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Otrada [13]
4 years ago
13

Find the amount of empty space within a cylinder containing three solid spheres, where each sphere has a radius of 3 cm. (Volume

of a sphere =4/3πr^3)
Mathematics
1 answer:
zimovet [89]4 years ago
3 0

Answer:

Step-by-step explanation:

cylinder's height=3×(diameter of sphere)=3×6=18 cm

radius of cylinder=3 cm

volume of cylinder=π r²h=π(3)²×18=162 π cm³

volume of sphere=4/3 π(3)³=36 π cm³

reqd. empty space=162 π-3×36π=54 πcm³

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Light travels at approximately 2.998*10^5 kilometers per second. There are 6.048*10^5 seconds in one week. About how many kilome
BartSMP [9]

Answer:

okay, you have pay special attention to time.i.e 60secs = 1 minute, 60 minutes = 1 hour, 24 hours in one day, and 7 days in one week. No. of seconds in one week we are told is 6.1048 x 10 ^5 seconds.  

Step-by-step explanation:

s = d/t [ speed = distance/time]

therefor, rearranging, we get d = s x t

Since speed = 2.998*10^5 Km/s and time = 6.048^10^5

d = (2.998 x 10^5) x (6.048 x10^5) = (2.998 x 6.048) x 10 ^(5+5)

d = 18.131904 X 10^10 km

d = approximately 18.132 x 10^10 km (to 3 decimal places)

6 0
3 years ago
amy purchases 27 teeshirts for a certain amount of money. using m for the total amount of money in dollars that amy spent on tee
Sophie [7]
<span>One T-shirt is m dollars. The number of T-shirts is n. Amy bought 27 T-shirts. 

27n = m, so n = m/27.</span><span>
Hope that helps! (:</span>
4 0
3 years ago
Help pleaseeeeeeeeeeeeeeeeeeeeeee
bixtya [17]

Answer:  \bold{(1)\ \dfrac{19,683}{64}\qquad (2)\ 16}

<u>Step-by-step explanation:</u>

(1)           (12, 18, 27, ...)

The common ratio is:

r=\dfrac{a_{n+1}}{a_n}\quad r =\dfrac{18}{12}=\boxed{\dfrac{3}{2}}\quad \rightarrow \quad r=\dfrac{27}{18}=\boxed{\dfrac{3}{2}}

The equation is:

a_n=a_o(r)^{n-1}\\\\Given:a_o=12,\  r=\dfrac{3}{2}\\\\\\Equation:\\a_n =12\bigg(\dfrac{3}{2}\bigg)^{n-1}\\\\\\\\9th\ term:\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{9-1}\\\\\\a_9=12\bigg(\dfrac{3}{2}\bigg)^{8}\\\\\\.\quad =\large\boxed{\dfrac{19643}{64}}

(2)\qquad \bigg(\dfrac{1}{16},\dfrac{1}{8},\dfrac{1}{4},\dfrac{1}{2}\bigg)\\\\\\\text{The common ratio is}:\\\\r=\dfrac{a_{n+1}}{a_n}\quad  r=\dfrac{\frac{1}{8}}{\frac{1}{16}}=\boxed{2}\quad \rightarrow \quad r=\dfrac{\frac{1}{4}}{\frac{1}{8}}=\boxed{2}

The equation is:

a_n=a_o(r)^{n-1}\\\\Given:a_o=\dfrac{1}{16},\  r=2\\\\\\Equation:\\a_n =\dfrac{1}{16}(2)^{n-1}\\\\\\\\9th\ term:\\a_9=\dfrac{1}{16}(2)^{9-1}\\\\\\a_9=\dfrac{1}{16}(2)^{8}\\\\\\.\quad =\large\boxed{16}

3 0
3 years ago
Circle has rad of 1.5m what angle subtended at center of circle by arc of 1m
Mumz [18]
120 degrees or 0.67 radians
5 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B6%7D%20%20%2B%20%28%20%5Cfrac%7B4%7D%7B9%7D%20%29%20-%20%28%20-%202%29" id
Lady_Fox [76]

get a common denominator of 18

5/6 * 3/3 +4/9 * 2/2 - -2*18/18

15/18 +8/18 + 36/18

23/18 + 36/18

59/18

change to a mixed number

18 goes into 59 3 times with 5 left over

3 and 5 /18

6 0
3 years ago
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