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3 years ago

Both pairs of angles in activity A (

Mathematics

1 answer:

FromTheMoon [43]3 years ago

8 0

Answer:

90 degrees

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Step-by-step explanation:

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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 $tan^{-1}x$

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

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

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

$=-[c+\sum\limits^{ \infty}_{n=0} (-1)^{n}\frac{x^{2n+1}}{2n+1}]$

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

$=C-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

$tan^{-1}(0)=0 \implies C=0$

Hence,

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

7 0

4 years ago

In exercises 1 and 2, find m<1 and m<2. Tell which theorem you used in each case.

solniwko [45]

Answer:

m∠2 = 78°

Step-by-step explanation:

From the given picture,

lines 'm' and 'n' are the parallel lines and line 't' is the transverse line.

∠1 and angle with the measure of 78° are corresponding angles.

Therefore, m∠1 = 78°

m∠1 = m∠2 [Vertical angles are equal]

m∠2 = 78°

8 0

3 years ago

a number is multiplied by 12 that tree is added to the result if the number is 51 what is the original number

ivann1987 [24]

The original number would be 48. 12 multiplied by 4 is 48, and if you add a three to that you will get 51.

Hope this helped :)

6 0

3 years ago

454 / 762 = ?

Maslowich

Answer:

huh-

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers

If a fair coin is tossed, the probability that it will land heads up is ½. Olivia tosses a coin 4 times, and it lands on heads 4

disa [49]

Answer:

Step-by-step explanation:

The tosses before that were all by chance, the probability is still the same. Nothing changes.

6 0

3 years ago