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liberstina [14]
2 years ago
10

Can transformations always be applied to shapes, even if they're not in a plane?

Mathematics
1 answer:
Tatiana [17]2 years ago
8 0

A translation is a transformation of the plane in which a a plane figure slides along a straight line, and changes its position without turning. Each point moves the same distance and in the same direction. Hence all points subjected to the same translation undergo the same displacement.
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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}\\\\

.

\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

.

\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
Can u pls help me with this question asap ​
RideAnS [48]

Answer:

90

Step-by-step explanation:

Basically 90 precent of 100 is 90

7 0
3 years ago
The ages of three friends are consecutively one year apart. Together, their ages total 30 years. What is the age of the youngest
nadya68 [22]

Answer:

The age of the youngest friend is 9 years old.

Step-by-step explanation:

3a = 30 - 3

= 27 ÷ 3

= 9

= 9 + 10 + 11 = 30

= 9 is the smallest number. So, the youngest friend is 9 years old.

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4 0
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