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
irina [24]
3 years ago
13

Thomas needs to buy a cardboard sheet that will allow him to make his 224 in 3 box. To help construct the box, he decided to cut

out 2 inch squares from both the lengths and widths. Given that the length will need to be 6 inches longer than the width create an equation for the volume of the box, find the zeroes, the dimensions of the box, and graph the function.
Mathematics
1 answer:
Slav-nsk [51]3 years ago
4 0

Answer:

Part 1; The volume of the box Thomas wants to make is 224 = 2·w² + 12·w

Part 2; The zeros for the equation of the function, are w = -14, or w = 8

Part 3

The width of the box is 8 inch

The length of the box, is 14 inches

The height of the box, is given as 2 inches

Part 4

Please find attached the graph of the function

Step-by-step explanation:

Part 1

The volume of the box Thomas wants to make, V = 224 in.³

The dimensions he cuts out from the length and width = 2 in² each

The length of the box = 6 inches + The width of the box

Let <em>l</em> represent the length of the box and let <em>w</em> represent the width of the box, we have;

l = 6 + w

The height of the box, h = The length of the cut out square = 2 inches

The volume of the box, V = Length, l × Width, w × Height, h

∴ V = l × w × h

l = 6 + w, h = 2

∴ V = (6 + w) × w × 2

V = 2·w² + 12·w,

The equation of the volume of the box, V = 2·w² + 12·w, where, V = 224

∴ 224 = 2·w² + 12·w

Part 2

The zeros of the equation for the volume of the box, V = 2·w² + 12·w, where, V = 224 are found as follows;

V = 224 = 2·w² + 12·w

∴ 2·w² + 12·w - 224 = 0

Dividing by 2 gives;

(2·w² + 12·w - 224)/2 = w² + 6·w - 112 = 0

∴ (w + 14) × (w - 8) = 0

The zeros for the equation of the function, are w = -14, or w = 8

Part 3

We reject the value, w = -14, therefore, the width of the box, w = 8 inch

The length of the box, l = 6 + w

∴ l = 6 + 8 = 14

The length of the box, l = 8 inches

The height of the box, <em>h</em>, is given as h = 2 inches

Part 4

The graph of the function created with MS Excel is attached

You might be interested in
An identification code is to consist of 2 letters followed by 3 digits. how many different codes are possible if repetition is p
Vedmedyk [2.9K]
I like the 'question mark' at the end:

26 letters (English), 10 digits (0,1,...9)

26*26*10*10*10 = 676000

Now, this was for LLDDD (Letter Letter Digit Digit Digit)

It seems this is the order they want. Other wise, one should multiply by all the combinations in the order: LDLDD, DLLDD, etc ... (10 combinations), but again it seems they want this LLDDD

So 676000



5 0
3 years ago
B) ¿Cuál es la relación entre el diametro y el radio?<br>​
kow [346]

Answer:

La circunferencia es una línea curva, y su longitud depende del radio o del diámetro. La relación matemática entre el radio (o diámetro) y la circunferencia se da por la siguiente fórmula: C = 2πr = πD. Donde C es la circunferencia y π=3.14.

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Which set of angles could be the interior angles of a triangles
qwelly [4]

Answer:

Step-by-step explanation:

3

6 0
2 years ago
P (a) =2/5 p(b)=1/4 ( a and b=1/25I did two events independent or dependent please help
juin [17]

we have

p (a) =2/5 p(b)=1/4 ( a and b=1/25

Remember that

we know that for two independent events A,B.

⇒ P(A∩B)=P(A)*P(B)

we have

P(A)=2/5 and P(B)=1/4

so

P(A∩B)=(2/5)*(1/4)=2/20=1/10

that means

<h2>events are dependent</h2>
8 0
9 months ago
April sold 75 tickets to the school Christmas play and collected $495. If adult tickets cost $8 and children tickets were $5 how
Ostrovityanka [42]

40 adult tickets were sold and 35 children tickets were sold

<em><u>Solution:</u></em>

Let "a" be the number of adult tickets sold

Let "c" be the number of children tickets sold

Cost of 1 adult ticket = $ 8

Cost of 1 children ticket = $ 5

<em><u>Given that April sold 75 tickets to the school Christmas play and collected $495</u></em>

Number of tickets sold = 75

number of adult tickets sold + number of children tickets sold = 75

a + c = 75 ----- eqn 1

<em><u>Given that April collected $495</u></em>

Thus we can frame a equation as:

number of adult tickets sold x Cost of 1 adult ticket + number of children tickets sold x Cost of 1 children ticket = $ 495

a \times 8 + c \times 5 = 495

8a + 5c = 495 ----- eqn 2

<em><u>Let us solve eqn 1 and eqn 2 to find values of "a" and "c"</u></em>

From eqn 1,

a = 75 - c ---- eqn 3

Substitute eqn 3 in eqn 2

8(75 - c) + 5c = 495

600 - 8c + 5c = 495

-3c = 495 - 600

-3c = - 105

<h3>c = 35</h3>

Substitute c = 35 in eqn 3

a = 75 - 35

<h3>a = 40</h3>

Thus 40 adult tickets were sold and 35 children tickets were sold

8 0
3 years ago
Other questions:
  • To convert 400 L to mL, you would move the decimal point _____ places to the _____.
    7·1 answer
  • Which expression is equivalent to (8^2)-4 ??
    7·2 answers
  • All of the following are equivalent ratios except...<br><br>a) AR:RC<br>b) BS:BC<br>c) AR:AC
    10·1 answer
  • In the image, point A marks the center of the circle.
    11·2 answers
  • For which values is this function undefined?
    12·1 answer
  • Cos ²a/2 = (tana + sina/ 2 tan a)<br><br>​
    13·1 answer
  • ABC ∆ where Angle A =90° , AB = 12 m, AC = 9 m . Find BC ?
    15·1 answer
  • Which set of ordered pairs does not represent a function? O {(-3,-9), (7,9), (9, 1), (7,3)} O {(-3,8),(-6,5), (-5, -6), (1,-6)}
    15·2 answers
  • 4(x + 2)- 6 = 14
    10·1 answer
  • Two angles of a quadrilateral measure 130 and 10. The other two angles are in a ratio 2.9. What are the measures of those two a
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!