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Novosadov [1.4K]
3 years ago
13

PLZ HELP!!!! There is a box in your kitchen pantry that is a rectangular prism. Its volume is 64 cubic inches. How many differen

t Surface Areas are possible? What is the maximum Surface Area? What is the minimum Surface Area?
Mathematics
1 answer:
WINSTONCH [101]3 years ago
7 0
We know that the volume of a rectangular prism is given by:
V = A · h
where:
A = surface area 
h = height

Therefore, you can solve for A:
A = V / h
   = 64 / h

Now, you need to ask yourself by how many numbers you can divide 64. The possible heights are 64, 32, 16, 8, 4, 2 and 1.

Hence:
A) there are 7 possible surface areas (one for each possible height).

B) the <span>maximum Area will be that of the box with the minimum height:
A = 64 / 1 = 64

C) the minimum Area will be that of the box with the maximum height:
A = 64 / 64 = 1</span>
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According to the graph of H(w) below, what happens when w gets close to zero?
WINSTONCH [101]
D Because it will never be equal to 0 and it never changes its area to get bigger or smaller
8 0
3 years ago
Read 2 more answers
a daily newspaper has 10225 subscribers when it began publication. six years old later it has 8200 subscribers what is the avera
seraphim [82]

Answer:

The rate of change in number of subscriber for the six years is 3.62%

Step-by-step explanation:

Given as :

The initial subscriber of newspaper = p = 10225

The subscriber of newspaper after 6 years of publish = P = 8200

The time period = t = 6 years

Let The average yearly rate of change = r%

<u>Now, According to question</u>

The subscriber of newspaper after n years = initial subscriber × (1-\dfrac{\textrm rate}{100})^{\textrm time}

Or, P = p × (1-\dfrac{\textrm r}{100})^{\textrm t}

Or, 8200 = 10225 × (1-\dfrac{\textrm r}{100})^{\textrm 6}

Or, \dfrac{8200}{10225} =  (1-\dfrac{\textrm r}{100})^{\textrm 6}

Or, 0.80195 =  (1-\dfrac{\textrm r}{100})^{\textrm 6}

<u>Taking power \dfrac{1}{6} both side</u>

So, (0.80195 )^{\frac{1}{6}} = ((1 - \frac{r}{100} )^{6})^{\frac{1}{6}}

Or, 0.9638 = 1 - \dfrac{r}{100}

Or,  \dfrac{r}{100} = 1 - 0.9638

Or,  \dfrac{r}{100} = 0.0362

Or, r = 0.0362 × 100

i.e r = 3.62

So, The rate of change in subscriber = 3.62%

Hence, The rate of change in number of subscriber for the six years is 3.62% . Answer

4 0
3 years ago
What would be a line perpendicular to (2,3) (5,5)?
ladessa [460]

9514 1404 393

Answer:

  3x + 2y = 0   or   y = -3/2x

Step-by-step explanation:

The relationship between a line and its perpendicular is that their slopes are opposite reciprocals of each other. So, the thing you need to know about the line through the two given points is its slope. That is found using the slope formula:

  m = (y2 -y1)/(x2 -x1) . . . . . . where the two give points are (x1, y1) and (x2, y2)

Putting your point coordinates in this formula gives ...

  m = (5 -3)/(5 -2) = 2/3

Then the perpendicular line will have a slope that is the opposite reciprocal:

  slope of perpendicular = -1/m = -1/(2/3) = -3/2

You have not said whether the perpendicular line must meet any other requirement, so the simplest one we can write is ...

  y = mx + b . . . . . m is the slope and b is the y-intercept

  y = -3/2x . . . . . . has a y-intercept of 0 (goes through the origin)

Multiplying by 2 and adding 3x gives ...

  3x + 2y = 0 . . . . . standard form equation

_____

<em>Comment on the attachment</em>

The geometry program I used to create the attachment wrote the equation of the line through the given points as ...

 2x -3y = -5 . . . . . standard form equation

The equation of a perpendicular line can be created from this form by swapping the x- and y-coefficients and negating one of them. Simply swapping the coefficients would give ...

  -3x +2y = <something>

In standard form, we want the leading coefficient to be positive, so we can choose to negate the x-coefficient. The <something> can be zero to make the line go through the origin.

  3x +2y = 0 . . . . . a perpendicular in standard form

__

If you need to have the line go through a particular point, you can determine the constant value (on the right of the = sign) by putting the point coordinates in for x and y.

_____

Method summary:

  • find the slope of the given line
  • determine its opposite reciprocal to find the slope of the perpendicular line
  • use that new slope in an appropriate form to have the line go where you want it to go. (Point-Slope Form is often useful)

3 0
3 years ago
The cube of the difference of a number and 4
lbvjy [14]

Answer:

(x - 4)³

Step-by-step explanation:

"The cube of x" would be x³.  The difference of a number and 4 would be x - 4.

Therefore, "the cube of the difference of a number and 4" would be

(x - 4)³

6 0
3 years ago
Expand and simplify (x-2)(2x+4)
d1i1m1o1n [39]

Answer:

2 {x}^{2}  - 8

hope it's helpful ❤❤❤

THANK YOU.

7 0
2 years ago
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