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AnnyKZ [126]
2 years ago
12

Find the measure of unknown angle​

Mathematics
1 answer:
inna [77]2 years ago
8 0

Answer:

a = 85° , b = 30° , c = 65°

Step-by-step explanation:

∠ a and 85° are alternate angles and are congruent , so

a = 85°

∠ c and 65° are alternate angles and are congruent , so

c = 65°

a, b and c lie on a straight line and sum to 180° , that is

a + b + c = 180°

85° + b + 65° = 180°

150° + b = 180° ( subtract 150° from both sides )

b = 30°

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3 0
3 years ago
SOLUTION We observe that f '(x) = -1 / (1 + x2) and find the required series by integrating the power series for -1 / (1 + x2).
Ann [662]

Answer:

Required series is:

\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....

Step-by-step explanation:

Given that

                           f'(x) = -\frac{1}{1 + x^{2}} ---(1)

We know that:

                  \frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^{2}} ---(2)

Comparing (1) and (2)

                           f'(x)=-(tan^{-1}x) ---- (3)

Using power series expansion for tan^{-1}x

f'(x)=-tan^{-1}x=-\int {\frac{1}{1+x^{2}} \, dx

= -\int{ \sum\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx

= -\sum{ \int\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx

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=C+\sum\limits^{ \infty}_{n=0} (-1)^{n+1}\frac{x^{2n+1}}{2n+1}

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\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....

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