=

Y=arccos(1/x) Please help me do them all! I don’t know derivatives :(

Stells [14]

Answer:

$f(x) = {sec}^{ - 1} x \\ let \: y = {sec}^{ - 1} x \rightarrow \: x = sec \: y\\ \frac{dx}{dx} = \frac{d(sec \: y)}{dx} \\ 1 = \frac{d(sec \: y)}{dx} \times \frac{dy}{dy} \\ 1 = \frac{d(sec \: y)}{dy} \times \frac{dy}{dx} \\1 = tan \: y.sec \: y. \frac{dy}{dx} \\ \frac{dy}{dx} = \frac{1}{tan \: y.sec \: y} \\ \frac{dy}{dx} = \frac{1}{ \sqrt{( {sec}^{2} \: y - 1}) .sec \: y} \\ \frac{dy}{dx} = \frac{1}{ |x | \sqrt{ {x }^{2} - 1} } \\ \therefore \frac{d( {sec}^{ - 1}x) }{dx} = \frac{1}{ |x | \sqrt{ {x }^{2} - 1} } \\ \frac{d( {sec}^{ - 1}5x) }{dx} = \frac{1}{ |5x | \sqrt{25 {x }^{2} - 1} }\\\\y=arccos(\frac{1}{x})\Rightarrow cosy=\frac{1}{x}\\x=secy\Rightarrow y=arcsecx\\\therefore \frac{d( {sec}^{ - 1}x) }{dx} = \frac{1}{ |x | \sqrt{ {x }^{2} - 1} }$

4 0

3 years ago

A health inspector must visit 44 of 1414 restaurants on monday. in how many ways can she pick a first comma second comma third c

ira [324]

Let's make clear the question, because it may be confusing:
"A health inspector must visit 4 of 14 restaurants on Monday. In how many ways can she pick a first, second, third, and fourth restaurant to visit?"

In order to solve the problem, you need to use permutations: you have 14 possible restaurants to choose as first, the second one will be chosen among the 13 restaurants left, the third one among the remaining 12 and the fourth one will be one of the remaining 11.

Therefore, the total number of possibilities is:
14 × 13 × 12 × 11 = 24024

There are 24024 possible ways to choose the four restaurants to visit.

4 0

3 years ago

Factorise: 8x^3 + 27y^3 + 36x^2y + 54xy^2

Free_Kalibri [48]

Answer:

=(2x−3y)(2x−3y)(2x−3y)

Step-by-step explanation:

8x

3

−27y

3

−36x

2

y+54xy

2

=(2x)

3

−(3y)

3

−3×(2x)

2

×3y+3×2x×(3y)

2

Using,(a−b)

3

=a

3

−b

3

−3a

2

b+3ab

2

=(2x−3y)

3

=(2x−3y)(2x−3y)(2x−3y)

5 0

2 years ago

If U={1,2,3,4,5,6,7,8},A={1,2,3,4},B={3,4,5,6,7}.find(AUB)'

EastWind [94]

Answer:

12345678910

iya lina beb

7 0

3 years ago

Points Q and R are midpoints of the sides of triangle ABC.

givi [52]

we know that

In the figure triangle ABC and triangle AQR are similar triangles

so

by proportion

$\frac{QR}{AQ} =\frac{BC}{AB} \\ \\ \frac{2p+3}{4p} =\frac{6p-4}{8p} \\ \\ 2*(2p+3)=(6p-4)\\ \\ 4p+6=6p-4\\ \\ 6p-4p=6+4\\ \\ 2p=10\\ \\ p=5$

$AQ=4p\\ AQ=4*5\\ AQ=20\ units$

therefore

the answer is

AQ is $20\ units$

6 0

3 years ago

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