Commutative property across multiplication for 2x10x7

How many 1/3 cubes does it take to fill a box with a width of 2 2/3 inches length 3 1/3 inches and height 2 1/3

Paladinen [302]

Answer:

560

Step-by-step explanation:

I assume 1/3 is the side length of the cubes.

There's two ways to solve this:

1. Find the volume of the box, then divide by the volume of the cubes.

Or 2. Find the number of cubes per each side length, the find the volume in terms of cubes.

Either way, we need to convert the mixed fractions to improper fractions.

W = 2⅔ = (2×3+2)/3 = 8/3 inches

L = 3⅓ = (3×3+1)/3 = 10/3 inches

H = 2⅓ = (2×3+1)/3 = 7/3 inches

Using the first method, the volume of the box is:

V = (8/3 in) (10/3 in) (7/3 in) = 560/27 in³

The volume of a cube is:

V = (1/3 in)³ = 1/27 in³

So the number of cubes in the box is:

(560/27 in³) / (1/27 in³) = 560

Using the second method, the cubes per each side of the box is:

W = (8/3 in) / (1/3 in) = 8

L = (10/3 in) / (1/3 in) = 10

H = (7/3 in) / (1/3 in) = 7

So the number of cubes is:

8 × 10 × 7 = 560

7 0

2 years ago

April shoots an arrow upward into the air at a speed of 64 feet per second from a platform that is 11 feet high. The height of t

kogti [31]

Answer:

Maximum height of the arrow is 203 feets

Step-by-step explanation:

It is given that,

The height of the arrow as a function of time t is given by :

$h(t)=-16t^2+64t+11$ ..........(1)

t is in seconds

We need to find the maximum height of the arrow. For maximum height differentiating equation (1) wrt t as :

$\dfrac{dh(t)}{dt}=0$

$\dfrac{d(-16t^2+64t+11)}{dt}=0$

$-32t+64=0$

t = 2 seconds

Put the value of t in equation (1) as :

$h(t)=-16(2)^2+64(2)+11$

h(t) = 203 feet

So, the maximum height reached by the arrow is 203 feet. Hence, this is the required solution.

8 0

3 years ago

. Ms. Johnson, a circus ringleader, made a cake in the shape of a circus tent to use as the centerpiece at a celebration. As sho

Effectus [21]

The formula for the volume of a cylinder is V=πr²h. Substituting the information we have, we get 1470=(3.14)(6²)h
1470=113.04h
Divide both sides by 113.04:
1470/113.04 = 113.04h/113.04
13 ≈ h
The height of the cylinder is 13 inches. We know that the height of the cone is 1/2 the height of the cylinder; 1/2(13) = 6.5 inches. The formula for the volume of a cone is:
V=1/3πr²h
The cone and the cylinder have the same radius, and we now know that the height of the cone is 6.5. Substituting this information in we have:
V=1/3(3.14)(6²)(6.5) = 244.92 in³
The total volume of the cake would be the volume of the cylinder added to the volume of the cone:
1470+244.92 = 1714.92 in³.

The formula for the volume of a sphere, for the ball cake, is
V=4/3πr³. Using the radius of 3 we have:
V=4/3(3.14)(3³)=113.04 for the volume of the circus ball cake.
The formula for the area of the cone-shaped hat cake is V=1/3πr²h. We want it to have the same volume as the circus ball cake, and we know the radius is still 3:
113.04=1/3(3.14)(3²)h
This simplifies to
113.04=9.42h
Divide both sides by 9.42:
113.04/9.42 = 9.42h/9.42
The hat cake would have to have a height of 12 inches to have the same volume.

6 0

3 years ago

Help ASAP!!! I need ssomeoje to answer this

MissTica

Answer:

(1,-1)

Step-by-step explanation:

it's one coordinate to the right so it's positive 1, then it goes down 1 so it's negative:) hope I helped!

4 0

2 years ago

When graphed, which function has a horizontal asymptote at 4?

shusha [124]

Hope you Understand :)

8 0

3 years ago