1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kvv77 [185]
3 years ago
14

You work for a cereal company as a box designer. Your job is to find the dimensions of a box. The volume of the box is given by

the following:
v(x)=8x^3-108x^2+360


a. Use a graphing calculator to determine the length, width, and height of the box so it will hold the largest possible volume.


b. Factor the polynomial completely to find the x-intercepts of the graph. In context of this problem, what do the intercepts represent?


c. What is the domain and range for the box?
Mathematics
1 answer:
ivolga24 [154]3 years ago
7 0

Question:

You work for a cereal company as a box designer. Your job is to find the dimensions of a box. The volume of the box is given by the following:

v(x)=8·x³-108·x²+360·x

Answer:

a. To hold the largest possible volume, the length, height, and width are;

Length, l of the box = 10.583

Width, w of the box = 3.791

Height, h of the box = 8.835

b. The x intercepts are;

x = 0

x = 15/2

x = 6

The intercept represents the points of the function at which the volume of the box change from negative to negative and back to positive

c. The domain range is all real numbers, that is from -∞ to +∞

Step-by-step explanation:

Since the volume V(x) = 8·x³ - 108·x² + 360·x, we have fo maximum volume;

\frac{\mathrm{d} \left (8\cdot x^{3} - 108\cdot x^{2} + 360\cdot x  \right )}{\mathrm{d} x}= 0

Therefore. 24·x² - 216·x + 360 = 0

Solving the quadratic equation, we have

(2·x - (9 - √21))(2·x - (9 + √21))

Therefore, x = (9 - √21)/2 or x = (9 + √21)/2

P

Therefore, from the v(x) equation we have by factorizing;

v(x) = 8·x³ - 108·x² + 360·x = 4·x·(2·x - 15)·(x - 6)

Plugging the possible values of x for maximum v(x), we obtain

For x = (9 - √21)/2, v(x) = 354.468

For x = (9 + √21)/2, v(x) = -30.468

Hence the for maximum v(x), x = (9 - √21)/2

The sides are thus;

4·x·(2·x - 15)·(x - 6)

Where:

4·x = 8.835

\left |2\cdot x - 15  \right | = 10.583

\left | x - 6\right | = 3.791

The length, l of the box = 10.583

The width, w of the box = 3.791

The height, h of the box = 8.835

b. The factorization of the polynomial gives;

v(x) =  4·x·(2·x - 15)·(x - 6)

Therefore, the x intercepts are;

x = 0

x = 15/2

x = 6

The intercept represents the points of the function at which the volume of the box will be positive, hence the possible values of the dimensions

c. The domain of the function v(x) = 8·x³ - 108·x² + 360·x (which is a polynomial without variables or radicals as the denominator) is the set of all real numbers from -∞ to ∞.

You might be interested in
What is the slope of the line shown?
sashaice [31]
The slope would be -1/3
3 0
3 years ago
Read 2 more answers
Find the value of x to the nearest tenth. (figure not drawn to scale)
givi [52]

Answer:

16 +6=22 9 +x = 22

x=22-9

x= 13

4 0
3 years ago
Hello can somedy help me please<br> thank you in advance
uysha [10]

Answer:

circumference of the circle=2πr

2 \times 3.142 \times 0.9 \\5.6556cm

5.7 cm

5 0
2 years ago
What is the mean and MAD of 12,16,15,11,31
Dmitry_Shevchenko [17]

Answer:

The mean is 17.

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Please i need help jk im lazy ZZZzzzzzz
Bond [772]

Answer:

the first one is $6.66

Step-by-step explanation:

the 3 items added up is 74 cents, then 74 is multiplyed by 9.

5 0
2 years ago
Other questions:
  • I don't get this at all
    6·1 answer
  • Simplify 3*a*2*b<br> *=multiply
    11·1 answer
  • [3x^(2/3)] • [7x^(1/4)]<br><br> photo of equation above
    14·2 answers
  • PLEASE HELP! ITS DUE TODAAY!
    9·2 answers
  • Help me solve this please I need help
    11·2 answers
  • 2x+3 ft <br>2x+3 ft <br>polynomial expression<br>​
    6·1 answer
  • Im thinking its a22<br>consider the matrix<br><br><br>a32<br><br>a23<br><br>a33<br><br>a22​
    14·1 answer
  • What is this answer?
    9·2 answers
  • Darnell's team scored 40 points at the game. Darnell scored 15% of the team's points. How many points did Darnell score?
    14·1 answer
  • Help pleaseeeeeeeeeeeeeee
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!