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3 years ago

Find the value of x.

Mathematics

1 answer:

larisa86 [58]3 years ago

4 0

Answer:

savageserbs friends y.o.u.t.u.b.e

Step-by-step explanation:

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11111nata11111 [884]

Answer:
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3 0

3 years ago

Read 2 more answers

Solve the following equation:

Rama09 [41]

Complete the square.

$z^4 + z^2 - i\sqrt 3 = \left(z^2 + \dfrac12\right)^2 - \dfrac14 - i\sqrt3 = 0$

$\left(z^2 + \dfrac12\right)^2 = \dfrac{1 + 4\sqrt3\,i}4$

Use de Moivre's theorem to compute the square roots of the right side.

$w = \dfrac{1 + 4\sqrt3\,i}4 = \dfrac74 \exp\left(i \tan^{-1}(4\sqrt3)\right)$

$\implies w^{1/2} = \pm \dfrac{\sqrt7}2 \exp\left(\dfrac i2 \tan^{-1}(4\sqrt3)\right) = \pm \dfrac{2+\sqrt3\,i}2$

Now, taking square roots on both sides, we have

$z^2 + \dfrac12 = \pm w^{1/2}$

$z^2 = \dfrac{1+\sqrt3\,i}2 \text{ or } z^2 = -\dfrac{3+\sqrt3\,i}2$

Use de Moivre's theorem again to take square roots on both sides.

$w_1 = \dfrac{1+\sqrt3\,i}2 = \exp\left(i\dfrac\pi3\right)$

$\implies z = {w_1}^{1/2} = \pm \exp\left(i\dfrac\pi6\right) = \boxed{\pm \dfrac{\sqrt3 + i}2}$

$w_2 = -\dfrac{3+\sqrt3\,i}2 = \sqrt3 \, \exp\left(-i \dfrac{5\pi}6\right)$

$\implies z = {w_2}^{1/2} = \boxed{\pm \sqrt[4]{3} \, \exp\left(-i\dfrac{5\pi}{12}\right)}$

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20n%20%284p%20%2B%20%5Csqrt%7B36%7D%20-%202%20%7Bn%7D%5E%7B2%7D%20" i

Neporo4naja [7]

Answer:

-16.

Step-by-step explanation:

2/3 * (-3) * (4*5 + 6 - 2(-3)^2)

= -2(20 + 6 - 18)

= -2 * 8

= -16.

4 0

2 years ago

M = -2; (-11, -12)

Juliette [100K]

Answer:

y=-2x-12

Step-by-step explanation:

4 0

3 years ago

What is tge total surface area of a solid sphere of diameter 14cm

Alborosie

The surface area of a sphere of radius r is A = 4π*r^3.

Since the radius in this case is 7 cm (half the 14 cm diameter), the area of this sphere is

A = 4π(7 cm)^2, or 196π cm^2.

7 0

3 years ago