Please help me with this

Answer:

- 4 + 4√3 i, where a = -4 & b = 4√3

Step-by-step explanation:

z = 8 cis(2π/3)

z = 8 [cos(2π/3) + i sin(2π/3) ]

z = 8 [cos(π - π/3) + i sin(π - π/3)]

z = 8 [ - cosπ/3 + i sin(π/3)]

z = 8[ - 1/2 + i √3/2 ]

z = - 4 + 4√3 i [in a + bi form]

Note that: cis x = cosx + i sinx

Answer:

[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]

Step-by-step explanation:

we are given [tex]\displaystyle cis(\dfrac{2\pi}{3})[/tex]

recall complex number trigonometric form:

[tex] \displaystyle \: r( \cos( \theta) + i \sin( \theta) )[/tex]

we are already given that [tex]\theta=\dfrac{2\pi}{3}[/tex]

recall complex number rectangular form

[tex] \displaystyle \: a + bi[/tex]

where [tex]\displaystyle a=r\cos(\theta)\: and\: b=r\sin(\theta)[/tex]

let's work with a:

substitute the value of [tex]\theta[/tex] and r

[tex] \displaystyle \: a = 8 \times \cos( \frac{2\pi}{ 3} ) [/tex]

recall unit circle

so [tex]\cos(\dfrac{2\pi}{3})[/tex] should be in Q:II

[tex] \displaystyle \: a = 8 \times - \frac{1}{2} [/tex]

simplify multiplication:

[tex] \displaystyle \: a = - 4[/tex]

let's work with b:

substitute the value of [tex]\theta[/tex] and r:

[tex] \displaystyle \: b = 8\sin( \frac{3\pi}{2} ) [/tex]

recall unit circle so [tex]\sin(\dfrac{3\pi}{2})[/tex] should be in Q:II

[tex] \displaystyle \: b = 8 \times \frac{ \sqrt{3} }{2} [/tex]

simplify:

[tex] \displaystyle \: b = 4 \sqrt{3} [/tex]

so

[tex] \displaystyle \: b i= 4 \sqrt{3} i[/tex]

hence,

[tex]a + bi = - 4 + 4 \sqrt{3} i[/tex]

Answer:

log (150)=2.176091259

Answer:

log104=2.107

log150=2.176

log1025=3.011

log10570=4.024

log7=0.845

Step-by-step explanation:

To solve these questions, you can just plug them into your calculator:

log104=2.107033339≈2.107

log150=2.176091259≈2.176

log1025=3.010723865≈3.011

log10570=4.024074987≈4.024

log7=0.84509804≈0.845

Answer:

Points I guess

Answer:

840cm² its 840cm²

Answer:

x = 16

Step-by-step explanation:

If the figure is a parallelogram, the opposite sides are the same length

3x+20 = 5x-12

Subtract 3x from each side

3x+20 -3x = 5x-12-3x

20 = 2x-12

Add 12 to each side

20+12 = 2x-12+12

32 = 2x

Divide each side by 2

32/2 = 2x/2

16 =x

Answer:

a. $4

b. Noah has 5/5. Elena has 4/5.

Step-by-step explanation:

Noah has $5.

a.

Elena has 80% of Noah's money.

80% of $5 = 0.80 * $5 = $4

b.

Noah has $5. We can consider $5 to be the full amount.

A full amount is 100% or 1 or 5/5.

Elena has 80% of Noah's money, so she has 80/100 of Noah's money.

80/100 reduces to 4/5.

Noah has 5/5, and Elena has 4/5.

The money that Elena has is $2.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The given problem can be solved as follows,

(a) The amount of money Elena has is 40% of that of Noah.

It can be written as follows,

40% × 5

= 40/100 × 5

= 2

(b) Since the Elena has 40% of the Noah's money,

In the form of fraction it can be written as follows,

40% = 40/100

        = 2/5

This can be represented in a diagram as follows,

In the diagram shown the circle has in total 5 sectors of which 2 yellow sectors represent Elena's money.

Hence, the amount of money Elena has is $2 which is shown in the diagram.

To know more about percentage click on,

brainly.com/question/29306119

#SPJ2

Answer:

2

Step-by-step explanation:

16×5/8=10

16×1/4=4

16 - 10 - 4 =2

Answer:

0.03

Step-by-step explanation:

.25% for the tails times .5 for the odd number on the dice times 0.25 for the clubs because it is a 13/52 chance you will pull a clubs and put that all together and you get 0.03125 simplified and you get 0.03

Answer:

0.03

Step-by-step explanation:

The probability of landing on 1 tail is 1/2, since it is 1 out of 2 options, a tail or a head. If you want the probability of two tails, it would be 1/2 * 1/2 = 1/4.

Next we can take the probability of rolling an odd number on a fair die. A fair die has 3 even numbers: 2,4,6; and 3 odd numbers: 1,3,5. Since 3/6 or 1/2 of the numbers are odd, there is a 50% chance that it would roll an odd number.

Finally, drawing a club out of standard deck of cards is 1/4, since there are 4 choices: hearts, spades, clubs, or diamonds. You now get the idea, and you can figure out that the probability would be 1/4.

Our last step is to multiply all the answers we get, since to get all of them at once would lower your chances. 1/4 * 1/2 * 1/4 = 1/32 = 0.03125; rounded to 0.03.

Answer:

{(3,1),(2,4),(6,8)}

Step-by-step explanation:

Since for inverse of (x,y), it's(y,x)

i.e. the forst term and second term of order pair switch their places

Answer:

$14,000

Step-by-step explanation:

Answer:

Answer A

Step-by-step explanation:

ok.........................................

Answer:

54.85 un²

Step-by-step explanation:

Calculate the square and the circle and add them together.

[tex]2\pi[/tex]r

radius = 3

[tex]2\pi[/tex]3

Circumference = [tex]2\pi[/tex]r = 2 × [tex]\pi[/tex] × 3 = 18.84956

18.84956 rounds to 18.85

The circle's area is 18.85 un².

The square is 6 by 6.

6 × 6 = 36

The square's area is 36 un².

18.85 un² + 36 un² = 54.85 un²

Answer:

70%

Step-by-step explanation:

42/60 = 7/10

i am just doing this so I can get more answers

Step-by-step explanation:

9514 1404 393

Answer:

  b.  60

Step-by-step explanation:

We assume the percentage for the sample holds for the whole class, so the estimated number preferring November is ...

  0.248 × 230 = 57.04 ≈ 60

About 60 students prefer November.

Answer:

B

Step-by-step explanation:

Answer:

8.3

Step-by-step explanation:

Given,

Circumference of the circle = 52 cm

Therefore ,

By the problem,

[tex] = > 2\pi r = 52[/tex]

[tex] = > 2 \times 3.14 \times r = 52[/tex]

[tex] = > r = \frac{52}{3.14 \times 2} [/tex]

=> r = 8.2802547771

Rounded to nearest tenth,

=> r = 8.3 (Ans)

Answer:

Step-by-step explanation:

Answer:

y=-4x-5

Step-by-step explanation:

as considering (x,y) as(-2,3)this shows the perpendicularity

Answer:

×= 2 this is what I got as a result to my equations

Answer:

To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function!

Answer:

1/3 divided by 4

Step-by-step explanation:

Because you start off with 1/3 and then you split it into 4, 1/12's and 4*1/12 is equal to 1/3

So the answer is 1/3 divided by 4

Answer:

c. No, there are more than two possible outcomes for each trial.

Step-by-step explanation:

Binomial probability distribution:

Only two possible outcomes, success or failure.

In each trial, the probability of a success must be the same.

The number of trials must be fixed.

You ask ten randomly chosen college students to rate their experience at the dining hall on a scale of 1-5.

There are 10 trials, which is a fixed number and respects the binomial distribution. However, there are five possible outcomes(numbered 1 to 5). Since there is more than two possible outcomes, the scenario cannot be modeled using a binomial distribution, and the correct answer is given by option c.

Answer:

Answer:

62.5ft

Step-by-step explanation:

It doesnt matter if there's bumps along the side, the height will still reach to the same point.

Using trigonometry we have a adjacent and the opposite.

Hypotenuse is opposite the right angle

Opposite is opposite the angle

Adjacent is the last side to remain

Soh Cah Toa

We'll be using toa (Tan) because o and a (opposite and adjacent)

rearranging the original formuma :

Side × tan(Angle)

80 × tan (38) =62.50285....ft

the answer is B) both expressions are equivalent to 76 when t=3

Hope this helps :)

Answer:

D

Step-by-step explanation:

Hope i helped :)

Answer:

-60

Step-by-step explanation:

-45+s=-105

s=-105+45

s=-60

Answer:

33.97 m

Step-by-step explanation:

Given that,

The height of a man = 2 m

He stands on a horizontal ground 30m from a tree.

The angle of elevation of the top of the tree from his eyes is 28°.

We need to find the distance between the man eyes to the top of the tree. Let the height of the tree be h

Using trigonometry to find such that,

 [tex]\tan28=\dfrac{h}{30}\\\\h=\tan28\times 30\\\\h=15.95[/tex]

Now let us consider that the distance between the man eyes to the top of the tree is x. Using Pythagoras theorem,

[tex]x^2=30^2+15.95^2\\\\x=33.97\ m[/tex]

So, the distance between the man eyes to the top of the tree is 33.97 m.