Compute $121_3+2122_3-1200_3-2111_3$. Express your answer in base 3.
1 answer:
Answer:
-221 base 3
Step-by-step explanation:
We are to calculate the value of the numbers in base 3. One of the ways to do that is to first convert each number to base 10. Do the arithmetic, then convert back to base 3.
121 base 3 +2122 base 3 - 1200 base 3 - 2111 base 3
Let's convert to base10
See attachment for details
From the workings,
121 base 3 + 2122 base 3 - 1200 base 3 - 2111 base 3 = -221 base 3
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Answers:
a = -6/37
b = -1/37
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Explanation:
Let's start things off by computing the derivatives we'll need
Apply substitution to get
I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.
The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero
a-6b = 0
a = 6b
At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)
-6a -b = 1
-6(6b) - b = 1 .... plug in a = 6b
-36b - b = 1
-37b = 1
b = -1/37
Use this to find 'a'
a = 6b
a = 6(-1/37)
a = -6/37