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olasank [31]
3 years ago
6

Is 729 a perfect cube? What is the number whose cube is 729?

Mathematics
1 answer:
maria [59]3 years ago
7 0

Answer:

 729 is a perfect cube. The number whose cube is 729 is 9.

Explanation:

 Let us find the cubes of natural numbers from starting

     1 x 1 x 1 = 1

     2 x 2 x 2 = 8

     3 x 3 x 3 = 27

     4 x 4 x 4 = 64

     5 x 5 x 5 = 125

     6 x 6 x 6 = 216

     7 x 7 x 7 = 343

     8 x 8 x 8 = 512

     9 x 9 x 9 = 729

    10 x 10 x 10 = 1000

So we got that 729 is the cube of 9, so 729 is a perfect cube.

The number whose cube is 729 is 9.

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1. A movie theater designs two bags to hold 96 cubic inches of popcorn. a. Find the height of each bag b. Which bag should the t
MrRissso [65]
I have attached a screenshot with the images of the two popcorn bags used by the theater.

Part (a):
Bag A:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 3 in
width = 4 in
Therefore:
96 = 3 * 4 * height
96 = 12 * height
height of bag A = 8 in
Bag B:
Volume of bag = area of base * height
Volume of bag = length * width * height
We have:
volume = 96 in³
length = 4 in
width = 4 in
Therefore:
96 = 4 * 4 * height
96 = 16 * height
height of bag B = 6 in

Part (b):
To determine the amount of paper needed, we will need to calculate the surface of each bag. Excluding the top base, each bag will have 5 faces. Four side faces (each two opposite are equal) and the base.
Bag A:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (3*4) + 2(8*4) + 2(8*3) 
Surface area = 12 + 64 + 48 
Surface area of bag A = 124 in²
Bag B:
Surface area = area of base + 2*area of front face + 2*area of side face
Surface area = (4*4) + 2(6*4) + 2(6*4) 
Surface area = 16 + 48 + 48 
Surface area of bag B = 112 in²
From the above calculations, we can deduce that the theater should choose bag B in order to reduce the amount of paper needed.

Hope this helps :)



6 0
3 years ago
A like has two-fold Symmetry
Vikki [24]

Answer:

yes

Step-by-step explanation:


5 0
3 years ago
Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 mi
tensa zangetsu [6.8K]
Short Answer: 18 minutes
Remark

The answer to this problem is less than the smallest time of the two people working together. that fact lets out C and D (38 minutes and 75 minutes). Now you have to choose 15 minutes and 18 minutes. There's a method. No guessing needed.

Givens
Let the time for Sophie = S
Let the time for Simon = M
Let the job to completion = 1 
S = 45 minutes
M = 30 minutes

Step One
Convert minutes to hours.
45 minutes = 45 / 60 = 3/4 hour = 0.75 hour
30 minutes = 30 / 60 = 1/2 hour = 0.50 hour

Step Two
Set up the Equation
The formula is a form of job / hour.
Let the time = t that they both have to work

job = 1 in these problems.
1/S + 1/M = 1/t
1/0.75 + 1/0.5 = 1/t

Solve
1 ÷ 0.75 = 1.33333
1 ÷ 0.5 = 2

1.3333 + 2 = 3.33333 
3.3333 = 1 / t                    Multlply both sides by t
3.3333*t = 1
t = 1 / 3.333333333
t = 0.3 of an hour


1 hour = 60 minutes
0.3 hours = x              Cross Multiply
x = 60 * 0.3
x = 18 minutes

Answer working together it took them 18 minutes  <<<<< 
6 0
3 years ago
Read 2 more answers
Use the Law of Sines to find each missing side or angle. Round to the nearest tenth.
Gre4nikov [31]
(22 x sin(65))/sin(53) =24.96604654 rounded of to nearest tenth = 25
So X = 25
5 0
1 year ago
Rachel used 9 cups of flour and 4 teaspoons of sugar.
Firdavs [7]

Answer:

54 cups of flour

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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