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1 year ago

Question 16 of 25

Mathematics

2 answers:

andrew-mc [135]1 year ago

8 0

Answer:

$\textsf {D}$

Step-by-step explanation:

$\textsf {The Law of Sines states that the ratio of sine of an angle} \\\textsf{to the length of the opposite side is the same for all parts of the triangle.}$

$\textsf {Hence, the derived formula is :}$

$\implies \mathsf {\frac{sinA}{a} = \frac{sinB}{b} }$

$\textsf {* a = opposite side of angle A}\\\textsf {* b = opposite side of angle B}$

Reil [10]1 year ago

4 0

Answer:

Option D

Step-by-step explanation:

The formula of sine is

sinA=Opposite/Hypotenuse

So it's same thorughout out the triangle for the same angle.

Sin is commonly used as Perpendicular/Height divided by Hypotenuse

You might be interested in

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

3 years ago

Can anyone help me with 24,27,30 and 33 please

mamaluj [8]

24) 9/19

27 is a bit tricky for me.. sorry ):

30) On the 7th it will be 1/120
33) C

7 0

2 years ago

The price of a swimming pool

Goryan [66]

Answer:

$Sales\:\:Price=List\:\:Price-Discount$
Sales price= $ $1167.25$ List price=L Discount $=19.5\%\:of\:L=0.195L$
$1167.25=L-0.195L$

Step-by-step explanation:

The percentage discount is $19.5\%$

The discount is always given on the list price.

$Sales\:\:Price=List\:\:Price-Discount$

Let the list price be L, then

List price=L

Sales price= $ $1167.25$

Discount $=19.5\%\:of\:L=0.195L$

We substitute into the equation to get:

$1167.25=L-0.195L$

$1167.25=0.805L$

Divide both sides by 0.805

$\frac{1167.25}{0.805}=L$

$1450=L$

The list price of the swimming pool is $1450

5 0

3 years ago

if you deposit $10000 at 11%(simple interest), how long will it be until the total amount in the account is $21000?

ki77a [65]

10000:100*11=1100 income per year

21000-10000=11000 need to have income

11000:1100=10 years will pass time

4 0

3 years ago

If x + y = x y = 5 then x ^2 y + X Y ^ 2 equals

VikaD [51]

Answer:

Step-by-step explanation:

Note x^2y + xy^2 = xy(x+y)

We know xy = 5 and x+y = 5, so

5*5=25

3 0

3 years ago