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3 years ago

Write -4-10 in addition

Mathematics

1 answer:

Llana [10]3 years ago

8 0

Answer:

Step-by-step explanation:

In mathematics, sum can be defined as the result or answer we get on adding two or more numbers or terms.

(-4)-10=14

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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

An amusement park charges $120 for a one-week pass. If the pass is put on sale at a 25% discount, what is the amount of the sale

Flura [38]

Answer:

100 - 25 = 75

120/100 X 75 = 90

sale price is $90

8 0

3 years ago

the hypotonuse of a right triangle measures 15cm and one of its legs meauseres 8cm find the measure of the other leg

Elza [17]

Answer:

12.6 cm

Step-by-step explanation:

(other leg)² = (15)² - (8)²

(other leg)² = 225 - 64

other leg = √161 ≈ 12.6 cm

8 0

2 years ago

Read 2 more answers

What is the value of 1027 A. 100 B. 1,000 C. 10,000 D. 100,000

My name is Ann [436]

Answer:

huh? this doesn't even make sense or I'm just tripib

Step-by-step explanation:

-xoxo

7 0

3 years ago

Find the minimum value of the function f(x) = 1.5x2 + 10x + 12 to the nearest hundredth.

slamgirl [31]

Answer:

-14/3

Step-by-step explanation:

Use derivative = 0 to find turning point(S)

D f(x) = 3x + 10 = 0

3x = - 10

X = - 10/3

When X = - 10/3

F(x) = 1.5(10/3)^2 - 10(10/3) + 12

= (3*10*10) / (2*3*3) - 100/3 +12

= 50/3 - 100/3 + 36/3

= - 14/3

4 0

2 years ago