Mathematics, 19.09.2019 20:10 sierram298

Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. the cardboard is 10 cm by 10 cm. the volume v(x) in cubic cm of the open top box is a function of the side length x in cm of the square cutouts

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Answer from: ashanty45

The volume of a shape is the amount of space in it;

The volume as a function of side length (x) is: V(x)= 4x^3 - 40x^2 + 100x

From the question, we have the dimension of the cardboard to be;

Length = 10

Width = 10

When side length (x) is removed from the cardboard, the dimension of the box becomes:

Length = 10 - 2x

Width = 10 - 2x

Height = x

So, the volume of the box is:

$Volume = Length \times Width \times Height$

Substitute known values

$Volume = (10 - 2x) \times (10 - 2x) \times x$

Expand

$Volume = (10 - 2x) \times (10x - 2x^2)$

Expand

Volume = 100x - 20x^2 - 20x^2 + 4x^3

Volume = 100x - 40x^2 + 4x^3

Rewrite as:

Volume = 4x^3 - 40x^2 + 100x

Express as a function

V(x)= 4x^3 - 40x^2 + 100x

Hence, the required function is: V(x)= 4x^3 - 40x^2 + 100x

Read more about volume functions at:

link

Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding

Answer from: tinytoonjr8052

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

The domain for x is all real numbers greater than zero and less than 5 com

Step-by-step explanation:

The question is

What is the volume of the open top box as a function of the side length x in cm of the square cutouts?

see the attached figure to better understand the problem

Let

x -----> the side length in cm of the square cutouts

we know that

The volume of the open top box is

V=LWH

we have

$L=(10-2x)\ cm$

$W=(10-2x)\ cm$

$H=x)\ cm$

substitute

$V(x)=(10-2x)(10-2x)x\\\\V(x)=(100-40x+4x^{2})x\\\\V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

Find the domain for x

we know that

$(10-2x) 0\\10 2x\\ 5 x\\x < 5\ cm$

The domain is the interval (0,5)

The domain is all real numbers greater than zero and less than 5 cm

therefore

The volume of the open top box as a function of the side length x in cm of the square cutouts is

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

Answer from: Quest

we need the options

step-by-step explanation:

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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