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brilliants [131]
3 years ago
14

Change from base 10 to the give base

Mathematics
1 answer:
kondor19780726 [428]3 years ago
3 0

Writing numbers in base 10 means to write them as a combination of powers of 10, for example

1925 = 1\cdot 10^3 + 9\cdot 10^2 + 2\cdot 10^1+5\cdot 10^0

So, writing numbers in any base means to do the same thing: for example, in base 3, we have

102_3 = 1\cdot 3^2 +0\cdot 3^1 +2\cdot 3^0 = 12_{10}

So, in order to write 80 in base 3, we have to find out the largest power of 3 that fits: we have

3^0=3,\ \ 3^1=3,\ \ 3^2=9,\ \ 3^3=27,\ \ 3^4=81

So, since 3^4 is too much, our number will have 4 digits:

abcd_3 = a\cdot 3^3 +b\cdot 3^2 +c\cdot 3^1 + d\cdot 3^0

In order to find the digits, again we see "how much it fits": we have

0\cdot 3^3 = 0\ \ 1\cdot 3^3 = 27,\ \ 2\cdot 3^3 = 54

So, we choose a=2. The remainder is 80-54=26

Now we need to fix the coefficient for 3^2: we have

0\cdot 3^2 = 0\ \ 1\cdot 3^2 = 9,\ \ 2\cdot 3^2 = 18

Again we choose b=2

Keep going like this and you'll find out that

80_3 = 2222

This was actually a special case, because our number is exactly one less than a power of 3: we have

80=3^4-1

and just like in base 10, when we subtract 1 from a power of 10 we get a number composed by 9 only:

10000000-1 = 9999999

In every base, when we subtract 1 from a power of the base we get a number composed by (base-1) only:

(10000-1)_3 = 2222

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<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ Angles on a straight line equal 180 degrees:

5k - 3 + 9 + k = 180

Simplify:

6k + 6 = 180

Subtract 6 from both sides:

6k = 174

Divide both sides by 6:

k = 29

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7 0
3 years ago
Change each of the following angles in degrees to angles in radians
grin007 [14]

Answer:

d: 2.6179, e: 4.1887, f: 5.2359 all in rad

Step-by-step explanation:

(d): 150°degrees

150° × π / 180°

= 0.83333333333π rad

= 2.6179 rad

(e):240°degrees

240° × π / 180°

= 1.3333333333π rad

= 4.1887 rad

(f): 300°degrees

300° × π / 180°

= 1.6666666667π rad

= 5.2359 rad

If all my stuff is correct please give me an 5/5 and a thanks. :)

7 0
3 years ago
Doreen is flipping two fair coins. What is the probability that both coins land on heads?
andrezito [222]

Answer:

There are four different possible outcomes: both coins are heads, the red coin is heads and the blue coin is tails, the red coin is tails and the blue coin is heads, or both coins are tails. Each outcome has equal probability. So the probability of both being heads is 1/4.

Step-by-step explanation:


6 0
2 years ago
Quadrilateral CARD is similar to quadrilateral SNOW.
Masja [62]

Answer:

13 I think if i´m right please mark me brainliest please thank you and have a great day

Step-by-step explanation:

5 0
3 years ago
PLEASE HELP WORTH 16 POINTS WILL REPORT LINKS
Igoryamba

Answer:

Angle A = 30.8

Angle B = 33.2

Step-by-step explanation:

180 - 116 = 64  

This means that the other two angles need to add up to 64.

I just plugged in numbers until it worked.

I got that x = 14.6

2x + 4

2(14.6) + 4

29.2 + 4

33.2

3x - 13

3(14.6) - 13

43.8 - 13

30.8

Those are your angles. To make sure they are correct you just need to add up all the angles and make sure that they equal to 180.

116 + 33.2 + 30.8 =

180

6 0
2 years ago
Read 2 more answers
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