Ask question

Ask question

All categories

3 years ago

12

Eli is moving to a new city. He packs his belongings in cube-shaped boxes that each have a volume of one cubic foot. He places t

he boxes in a storage unit that is shaped like a rectangular prism. The floor of the storage unit can be completely covered by a layer of 150 boxes. If 6 layers of boxes can completely fill the storage unit, what is its volume?

1 answer:

klemol [59]3 years ago

4 0

Answer:

jnnm mnn m

Step-by-step explanation:

You might be interested in

PLEASE ANSWER AS SOON AS POSSIBLE WILL GIVE "Brainliest" TO THE FIRST CORRECT PERSON!!!

saw5 [17]

Answer: $x=18$ ; $y=6\sqrt{3}$

Step-by-step explanation:

You can write two expressions that are in terms of 'x' and 'y'. This is a right triangle, so Pythagorean's theorem can be used. We can also use the angle to find the sine of 30 degrees.

<u>Pythagorean's Theorem:</u>

The values 'a' and 'b' are the two shorter sides of the triangle, while the value 'c' is the longest side of the triangle; the hypotenuse.

$a^2+b^2=c^2$

$x^2+y^2=(12\sqrt{3} )^2$

$x^2+y^2=12^2*\sqrt{3} ^2=432$

<u>Sine of the Angle:</u>

Sine is defined to be the opposite side divided by the hypotenuse. Let's take the sine of 30 degrees:

$sin(\alpha )=opposite/hypotenuse$

$sin(30)=y/12\sqrt{3}$

$\frac{1}{2} =y/12\sqrt{3}$

$y=6\sqrt{3}$

Plug this value of 'y' into the first expression derived from Pythagorean's theorem:

$x^2+y^2=432$

$x^2+(6\sqrt{3} )^2=432$

$x^2+108=432$

$x^2=432-108=324$

$x=\sqrt{324}$

$x=18$

Use this value of 'x' to solve for 'y' in the expression from Pythagorean's theorem:

$(\sqrt{324})^2+y^2=432$

$324+y^2=432$

$y^2=432-324=108$

$y=\sqrt{108}$

$y=\sqrt{36*3}$

$y=6\sqrt{3}$

7 0

2 years ago

Which shows the dimensions of two rectangular prisms that have volumes of 240 ft3 but different surface areas?

bulgar [2K]

Calculate the volume and surface areas of both rectangular prisms for each option.

A:

Rectangular Prism #1
$\sf V=lwh$
$\sf V=(8)(5)(6)=240~ft^3$

$\sf A=2((8)(5)+(6)(5)+(6)(8))$
$\sf A=236~ft^2$

Rectangular Prism #2
$\sf V=lwh$
$\sf V=(5)(6)(8)=240~ft^3$

$\sf A=2((5)(6)+(8)(6)+(8)(5))$
$\sf A=236~ft^2$

This is incorrect, they have the same volume of 240 cubic feet and the same surface areas.

B:

Rectangular Prism #1
$\sf V=lwh$
$\sf V=(8)(5)(6)=240~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((8)(5)+(6)(5)+(6)(8))$
$\sf A=236~ft^2$

Rectangular Prism #2
$\sf V=lwh$
$\sf V=(10)(8)(3)=240~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((10)(8)+(3)(8)+(3)(10))$
$\sf A=268~ft^2$

$\boxed{\sf Correct~Answer}$ : Both have the same volume of 240 cubic feet, but different surface areas.

C:

Rectangular Prism #1
$\sf V=lwh$
$\sf V=(15)(8)(2)=240~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((15)(8)+(2)(8)+(2)(15))$
$\sf A=332~ft^2$

Rectangular Prism #2
$\sf V=lwh$
$\sf V=(6)(4)(15)=360~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((6)(4)+(15)(4)+(15)(6))$
$\sf A=348~ft^2$

This is incorrect, they have different surface areas, but only Rectangle #1 has a volume of 240 cubic feet.

D:

Rectangular Prism #1
$\sf V=lwh$
$\sf V=(12)(6)(5)=360~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((12)(6)+(5)(6)+(5)(12))$
$\sf A=324~ft^2$

Rectangular Prism #2
$\sf V=lwh$
$\sf V=(8)(10)(3)=240~ft^3$

$\sf A=2(wl+hl+hw)$
$\sf A=2((8)(10)+(3)(10)+(3)(8))$
$\sf A=268~ft^2$

This is incorrect, they both have different surface areas but only Rectangle #2 has a volume of 240 cubic feet.

5 0

4 years ago

Ols help and hurry ASAP Find m4+ 1/m4 , if m− 1/m =3.

Alexeev081 [22]

Answer: 257/16

Step-by-step explanation:

You are given the algebraic expression: m^4+ 1/m^4

if m− 1/m = 3

Solve for m by cross multiplying

m - 1 = 3m

Collect the likes terms

3m - m = -1

2m = -1

m = -1/2

Substitutes m into the algebraic expression above.

(- 1/2)^4 + 1/(- 1/2)^4

Open the bracket

1/16 + 1/(1/16)

1/6 + 16

16(1/16) or 257/16

5 0

4 years ago

How many solutions does this system of equations have? infinitely many exactly two none exactly one

NISA [10]

There are no solutions. The slopes of both lines are the same so they are parallel: they will never intersect. Therefore, there cannot be a solution.

7 0

4 years ago

Read 2 more answers

PLEASE HELP<br> What is the value of f(2)?

Sonbull [250]

Step-by-step explanation:

I think your answer is 3

....

7 0

3 years ago