All categories

3 years ago

84 cubic inches 90 cubic inches 100 cubic inches 126 cubic inches

Mathematics

1 answer:

igomit [66]3 years ago

8 0

Answer: Second Choice. 90 cubic inches

Concept:

Here, we need to know how to calculate the volume of a rectangular prism

Volume (rectangular prism) = w · l · h

w = width

l = length

h = height

Solve:

<u>Given information</u>

l = 6"

w = 3"

h = 5"

<u>Given expression</u>

V = w · l · h

<u>Substitute values into the expression</u>

V = (3) (6) (5)

<u>Simplify by multiplication</u>

V = 18 · 5

$\boxed{V_{rectangular prism}=90}$

Hope this helps!! :)

Please let me know if you have any questions

You might be interested in

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

Hi please help!!

valkas [14]

The table of values of the function y = 2x^2 is:

x 0 1 2 3 4

y 0 2 8 18 32

<h3>How to complete the table?</h3>

The equation of the function is given as:

y = 2x^2

When x= 0, we have

y = 2 * 0^2 = 0

When x= 1, we have

y = 2 * 1^2 = 2

When x= 2, we have

y = 2 * 2^2 = 8

When x= 3, we have

y = 2 * 3^2 = 18

When x= 4, we have

y = 2 * 4^2 = 32

So, the table of values is:

x 0 1 2 3 4

y 0 2 8 18 32

Read more about functions and tables at:

brainly.com/question/15602982

#SPJ1

5 0

1 year ago

Need by tomorrow please help

nikklg [1K]

1 - 9
2 -28
3 54
4 -100
5 -60
6 0
7 49
8 -135
9 -96
10 300
11 0
12 192

6 0

3 years ago

Read 2 more answers

Original price: $33.75, markdown 75%

Cloud [144]

Answer:

$25.31

Step-by-step explanation:

If you multiply 33.75 by .75 you get your answer.

4 0

3 years ago

Read 2 more answers

The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 136 feet, what is the length of the

Goshia [24]

Add the ratios 3:1 = 4
divide perimeter 128 by 4 = 32
multiply this by each ratio so 3:1 becomes 96length:32width
remember there are two lengths and two widths in the perimeter so divide by 2 to find the length = 48

8 0

3 years ago

Read 2 more answers