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nata0808 [166]
2 years ago
12

Help I’m so confused

Mathematics
1 answer:
Vinvika [58]2 years ago
5 0

Answer:

The measure of arc AC is 136^o

Step-by-step explanation:

Notice that angle BAC (whose measure is given as 34 degrees) is an inscribed angle, and according toe the inscribed angle theorem, the measure of an inscribed angle is half the measure of the central angle that subtends the same chord.

Then, the central angle that subtends the cord BC, is twice 34 degrees (2\,*\,34^o = 68^o)

Then, since they give us also the measure of the arc AB which is 156^o, then the measure of arc AC can be estimated as the needed measure to complete 360^o as the sum of all three arcs. That is:

AC + AB+ BC = 360^o\\AC + 156^o+2\,*\,34^o = 360^o\\AC + 156^o+68^o = 360^o\\AC=360^o-156^o-68^o\\AC=136^o

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4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.
nikitadnepr [17]

Answer:

\sum_{n=0}^9cos(\frac{\pi n}{2})=1

\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0

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Step-by-step explanation:

\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))

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2nd

\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}

=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0

3th

\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))

=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}

What we use?

We use that

e^{i\pi n}=cos(\pi n)+i sin(\pi n)

and

\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}

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Step-by-step explanation:

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