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
MakcuM [25]
3 years ago
14

A box with an open top will be constructed from a rectangular piece of cardboard. The piece of cardboard is 10 inches wide and 1

4 inches long. The box will be constructed by cutting out equal squares of side x at each corner and then folding up the sides. What is the appropriate domain for the function V(x) that gives the volume of the box as a function of x?
Mathematics
1 answer:
kupik [55]3 years ago
5 0

Answer:

Domain of the function is  { x : x∈R, x>0 } or (0,∞).

Step-by-step explanation:

It is given that the dimensions of a rectangular piece of cardboard are

Length = 14 inch

Width = 10 inch

The box will be constructed by cutting out equal squares of side x at each corner and then folding up the sides. So the dimensions of the box are

Length = 14-2x inch

Breadth = 10- 2x inch

Height = x inch

The volume of cuboid box is

V=length\times breadth \times height

The volume function of the box is

V=(14-2x)\times (10-2x)\times x

V=(14-2x)(10-2x)x

The volume function is V=(14-2x)(10-2x)x.

It is a polynomial function and domain of a polynomial function is all real numbers.

Here, x represents the height of the box. So, value of x must be a positive real number.

Domain of the function is

Domain = { x : x∈R, x>0 }

It can be written as (0,∞).

Therefore, domain of the function is  { x : x∈R, x>0 } or (0,∞).

You might be interested in
ПОЖАЛУЙСТА ПОМОГИТЕ РЕШИТЬ ДАЮ 23 ОЧКА!!!
posledela

(Простите, пожалуйста, мой английский. Русский не мой родной язык. Надеюсь, у вас есть способ перевести это решение. Если нет, возможно, прилагаемое изображение объяснит достаточно.)

Use the shell method. Each shell has a height of 3 - 3/4 <em>y</em> ², radius <em>y</em>, and thickness ∆<em>y</em>, thus contributing an area of 2<em>π</em> <em>y</em> (3 - 3/4 <em>y</em> ²). The total volume of the solid is going to be the sum of infinitely many such shells with 0 ≤ <em>y</em> ≤ 2, thus given by the integral

\displaystyle 2\pi \int_0^2 y \left(3-\frac34 y^2\right) \,\mathrm dy = 2\pi \left(\frac32 y^2 - \frac3{16} y^4\right)\bigg|_0^2 = 6\pi

Or use the disk method. (In the attachment, assume the height is very small.) Each disk has a radius of √(4/3 <em>x</em>), thus contributing an area of <em>π</em> (√(4/3 <em>x</em>))² = 4<em>π</em>/3 <em>x</em>. The total volume of the solid is the sum of infinitely many such disks with 0 ≤ <em>x</em> ≤ 3, or by the integral

\displaystyle \pi \int_0^3 \left(\sqrt{\frac43x}\right)^2 \,\mathrm dx = \frac{2\pi}3 x^2\bigg|_0^3 = 6\pi

Using either method, the volume is 6<em>π</em> ≈ 18,85. I do not know why your textbook gives a solution of 90,43. Perhaps I've misunderstood what it is you're supposed to calculate? On the other hand, textbooks are known to have typographical errors from time to time...

8 0
3 years ago
What formula should be used to find the circumference of a circle
Inessa05 [86]
The circumference = π x the diameter of the circle (Pi multiplied by the diameter of the circle). Simply divide the circumference by π and you will have the length of the diameter. The diameter is just the radius times two, so divide the diameter by two and you will have the radius of the circle
3 0
3 years ago
Read 2 more answers
Does this mean they are calling me on insta?
patriot [66]

Answer:

yessss this mean they are calling you

have a great day

<h2> BRINDLIST plz </h2>

<u>Mrslenbox</u>

8 0
3 years ago
Applying properties of Exponents In Exercise, use the properties of exponents to simplify the expression.
Nastasia [14]

Answer:

(a) 4^7

(b) 7^6

(c) \dfrac{1}{16}

(d) 3^{4}

Step-by-step explanation:

We need to simplify the given expressions.

(a)

Consider the given expression is

(4^5)(4^2)

Using the property of exponent, we get

=4^{5+2}            [\because a^ma^n=a^{m+n}]

=4^7

(b)

Consider the given expression is

(7^2)^3

Using the property of exponent, we get

=7^{2\times 3}            [\because (a^m)^n=a^{mn}]

=7^6

(c)

Consider the given expression is

2^{-4}

Using the property of exponent, we get

=\dfrac{1}{2^{4}}            [\because a^{-n}=\dfrac{1}{a^n}]

=\dfrac{1}{16}

(d)

Consider the given expression is

\dfrac{3^8}{3^4}

Using the property of exponent, we get

=3^{8-4}            [\because \dfrac{a^m}{a^n}=a^{m-n}]

=3^{4}

6 0
3 years ago
HELP ME! ITS WORTH 55 POINTS PLZ DONT LIE!
storchak [24]

Answer:                              

Explanation:                

6 0
3 years ago
Other questions:
  • The sum of 3/4 and 18/19 is closest to 0, 1, 2
    14·2 answers
  • This is literally 20 points of my grade pls help! very desperate.
    14·1 answer
  • What is 10% as a decimal?
    5·1 answer
  • Write an equation to find the value of x:
    15·2 answers
  • Which of the following statements could be used to describe the location of point P, shown on the number line below?
    8·2 answers
  • Kylie needs to build a fence around his square shaped backyard each side measures 90 1/4 feet the materials for the fence cost $
    6·1 answer
  • Which number, when rounded to the nearest tenth, is 43.6
    11·2 answers
  • What is the probability of tossing 4 heads? a) 1/2 b) 1/16 c) 1/33 d) 1/4
    8·1 answer
  • Find the slope of the line that passes through each pair of points.<br> C(0, –2), D(3, -2)
    10·1 answer
  • Whats 40% as a decimal and just a normal convo between me and my Childhood Bestfriend.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!