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3 years ago

What is the volume of the rectangular prism above?

Mathematics

2 answers:

Aleks04 [339]3 years ago

6 0

Answer:

1/15 cubic meters

Step-by-step explanation:

Formula for volume of a rectangular prism is <u><em>width times length times height.</em></u>

1/4 x 1/3 x 4/5 = 1/15

PolarNik [594]3 years ago

6 0

1/12 EZ I think that's the answer

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Let Ebe the set of all even positive integers in the universe Zof integers, and XE : Z R be the characteristic function of E.

AnnZ [28]

Answer:

$\mathbf{X_E (2) = 1}$

$\mathbf{X_E (-2) = 0 }$

$\mathbf{\{ x \in Z: X_E(x) = 1\} = E}$

Step-by-step explanation:

Let E be the set of all even positive integers in the universe Z of integers,

i.e

E = {2,4,6,8,10 ....∞}

$X_E : Z \to R$ be the characteristic function of E.

∴

$X_E(x) = \left \{ {{1 \ if \ x \ \ is \ an \ element \ of \ E} \atop {0 \ if \ x \ \ is \ not \ an \ element \ of \ E}} \right.$

For XE(2)

$\mathbf{X_E (2) = 1}$ since x is an element of E (i.e the set of all even numbers)

For XE(-2)

$\mathbf{X_E (-2) = 0 }$ since - 2 is less than 0 , and -2 is not an element of E

For { x ∈ Z: XE(x) = 1}

This can be read as:

x which is and element of Z such that X is also an element of x which is equal to 1.

∴

$\{ x \in Z: X_E(x) = 1\} = \{ x \in Z | x \in E\} \\ \\ \mathbf{\{ x \in Z: X_E(x) = 1\} = E}$

E = {2,4,6,8,10 ....∞}

5 0

3 years ago

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 3 centimeters by 5 centimeters. Six

kherson [118]

Answer:

x = 0.53 cm

Maximum volume = 1.75 cm³

Step-by-step explanation:

Refer to the attached diagram:

The volume of the box is given by

$V = Length \times Width \times Height \\\\$

Let x denote the length of the sides of the square as shown in the diagram.

The width of the shaded region is given by

$Width = 3 - 2x \\\\$

The length of the shaded region is given by

$Length = \frac{1}{2} (5 - 3x) \\\\$

So, the volume of the box becomes,

$V = \frac{1}{2} (5 - 3x) \times (3 - 2x) \times x \\\\V = \frac{1}{2} (5 - 3x) \times (3x - 2x^2) \\\\V = \frac{1}{2} (15x -10x^2 -9 x^2 + 6 x^3) \\\\V = \frac{1}{2} (6x^3 -19x^2 + 15x) \\\\$

In order to maximize the volume enclosed by the box, take the derivative of volume and set it to zero.

$\frac{dV}{dx} = 0 \\\\\frac{dV}{dx} = \frac{d}{dx} ( \frac{1}{2} (6x^3 -19x^2 + 15x)) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\\frac{dV}{dx} = \frac{1}{2} (18x^2 -38x + 15) \\\\0 = \frac{1}{2} (18x^2 -38x + 15) \\\\18x^2 -38x + 15 = 0 \\\\$

We are left with a quadratic equation.

We may solve the quadratic equation using quadratic formula.

The quadratic formula is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where

$a = 18 \\\\b = -38 \\\\c = 15 \\\\$

$x=\frac{-(-38)\pm\sqrt{(-38)^2-4(18)(15)}}{2(18)} \\\\x=\frac{38\pm\sqrt{(1444- 1080}}{36} \\\\x=\frac{38\pm\sqrt{(364}}{36} \\\\x=\frac{38\pm 19.078}{36} \\\\x=\frac{38 + 19.078}{36} \: or \: x=\frac{38 - 19.078}{36}\\\\x= 1.59 \: or \: x = 0.53 \\\\$

Volume of the box at x= 1.59:

$V = \frac{1}{2} (5 – 3(1.59)) \times (3 - 2(1.59)) \times (1.59) \\\\V = -0.03 \: cm^3 \\\\$

Volume of the box at x= 0.53:

$V = \frac{1}{2} (5 – 3(0.53)) \times (3 - 2(0.53)) \times (0.53) \\\\V = 1.75 \: cm^3$

The volume of the box is maximized when x = 0.53 cm

Therefore,

x = 0.53 cm

Maximum volume = 1.75 cm³

7 0

3 years ago

The average reading score on certain tests is given by y = 0.153x + 255.4, where x is the number of years past 1970. In what yea

nirvana33 [79]

Average reading score is given by the expression,

y = 0.153x + 255.4

Here, x in the number of years past 1970.

To find the year in which the average reading score is 259.378, substitute the value of 'y' in the given expression.

y = 0.153x + 255.4

259.378 = 0.153(x) + 255.4

0.153x = 259.378 - 255.4

0.153x = 3.978

x = $\frac{3.978}{0.153}$

x = 26

That means given average reading score 259.378 will be 26 years after 1970.

Therefore, 1996 is the year in which the average reading score will be 259.378.

Learn more,

brainly.com/question/2883790

3 0

3 years ago

Find all numbers such that three times the number is greater than eight less than the number.

klio [65]

Answer:

ALL SUCH NUMBERS WHICH ARE GREATER THAN -4 satisfy the given condition.

Step-by-step explanation:

Here, assume such number = m

Now, given :

3 times the number = 3 x ( m) = 3 m

8 less than the given number = m - 8

Now, according to the question:

3 times the number > 8 less than the given number

or, 3 m > m - 8

or, 3m - m > m - 8 + m

or, 2 m > - 8

or, m > - 4

Hence, all SUCH NUMBERS WHICH ARE GREATER THAN -4 satisfy the given condition.

6 0

3 years ago

Check to see the given number is a solution of the equation or inequality x+9=17;8

timofeeve [1]

Yes, 8 is a solution to the equation

6 0

3 years ago