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3 years ago

In an arithmetic sequence , the 6th term is 9 and the 8th term is 15

1 answer:

8 0

Hopefully the math terms won't confuse anyone.

So in the series, a_6 = 9 and a_8 = 15. Since it's an arithmetic sequence, all the terms in the series can be represented as:
a_n = a_0 + n * k
where n is the nth number. K is a constant you add to reach the next term, and a_0 is the starting constant.
a_6 = a_0 + 6 * k
a_8 = a_0 + 8 * k
solving this system gives you that
k = 3 and a_0 = -9
for any term n for this arithmetic sequence,
a_n = -9 + 3 * k

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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

3 years ago

A 51-foot ladder is leaning up against a building . The top of the ladder reaches the wall at a height of 50 feet . How far is t

alexandr402 [8]

If 50^2 +b^2=51^2 then
2500+b^2=2601
b^2=100
b=10

4 0

3 years ago

Read 2 more answers

Firewood can be sold in cords. the wood is cut into equal lengths and stacked evenly in a rack. which geometric shape can be use

Nadya [2.5K]

To estimate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

<h3>What is a cylinder?</h3>

In mathematics, a cylinder exists as a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance. These bases exist normally circular (like a circle) and the center of the two bases exists joined by a line segment, which exists named the axis.

A cylinder exists as a closed solid that contains two parallel circular bases joined by a curved surface.

To calculate the volume of the chord of wood, since the wood exists cut into equal lengths and stacked evenly in a rack then we can use a cylinder as a model.

To learn more about cylinders refer to:

brainly.com/question/8531193

#SPJ4

7 0

1 year ago

Easy and simple but i don’t know which one goes to which. please help

Llana [10]

Answer:

They are placed in right order (quite interesting).

Step-by-step explanation:

Just drag each answer choice as they are placed.

Best Regards!

6 0

3 years ago

Find the unit price of 8 mugs for $38.32 A.) $4.99 B.) $4.97 C.) $4.79 D.) $4.77

Anastasy [175]

Answer:

C. 4.79

Step-by-step explanation:

I divided 38.32 by 8 to find the individual prices

8 0

2 years ago

Read 2 more answers