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3 years ago

Write each of the following percents in words. a. 5% b.34% c.143% b. 500%

Mathematics

1 answer:

luda_lava [24]3 years ago

4 0

Five percent, thirtyfour percent, onehundred and fourty three percent, and fivehundred percent. No explanation needed

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D/d{cosec^-1(1+x²/2x)} is equal to

SIZIF [17.4K]

Step-by-step explanation:

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

Let assume that

$\rm :\longmapsto\:y = {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

We know,

$\boxed{\tt{ {cosec}^{ - 1}x = {sin}^{ - 1}\bigg( \dfrac{1}{x} \bigg)}}$

So, using this, we get

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2x}{1 + {x}^{2} } \bigg)$

Now, we use Method of Substitution, So we substitute

$\red{\rm :\longmapsto\:x = tanz \: \rm\implies \:z = {tan}^{ - 1}x}$

So, above expression can be rewritten as

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( \dfrac{2tanz}{1 + {tan}^{2} z} \bigg)$

$\rm :\longmapsto\:y = sin^{ - 1} \bigg( sin2z \bigg)$

$\rm\implies \:y = 2z$

$\bf\implies \:y = 2 {tan}^{ - 1}x$

So,

$\bf\implies \: {cosec}^{ - 1}\bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = 2 {tan}^{ - 1}x$

Thus,

$\rm :\longmapsto\:\dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg)$

$\rm \: = \: \dfrac{d}{dx}(2 {tan}^{ - 1}x)$

$\rm \: = \: 2 \: \dfrac{d}{dx}( {tan}^{ - 1}x)$

$\rm \: = \: 2 \times \dfrac{1}{1 + {x}^{2} }$

$\rm \: = \: \dfrac{2}{1 + {x}^{2} }$

Hence, 

$\purple{\rm :\longmapsto\:\boxed{\tt{ \dfrac{d}{dx} {cosec}^{ - 1} \bigg( \dfrac{1 + {x}^{2} }{2x} \bigg) = \frac{2}{1 + {x}^{2} }}}}$

Hence, Option (d) is correct.

6 0

2 years ago

Which of the following is an example of a proper fraction?

mafiozo [28]

Answer:

I would appreciate if my answer is chosen as a brainliest answer

5 0

2 years ago

Could someone answer this

Ksenya-84 [330]

Answer:

y=-8

x=-7

Step-by-step explanation:

x-2y=9 x=2y+9

3x-5y=19

3(2y+9)-5y=19

6y+27-5y=19

y+27=19

y=-8

x=2(-8)+9=-16+9=-7

8 0

3 years ago

6=u/9.6 What does U=?

uranmaximum [27]

Answer:

U=57.6

Step-by-step explanation:

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3 years ago

I GIVE BRAINLIEST FOR ANSWERS AND EXPLANATION

irina1246 [14]

Answer:

18.1

Step-by-step explanation:

You can use the c = b/cos(a) which when subsituted gives u c= 16/cos(28) which when u solve gives u 18.12112

3 0

3 years ago

Read 2 more answers