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3 years ago

Please I need help on the first one. Can someone explain it to me or answer it

Mathematics

1 answer:

Ede4ka [16]3 years ago

8 0

[A]

This is because a complement is another angle that when you add both of the angles together, it equals 90 degrees.

18*4=72

18+72=90

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What is a complex series notation that equals one

Romashka [77]

we know the complex number has standard form a+ib

Inorder to find our answer ib^2 should.be 1

Ex:-

2-i

2:-

$\\ \sf\longmapsto 2+2i^2$

i^4=1

3 0

3 years ago

Read 2 more answers

Emily spent $55 from her savings on a new dress. explain how to descibe the change Emily's savings balance in 2 different ways

Step2247 [10]

S= savings before she bought the dress s - $55 would be her new balance after she bought the dress.

We could also talk about her savings now (after her purchase). If we let n=now
n + $55 would be her balance before she bought the dress.

8 0

4 years ago

Find the center, vertices, and foci for the ellipse 25x^2 + 64y^2 = 1600

Alisiya [41]

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Equation 25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

25x²/1600 + 64y²/ 1600 = 1600/1600

-Simplify

x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

$\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1$

3.- Find a, b and c

a² = 64 a = 8

b² = 25 b = 5

-Calculate c with the Pythagorean theorem

a² = b² + c²

-Solve for c

c² = a² - b²

-Substitution

c² = 8² - 5²

-Simplification

c² = 64 - 25

c² = 39

-Result

c = √13

4.- Find the center

C = (0, 0)

5.- Find the vertices

V1 = (-8, 0) V2 = (8, 0)

6.- Find the foci

F1 = (-√13, 0) F2 = (√13, 0)

7 0

3 years ago

Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

BartSMP [9]

By using De Moivre's theorem:

If we have the complex number ⇒ z = a ( cos θ + i sin θ)
∴ $\sqrt[n]{z} = \sqrt[n]{a} \ (cos \ \frac{\theta + 360K}{n} + i \ sin \ \frac{\theta +360k}{n} )$
k= 0, 1 , 2, ..... , (n-1)

For The given complex number ⇒ z = 81(cos(3π/8) + i sin(3π/8))


Part (A) find the modulus for all of the fourth roots

∴ The modulus of the given complex number = l z l = 81

∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
There is four roots and the angle between each root = $\frac{2 \pi}{4} = \frac{\pi}{2}$
The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
The angle of the fourth root = $\frac{35\pi}{32} + \frac{\pi}{2} = \frac{51\pi}{32}$

Part (C): find all of the fourth roots of this

The first root = $z_{1} = 3 ( cos \ \frac{3\pi}{32} + i \ sin \ \frac{3\pi}{32})$
The second root = $z_{2} = 3 ( cos \ \frac{19\pi}{32} + i \ sin \ \frac{19\pi}{32})$

The third root = $z_{3} = 3 ( cos \ \frac{35\pi}{32} + i \ sin \ \frac{35\pi}{32})$
The fourth root = $z_{4} = 3 ( cos \ \frac{51\pi}{32} + i \ sin \ \frac{51\pi}{32})$

7 0

4 years ago

Which equation can be used to find one-tenth of 119.9

mel-nik [20]

To find one tenth of 119.9 just divide 119.9 by 10

3 0

3 years ago