72 marble and 75% are red

Find the solution of the following equation whose argument is strictly between 270^\circ270 ∘ 270, degree and 360^\circ360 ∘ 360

Natasha2012 [34]

$\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]$

$\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]$

Argument of Complex number

Z=x+iy , is given by

If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

$\rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]$

5 0

3 years ago

a rectangular tank is 3/4 filled with water, when the metal prism is placed in the tank, it is 79/100 full. find the width w of

Llana [10]

The volume of the prism ... L x W x H ... is 0.04 of the volume of the tank.
If the prism is rectangular, then its width is (0.04 of the volume of the tank) divided by (L x H of the prism) .

5 0

3 years ago

Trevor covered a cylindrical can with paper for a project. The

Delicious77 [7]

Answer:

722 cm ^2

Step-by-step explanation:

6 0

3 years ago

If f(x) varies directly with x and f(x) = 4 when x = 12, then what is the value of f(x) when x = 60?

ANTONII [103]

ANSWER

$f(60)=3\times60=180$

EXPLANATION
We were given that
$f(x)$
varies directly as
$x.$

We can write this mathematically as,

$f(x) \propto \: x.$

This implies that,

$f(x) = kx$
where k is the constant of variation.

$f(4)=4k$

This implies that,

$4k=12$

$k = 3$

The equation becomes

$f(x)=3x$

When $x=60$

$f(60)=3\times60=180$

6 0

4 years ago

Trigonometry question! find y. round to the nearest tenth!

tresset_1 [31]

Answer:

Step-by-step explanation:

Look at the picture.

Use sine:

$sine=\dfrac{opposite}{hypotenuse}$