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3 years ago

Could someone check that I did this correctly? It's about complex numbers. Thank you!

Mathematics

1 answer:

Ivan3 years ago

3 0

Answer:

All your steps are correct. Well done!

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What is the solution -1 -7 ?

Effectus [21]

Answer:

-8

Step-by-step explanation:

Add the two numbers but maintain the negative sign.

3 0

2 years ago

1. 5/6x-2=1/x+1

Pani-rosa [81]

1. 30x-2=1x+1
28x=2x
14=x

4 0

3 years ago

The general solution of 2 y ln(x)y' = (y^2 + 4)/x is

Sav [38]

Replace $y'$ with $\dfrac{\mathrm dy}{\mathrm dx}$ to see that this ODE is separable:

$2y\ln x\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{y^2+4}x\implies\dfrac{2y}{y^2+4}\,\mathrm dy=\dfrac{\mathrm dx}{x\ln x}$

Integrate both sides; on the left, set $u=y^2+4$ so that $\mathrm du=2y\,\mathrm dy$ ; on the right, set $v=\ln x$ so that $\mathrm dv=\dfrac{\mathrm dx}x$ . Then

$\displaystyle\int\frac{2y}{y^2+4}\,\mathrm dy=\int\dfrac{\mathrm dx}{x\ln x}\iff\int\frac{\mathrm du}u=\int\dfrac{\mathrm dv}v$

$\implies\ln|u|=\ln|v|+C$

$\implies\ln(y^2+4)=\ln|\ln x|+C$

$\implies y^2+4=e^{\ln|\ln x|+C}$

$\implies y^2=C|\ln x|-4$

$\implies y=\pm\sqrt{C|\ln x|-4}$

4 0

2 years ago

The trail is a loop that is 3/4 of a mile long. On Monday, Selma land the loop in 1/6 of an hour. What is selmas unit rate in mi

Dafna11 [192]

Answer:

1/10

Step-by-step explanation:

3/4 add 1/6

4 0

2 years ago

Find the area of the shaded region. Round your answer to the nearest tenth.

Troyanec [42]

Area of the square = (9 m)^2 = 81 m^2

The four circular sectors combine to form a circle with diameter 9 m, hence radius 4.5 m.

Area of the circle = π (4.5 m)^2 = 20.25π m^2

Then the area of the shaded region is

81 m^2 - 20.25π m^2 ≈ 17.4 m^2

7 0

3 years ago