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pantera1 [17]
3 years ago
11

Gum is packaged in a square-based pyramid shaped box with a distance of 6 cm from the center of the base to the sides and a heig

ht of 12 cm.
a) How much material was used to create the box? (surface area)

b) What is the volume of the box?​
Mathematics
1 answer:
Juliette [100K]3 years ago
3 0

Answer:

18 cm

Step-by-step explanation:

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Given that h = 2,

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For an arithmetic sequence, a35=57. If the common difference is 5. Find a1 and the sum of the first 61 terms.
Flauer [41]

 

\displaystyle\bf\\a_{35}=57\\r=5\\----\\a_1=?\\S_{61}=?\\----\\Solve:\\1)\\a_1=a_{35}-(35-1)\times r=57-34\times 5=57-170=-113\\\boxed{\bf a_1=-113}\\\\

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\displaystyle\bf\\2)\\A_{61}=a_1+(61-1)\times r=-113+60\times5=-113+300=187\\\\S_{61}=(-113)+(-108)+(-103)+...+(-8)+(-3)+2+7+12+...+187\\\\S_{61}=SA+SB\\\\SA=(-113)+(-108)+(-103)+...+(-8)+(-3)=-(3+8+103+108+113)\\\\n=\frac{113-8}{5}+1=\frac{105}{5}+1=21+1=22~terms\\SA=-\Big( \frac{n(113+3)}{2} \Big)=-\Big( \frac{22\times116}{2} \Big)=-11\times116 =-1276

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\displaystyle\bf\\SB=2+7+12+...+187\\\\n=\frac{187-2}{5}+1=\frac{185}{5}+1=37+1=38~terms\\\\SB=\frac{n(187+2)}{2}=\frac{38\times189}{2}=19\times189=3591\\\\S_{61}=SA+SB=-1276+3591=2315\\\\\boxed{\bf S_{61}=2315}    

 

 

8 0
3 years ago
Hey! i’ll give brainliest please help
Phantasy [73]

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subject

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subject is a noun (person, place or thing)

verb is doing something *example: running

object is a thing *example: apple

conjunction is a word used to connect sentences *example: but

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Given the circle below secant kjI and tangent hi find the length of hi round to the nearest tenth if necessary.
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The length of the segment HI in the figure is 32.9

<h3>How to determine the length HI?</h3>

To do this, we make use of the following secant-tangent equation:

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