Are the two triangles below similar? N 259 50 5 105 50 3 01)

Find dy/dx given that y = sin x / 1 + cos x

kobusy [5.1K]

Answer:

$\frac{1}{1 + \cos(x) }$

Step-by-step explanation:

$y = \frac{ \sin(x) }{1 + \cos(x) }$

differentiating numerator wrt x :-

(sinx)' = cos x

differentiating denominator wrt x :- 

(1 + cos x)' = (cosx)' = - sinx

Let's say the denominator was "v" and the numerator was "u"

$(\frac{u}{v} )' = \frac{v. \: (u)' - u.(v)' }{ {v}^{2} }$

here,

since u is the numerator u= sinx and u = cos x
v(denominator) = 1 + cos x; v' = - sinx

$= \frac{((1 + \cos \: x) \cos \: x )- (\sin \: x. ( - \sin \: x) ) }{( {1 + \cos(x)) }^{2} }$

$= \frac{ \cos(x) + \cos {}^{2} (x) + \sin {}^{2} (x) }{(1 + \cos \: x) {}^{2} }$

since cos²x + sin²x = 1

$= \frac{ \cos \: x + 1}{(1 + \cos \: x) {}^{2} }$

diving numerator and denominator by 1 + cos x

$= \frac{1}{1 + \cos(x) }$

6 0

2 years ago

50% of what number is 15?

USPshnik [31]

Answer:

7.5

Step-by-step explanation:

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8 0

2 years ago

In what area did Taft's contributions equal or surpass Roosevelt's?

arsen [322]

Answer:

The area in which Taft contributed equal or surpass Roosevelt's was in conservation.....

Step-by-step explanation:

U 2 can help me by marking as brainliest........

6 0

1 year ago

Read 2 more answers

What is cos theta when sin theta = sqrt 2/3

Fittoniya [83]

Answer:

Value of cosθ is ±√7/3 .

Step-by-step explanation:

According to the Question , value of :

$\red{\implies sin\theta = \dfrac{\sqrt2}{3}}$

And , we know the identity of sine and cosine as ,

$\boxed{\pink{\sf\implies sin^2\theta + cos^2\theta = 1} }$

Using , this identity we have ;

$\implies sin^2\theta + cos^2\theta = 1 \\\\\implies \bigg( \dfrac{\sqrt2}{3}\bigg)^2 + cos^2\theta = 1 \\\\\implies \dfrac{2}{9} + cos^2\theta = 1 \\\\\implies cos^2\theta = 1 - \dfrac{2}{9} \\\\\implies cos^2\theta = \dfrac{9-2}{9} \\\\\implies cos\theta = \sqrt{\dfrac{7}{9}} \\\\\underline{\boxed{\blue{\bf \implies cos\theta = \pm \dfrac{\sqrt 7 }{3}}}}$

Now , here since θ is in 2nd quadrant and in 2nd quadrant cos is negative . Hence ,the value of cos will be :

$\boxed{\orange{\bf \implies cos\theta =-\dfrac{\sqrt7}{3}}}$

3 0

2 years ago

Abby counts 12 large boxes and 18 small boxes of pencils in the supply cabinet. Each large box contains 144 pencils . Each small

BigorU [14]

Answer:

2,160 pencils

Step-by-step explanation:

Large boxes = 12

Small boxes = 18

Each large box contains 144 pencils . Each small box contains 24 pencils

Total pencil in large boxes = Total large boxes × number of pencils per box

= 12 × 144

= 1,728 pencils

Total pencil in small boxes = Total small boxes × number of pencils per box

= 18 × 24

= 432 pencils

Estimate the total number of of pencils

Total number of pencils = total pencils in large boxes + total pencil in small boxes

= 1,728 pencils + 432 pencils

= 2,160 pencils

It is better to have an underestimate than an overestimate so that you won't disappoint your buyers when they request for a quantity of supply. If it is underestimated; you can meet demand, if it is overestimated; you can't meet demand

3 0

2 years ago

Are the two triangles below similar? N 259 50 5 105 50 3 01) ​

Are the two triangles below similar? N 259 50 5 105 50 3 01)