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Citrus2011 [14]
4 years ago
8

A box with a square base and open top must have a volume of 237276 cm^3. We wish to find the dimensions of the box that minimize

the amount of material used. Find a formula for the surface area of the box in terms of only x, the length of one side of the square base.[Hint: use the volume formula to express the height of the box in terms of x.]
Mathematics
1 answer:
svp [43]4 years ago
7 0

Answer:

A(x)=\dfrac{x^3+949104}{x}

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 237276 cubic centimetre. We want to find a formula for the surface area of the box in terms of only x, the length of one side of the square base.

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume,

V=x^2h=237276\\\\h=\dfrac{237276}{x^2}

Surface Area of the box = Base Area + Area of 4 sides

Area, A(x,h)=x^2+4xh

Substitute h derived above into A(x,h)

Area=x^2+4x(\frac{237276}{x^2})\\\\A(x)=x^2+\dfrac{949104}{x}\\\\A(x)=\dfrac{x^3+949104}{x}

Therefore, a formula for the surface area of the box in terms of only x, the length of one side of the square base is:

A(x)=\dfrac{x^3+949104}{x}

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According to the stem-and-leaf plot above, how many drivers travel above 60
frutty [35]

Answer:

B. 14

Step-by-step explanation:

When reading a stem and leaf plot, the outside numbers represent the tens and the inside numbers represent the units.

For example, take 5 | 4.

5 is the ten and 4 is the unit, making it 54.

If you understand that, then I think you'll understand how I got my answer.

3 0
3 years ago
A building is of unknown height. At a distance of 400 feet away from the building, an observer notices that the angle of elevati
Harman [31]

Given :

A building is of unknown height. At a distance of 400 feet away from the building .

An observer notices that the angle of elevation to the top of the building is 35º and that the angle of elevation to a poster on the side of the building is 15º .

To Find :

How far is the poster from the roof of the building .

Solution :

Height is given by :

h=d\times tan\theta

( Here , \theta is angle of elevation )

So , height of tower :

H=400\times tan 35^o\\\\H=280.08 \ feet

For height of poster :

h=400\times tan 15^o\\\\h= 107.18\ feet

Therefore , distance of poster from the roof of the building is :

( 280.08-107.18)  =  $$172.9\ feet

Hence , this is the required solution .

7 0
4 years ago
Find in factord form -9n+n^2=0
MArishka [77]

Answer:

n(-9+ n) =0

Step-by-step explanation:

-9n+n^2=0   Kind of use 'reverse distributive' property

n (-9 + n) = 0

6 0
2 years ago
7.C.J. says the quotient of -3/4 divided by 1/4 is - 1/3
Elanso [62]

The correct quotient is -3

The mistake CJ likely made is multiplying using the reciprocal of -3/4. The correct option is d. He multiplied using the reciprocal of -3/4

From the question,

We are to determine the correct quotient.

The given division operation to be carried out is -3/4 divided by 1/4

The correct quotient can be determined as shown below

-\frac{3}{4} \div \frac{1}{4}

Multiply -\frac{3}{4} by the reciprocal of \frac{1}{4}

The reciprocal of \frac{1}{4} is  \frac{4}{1}

Then, we get

-\frac{3}{4} \times \frac{4}{1}

This gives

-\frac{12}{4}

= -3

The correct quotient is -3

The mistake CJ likely made is multiplying using the reciprocal of -3/4.

Hence, the correct quotient is -3

The mistake CJ likely made is He multiplied using the reciprocal of -3/4. The correct option is d. He multiplied using the reciprocal of -3/4

Learn more here: brainly.com/question/13124034

6 0
3 years ago
Melissa’s family is driving out of state to her grandmother’s house. They know that it takes 20 gallons of gas to get there, and
katen-ka-za [31]

Answer:

The family budget to make the one-way trip should be $70.

Step-by-step explanation:

Given: The cost of three gallons of gasoline=$10.50

Therefore, the cost of one gallon of gasoline=

Since, they need 20 gallons for driving out of state to her grandmother’s house.

The cost of 20 gallons of gasoline =  

Therefore, The family budget to make the one-way trip should be $70.

Hope this <u><em>Helped!</em></u> :D

8 0
4 years ago
Read 2 more answers
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