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
ale4655 [162]
3 years ago
14

we want to build a box with square base of side x and height and in such a way that the volume is 128 cubic inches. If we know t

hat the sum of the length of the length of its edges is equal to 64 inches, what should be the box dimensions?
Mathematics
1 answer:
sergij07 [2.7K]3 years ago
7 0

Answer:

4 in × 4 in × 8 in or  

6.47 in × 6.47 in × 3.06 in

Step-by-step explanation:

Data:

(1)                  V = 128 in³

(2)                  l = w = x

(3) 4(l + w + h) = 64 in  (There are 12 edges)

Calculation:

The formula for the volume of the box is

(4)                 V = lwh

(5)              128 = x²h          Substituted (1) and (2) into (4)

(6)                  h = 128/x²     Divided each side by x²

          l + w +h = 16            Divided (1) by 4

          x + x + h = 16           Substituted (2) into 6

(7)          2x + h = 16           Combined like terms

     2x + 128/x² = 16           Substituted (6) into (7)

        2x³ + 128 = 16x²        Multiplied each side by x²

2x³ - 16x²+ 128 = 0            Subtracted 16x² from each side

    x³ - 8x² + 64 = 0           Divided each side by 2

According to the Rational Zeros theorem, a rational root must be a positive or negative factor of 64.

The possible factors are ±1, ±2, ±4, ±8, ±16, ±32, ± 64.

After a little trial-and-error with synthetic division (start in the middle and work down) we find that x = 4 is a zero.              

4|1   -8     0   64

 <u>|      4  -16  -64 </u>

   1  -4  -16      0

So, the cubic equation factors into (x - 4)(x² - 4x + 16) = 0

We can use the quadratic formula to find that the roots of the quadratic are

x = 2 - 2√5 and x = 2+ 2√5

We reject the negative value and find that there are two solutions to the problem.

x = 4 in and x = 2 + 2√5 ≈ 6.472 in

Case 1. x = 4 in

h = 128/x² = 128/4² = 128/16 = 8 in

The dimensions of the box are 4 in × 4 in × 8 in

Also, 4(l + w + h) = 4( 4 + 4 + 8) = 4 × 16 =  64 in

Case 2. x = 6.472 in

h = 128/x² = 128/6.472² = 128/41.89 = 3.056 in

The dimensions of the box are 6.47 in × 6.47 in × 3.06 in

Also, 4(l + w + h) = 4( 6.47 + 6.47 + 3.06) = 4 × 16.00 =  64 in

The two solutions are

(a) 4 in       × 4 in      × 8 in

(b) 6.47 in × 6.47 in × 3.06 in    

You might be interested in
Violet's Botanical Garden produced flowers throughout the year. A graph demonstrating how many flowers she produced over a 12-mo
Lady bird [3.3K]

Answer:

  The domain represents a 12-month period of flower production

Step-by-step explanation:

The <em>domain</em> is <em>the horizontal extent of the graph</em>. Both the problem statement and the graph itself tell you that is a 12 month time period.

7 0
3 years ago
Read 2 more answers
C. The King football team ordered 50 hats. The cost of shipping was
kari74 [83]
The answer is $4.99 each
6 0
3 years ago
An electric company charges an initial monthly fee for service and a fixed rate per kilowatt-hours (kWh) used. This table shows
Vlada [557]

<em>Here we are required to determine the initial monthly fee charged by the electric company.</em>

The initial fee charged by the electric company is; C = $10

To solve this, we need to evaluate the slope and intercepts of the equation of the straight line graph of the relation.

y = mx + c.

  • where m = slope of the relation.

  • and c = <em>intercept = the initial fee charged by the electric company</em>.

  • y = <em>Monthly charge at each time</em>.

  • x = Usage

To find the slope;

  • m = (y2 - y1)/(X2 - x1)

  • m = (28 -22)/(150 - 100)

  • m = 6/50

  • m = 0.12.

By substituting m into the equation y = mx + c, alongside a pair of values of usage and monthly charge, we can obtain the intercept, c (i.e the initial fee charged).

Therefore, m = 0.12 , y = 82 and X = 600;

we then have;

  • 82 = 0.12(600) + c.

  • C = 82 -72

  • C = $10.

Therefore, the initial fee charged by the electric company is; C = $10.

Read more:

brainly.com/question/22163485

8 0
2 years ago
Simply the equation 3x+1=2x+5<br>​
kipiarov [429]

Answer:4

Step-by-step explanation: 3x+1−2x=2x+5−2x

                                               x + 1 = 5

                                               x+1−1=5−1

                                                x=4

3 0
2 years ago
Read 2 more answers
birute deposite $500 In a savings account with a simple interest rate of 1.3% . how could you use this information to find the i
vladimir2022 [97]

Money Birute deposited in a savings account = $500

Rate of simple interest per annum = 1.3%

▪︎We need to find the interest she will earn in 4 years.

We know that :

\tt \: \color{hotpink}simple \: interest \color{plum}=  \frac{principal \times rate \times time}{100}

In this case :

Principal = $500

Rate = 1.3%

Time = 4 years

Which means :

The simple interest she will earn in 4 years :

= \tt \frac{500 \times 1.3 \times 4}{100}

= \tt \frac{2600}{100}

\color{plum} = \tt\bold{\$26}

Thus, the simple interest she will earn in 4 years = $26

Amount = Principal + Interest

Amount she will gain after 4 years :

=\tt 500 + 26

\color{plum} = \tt\bold{\$526}

Thus, the amount she will gain after 4 years = $526

Amount change in her account = 526 - 500 = 26

We know that :

\tt \: \color{hotpink}percentage \: of \:  change\color{plum} =  \frac{change}{original \: price}  \times 100

Which means :

Percentage of change in her savings account :

=\tt  \frac{26}{500} \times 100

=\tt  \frac{26 \times 100}{500}

=  \tt\frac{2600}{500}

\color{plum} = \bold{\tt\bold{5.2\%}}

<h2>○=> Therefore :</h2>

▪︎Simple interest after 4 years = $26

▪︎Money she will earn after 4 years = $526

▪︎Percentage of change in her savings account = 5.2%

6 0
2 years ago
Other questions:
  • the sum of three times one number, x, and five times a second number,y, is 77. if the sum of the two numbers is 19, find the two
    10·1 answer
  • 7 - 3x = -1 pls help
    14·1 answer
  • An artist pours 60 gallons of paint equally into 8 containers how much paint is in each container?
    12·2 answers
  • A satellite is in an approximately circular orbit 3600 kilometers from Earth surface. The radius of Earth is about 6400 km. What
    9·1 answer
  • A rock outcrop was found to have 95.82% of its parent U- 238 isotope remaining. Approximate the age of the outcrop. The half-lif
    10·1 answer
  • You invest $500 in an account that has a annual interest rate of 5%, compounded quarterly for four years. What is the equivalent
    13·1 answer
  • Given: triangle LNK, m of angle NLK =72 degrees. m of angle N=58 degrees. MP is perpendicular bisector of side LK and intersects
    12·1 answer
  • What is the surface area of the sphere below?
    5·1 answer
  • HELP ME HELP HELP HELP ME
    12·2 answers
  • #16 i
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!