^3 -44x^2 +105x

To maximum volume, we use the first derivative of the volume

\dfrac{dV}{dx} = 0

<=> 12x^2-88x+105=0

<=> \left(2x-3\right)\left(6x-35\right) = 0

<=> 2x -3 = 0 or 6x -35 = 0

<=> x = 3/2 or x = 35/6

To determine which value of x gives a maximum, we evaluate

\dfrac{d^2V}{dx^2} = 24x -88

  • If  x = 3/2, we have:

\dfrac{d^2V}{dx^2}= 24(3/2) -88  = -52

  • If x = 35/6, we have:

\dfrac{d^2V}{dx^2} = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

Height: 3/2 inches

Length: 15-2(3/2) = 12 inches

Width: 7 - 2(3/2) = 4 inches

5 0
2 years ago
On Monday, Noah finds 19 big grasshoppers and 9 small ones in his garden. What is the experimental probability of finding a smal
Lina20 [59]
That would be   9 /(19+9)   = 9/28 Answer
5 0
3 years ago
Read 2 more answers
Simplify each radical expression
nlexa [21]
31.
5 \sqrt{6}  - 3 \sqrt{6}  = 2 \sqrt{6}
32.
\sqrt{2} ( \sqrt{8}  +  \sqrt{6} ) \\  \sqrt{16}  +  \sqrt{12}  \\ 4 + 2 \sqrt{3}
33.
(3 \sqrt{2}  - 2 \sqrt{5} )(4 \sqrt{2}  + 2 \sqrt{5} ) \\ 12 \sqrt{4}  + 6 \sqrt{10}  - 8 \sqrt{10}  - 4 \sqrt{25}  \\ 24 - 2 \sqrt{10}  - 20 \\ 4 - 2 \sqrt{10}
pls mark me as brainliest
3 0
3 years ago
What is the slope of the line passing through the points (5,7) and (−1,19)?
N76 [4]
The slope is -2..........
6 0
3 years ago
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Connor wants to drive from Tucson to the Grand Canyon a distance of 338 miles if he drives a steady rate of 52 mph how many hour
alexandr1967 [171]

Answer:

6.5 Hours

Step-by-step explanation:

Divide 338 by 52 to get the answer

5 0
3 years ago
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