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adell [148]
3 years ago
9

How to convert base two to base three​

Mathematics
1 answer:
sladkih [1.3K]3 years ago
6 0

Consider this example: say we want to convert <em>x</em> = 11 0101 1001₂ to base 3.

The binary expansion of <em>x</em> is

<em>x</em> = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰

which in base 10 reduces to

<em>x</em> = 512 + 256 + 64 + 16 + 8 + 1 = 857

Recall the first several powers of 3:

3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729

Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.

• How many times does the 729 go into 857? 1 time, and it leaves a remainder of 128, or

857 = 1×729 + 128 = 1×3⁶ + 128

• How many times does 81 go into 128? Also 1 time, so

128 = 1×81 + 47 = 1×3⁴ + 47

• How many times does 27 go into 47? Also 1 time,

47 = 1×27 + 20 = 1×3³ + 20

• How many times does 9 go into 20? 2 times,

20 = 18 + 2 = 2×9 + 2 = 2×3² + 2

• How many times does 1 go into 2? Also 2 times,

2 = 2 + 1 = 2×1 + 0 = 2×3⁰

So we found

857 = 1×3⁶ + 1×3⁴ + 1×3³ + 2×3² + 2×3⁰

which is the ternary expansion of <em>x</em>,

<em>x</em> = 1 011 202₃

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last summer, at camp okey-fun-okey, the ratio of the number of boy campers to girl campers was 8:7. If there were a total of 195
Evgen [1.6K]

The ration of boy campers to total campers is 8:15, and the ratio of girl campers to total campers is 7:15.  Using this information, we can answer this question by setting up proportions.

<u>For boys:</u>

\frac{8}{15} =\frac{x}{195}

<em>*Cross multiply*</em>

15x=1560

<em>*Divide both sides by 15*</em>

x=104

There are 169 boy campers.


<u>For girls:</u>

\frac{7}{15} =\frac{x}{195}

<em>*Cross multiply*</em>

15x=1365

91=x

There are 91 girl campers.


Hope this helps!!

7 0
3 years ago
Read 2 more answers
a recipe includes 8 cups of flour and two third cups of shortening. write the ratio to the amount of flour to the amount of shor
Paul [167]
8:2/3 because you can't go lower than 2/3
8 0
3 years ago
Please help me out please please !!!!!
Sauron [17]

The surface area of a sphere is given by

S = 4\pi r^2

We deduce

r = \sqrt{\dfrac{S}{4\pi}}

So, in your case, the radius is

r = \sqrt{\dfrac{100\pi}{4\pi}}=\sqrt{25}=5

The volume of a sphere is given by

V=\dfrac{4}{3}\pi r^3

So, we have

V = \dfrac{4}{3} \pi 5^3 = \dfrac{500}{3}\pi

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What is the domain and derivative of f(x)=ln(2xsqrt(2+x))?
harkovskaia [24]
Domain is the numbers yo can use
we has a sqrt and a ln
we cant have any neagtive ln's or sqrts
x cannot be negative
it cannot be 0 either
domain is all numbers bigger than 0


deritivive
apply chain rule
dy/dx(f(g(x))=f'(g(x))g'(x)
and also
dy/dx (lnx)=1/x
and
dy/dx(f(x)g(x))=f'(x)g(x)+g'(x)f(x)
and from experience
dy/dx(sqrtx)=1/(2√x)


so

dy/dx(ln(2xsqrt(2+x)))=
(1/(2xsqrt(2+x))(2)(sqrt(2+x)+(x/(2sqrt(2+x))=
(3x+4)/(2x(x+2))



domain is all real numbers greater than 0
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7 0
3 years ago
Kathryn is 1.6 meters tall. Convert her height to feet. Round to the nearest tenth.
Andrej [43]

Answer:

1.6 m = 5.3 ft

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3 years ago
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