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3 years ago

If the ratio of radius of two spheres is 4:7, the ratio of their volume is?

Mathematics

1 answer:

Kazeer [188]3 years ago

6 0

Answer:

64 : 343

Step-by-step explanation:

First use the radii to find the volume

1) Radius of first sphere is 4 (taken from 4:7 ratio)

Insert it into the equation for volume of a sphere: V=4 /3πr^3

V = (4/3)(π)(4^3)

V = (4/3)(π)(64)

V = 256/3 π

Volume of the first sphere = 256/3 π

2) Radius of the second sphere is 7 (also taken from 4:7 ratio)

Insert it into the equation for volume of a sphere: V=4 /3πr^3

V = (4/3)(π)(7^3)

V = (4/3)(π)(343)

V = 1372/3 π

Volume of the second sphere = 1372/3 π

Next, calculate the ratio by dividing the two numbers

256/3 π ÷ 1372/3 π

Answer should be 64 : 343

The simple way to do this problem is to just cube the numbers:

4:7 becomes 4^3 : 7^3 = 64 : 343

Either way works.

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Solve the inequality

aev [14]

Answer:

x<3

Step-by-step explanation:

4x-7<5

4x<5+7

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2 years ago

Math help please, thank you!

CaHeK987 [17]

The answer to the first question of the attached document is option 1. We obtain the answer subtracting the term n from the series with the term n-1.For example:
-3 - (- 5) = 2
-1 - (- 3) = 2
1 - (- 1) = 2
So you can see that the common difference is the 2.

The answer to the second question is option 3:
y = | x + 7 |
We can confirm it by substituting values in the equation.
For example:
if we do y = 0 then x = -7
if we do x = 0 then y = 7.
As corresponds in the graph shown.
Remember also that as a general rule yes to the equationy = | x | whose vertex is in the point (0,0) we add a positive real number "a" of form y = | x + a | then the graph of y = | x | will move "to" units in the negative direction of x.

The answer to the third question is option 4.
The quotient of x and "and" is constant.
k = y / x
Rewriting:
y = kx
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3 0

2 years ago

Diego is 59.5 inches tall. His brother is 40.125 inches tall. How much taller than his brother is Diego?

Paha777 [63]

Answer:

Hello!!

Diego is 59.5 inches tall. His brother is 40.125 inches tall. How much taller than his brother is Diego?

Diego is 19.375 inches taller than his brother.

Step-by-step explanation:

$59.5-40.125=19.375$

Hope this helps!!

6 0

2 years ago

2 last questions:

podryga [215]

Problem 1

<h3>Answer: 26/32</h3>

-----------------------

Work Shown:

There are is 1 way to get 0 tails (aka 5 heads)

There are 5 ways to flip the coins so that exactly one coin shows tails and the rest are heads.

We have 1+5 = 6 ways of getting at most 1 tail. The phrasing "at most 1" means "1 is the largest number we can get".

There are 2^5 = 32 ways to flip five coins, so there are 32-6 = 26 ways of getting at least two tails. Note the events "getting at most 1 tail" and "getting at least 2 tails" are complementary events. One or the other must happen.

The probability of getting two or more tails is therefore 26/32.

========================================================

Problem 2

<h3>Answer: 56 total villages</h3>

-----------------------

Work Shown:

We'll work our way backwards starting with the last (7th) son

x = number of villages left before the 7th son gets his share

x/8 + 7 = number of villages the 7th son gets

x - (x/8+7) = 7x/8 - 7 = number of villages left after the 7th son gets his share

This amount should be 0, so,

7x/8 - 7 = 0

7x/8 = 7

7x = 7*8

7x = 56

x = 56/7

x = 8

There are 8 villages left before the 7th son gets his share; this means he gets x/8+7 = 8/8+7 = 1+7 = 8 villages. Or you can note that if there are 8 villages left, and he's the last in line, then he gets the remaining 8.

Plugging x = 8 into 7x/8 - 7 leads to 0.

----------

y = amount of villages left before the 6th son gets his share

y/8 + 6 = amount of villages the 6th son gets

y - (y/8+6) = 7y/8 - 6 = amount of villages left after 6th son gets his share

We match up the x = 8 found earlier with this new expression and we solve for y. This is because x represents the number of villages leftover after the 6th son gets his share. After the 6th son gets his share, that leftover x is then handled for the 7th son as discussed above.

7y/8 - 6 = x

7y/8 - 6 = 8

7y/8 = 14

7y = 14*8

7y = 112

y = 112/7

y = 16

There are 16 villages leftover before the 6th son gets his share.

This means the 6th son gets y/8 + 6 = 16/8 + 6 = 2+6 = 8 villages.

----------

z = amount of villages left before the 5th son gets his share

z/8 + 5 = amount of villages the 5th son gets

z - (z/8+5) = 7z/8 - 5 = amount of villages left after 5th son gets his share

You can probably spot the pattern by now. We'll follow the same idea as before. Set 7z/8-5 equal to the 16 villages and we get

7z/8-5 = y

7z/8-5 = 16

7z/8 = 16+5

7z/8 = 21

7z = 21*8

7z = 168

z = 168/7

z = 24

There are 24 villages before the 5th son gets his share.

He gets z/8 + 5 = 24/8 + 5 = 3 + 5 = 8 villages.

------------

I'll do one more iteration

w = amount of villages left before the 4th son gets his share

w/8 + 4 = amount of villages the 4th son gets

w - (w/8+4) = 7w/8 - 4 = amount of villages left after 4th son gets his share

Set that equal to the previous value 24 and solve for w

7w/8-4 = z

7w/8-4 = 24

7w/8 = 24+4

7w/8 = 28

7w = 28*8

7w = 224

w = 224/7

w = 32

There are 32 villages before the 4th son gets his share.

He gets w/8 + 4 = 32/8 + 4 = 4 + 4 = 8 villages.

------------

The rest of the steps to find the other village counts will follow this template. You should find that each son gets 8 villages. There are 7 sons, so that means there are 7*8 = 56 villages total.

------------

It makes sense that the answer is some multiple of 8 because when taking 1/8 of the value leads to an integer. In other words, (1/8)*x is an integer.

Furthermore, it also makes sense that each son gets a multiple of 8 villages because if let's say the first son gets 9 villages (some non-multiple of 8), then 56-9 = 47 is not a multiple of 8. Plugging that into x/8+2 for the second son will lead to some non-integer result. So it's a bit nice that everything is a multiple of 8.

A stronger verification is shown in the table below. The table keeps track of how many leftover villages there are for any given son, whether its before or after they get their share. At the top we start with 56 and then slowly make our way down to 0 villages.

8 0

3 years ago

Please help<br>find the area of the following shape. show all work.<br>

vivado [14]

Answer:

Step-by-step explanation:

8 0

1 year ago

If the ratio of radius of two spheres is 4:7, the ratio of their volume is?​

If the ratio of radius of two spheres is 4:7, the ratio of their volume is?