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3 years ago

ASAP PLS! Brainliest points!

Mathematics

1 answer:

nata0808 [166]3 years ago

3 0

Answer:

Step-by-step explanation:

y=2x because

3x2 =6

10x2=20

12x2=24

17x2=34

I hope it's the right answer .

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Integrate dx/3sinx+4cosx

german

$\displaystyle\int\frac{\mathrm dx}{3\sin x+4\cos x}$

A standard approach would be the tangent half-angle substitution:

$t=\tan\dfrac x2\implies\mathrm dt=\dfrac12\sec^2\dfrac x2\,\mathrm dx$

Then

$\sin x=2\sin\dfrac x2\cos\dfrac x2\implies\sin x=\dfrac{2t}{1+t^2}$

$\cos x=\cos^2\dfrac x2-\sin^2\dfrac x2\implies\cos x=\dfrac{1-t^2}{1+t^2}$

from which we get

$\mathrm dx=\dfrac2{1+t^2}\,\mathrm dt$

So the integral becomes

$\displaystyle\int\frac{\frac2{1+t^2}}{\frac{6t}{1+t^2}+\frac{4(1-t^2)}{1+t^2}}\,\mathrm dt=\int\frac{\mathrm dt}{3t+2(1-t^2)}=-\int\frac{\mathrm dt}{2t^2-3t-2}$

Rewrite the denominator as

$2t^2-3t-2=(2t+1)(t-2)$

and expand the integrand into its partial fractions:

$\dfrac1{2t^2-3t-2}=\dfrac15\left(\dfrac1{t-2}-\dfrac2{2t+1}\right)$

We have

$\displaystyle-\frac15\int\frac1{t-2}-\frac2{2t+1}\,\mathrm dt=-\frac15(\ln|t-2|-\ln|2t+1|)+C$

$=\dfrac15\ln\left|\dfrac{2t+1}{t-2}\right|+C$

$=\dfrac15\ln\left|\dfrac{2\tan\frac x2+1}{\tan\frac x2-2}\right|+C$

6 0

3 years ago

If Yoko walks 1 block in 3 minutes, how long does it take her to walk from the school to the library? How long does it take her

mojhsa [17]

Answer:

from school to the library it would take 21 minutes, home to school would be 5

Step-by-step explanation:

6 0

3 years ago

How can I change Celsius to Fahrenheit

Ket [755]

You can use the formula,

F = 9C/5 + 32

3 0

3 years ago

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Your class starts at 12:12PM and ended at 12:50PM what angle did the minute hand of watch sweep through during the class

Arisa [49]

we know that

12:50PM-12:12PM=38 minutes

30 minutes in the minute hand of watch is equal an angle of 180 degrees

by proportion

30/180=38/x-------> 30*x=180*38--------> x=180*38/30------> x=228°

therefore

the answer is

228 degrees

7 0

3 years ago

10 is 60% of what number please help

xxTIMURxx [149]

Answer:

600

Step-by-step explanation:

set x as the number

x0.10 = 60

x = 60/0.10

x = 600

6 0

3 years ago

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