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2 years ago

Given z^3 = 3 + square root 3i which letter represents z

Mathematics

1 answer:

Marianna [84]2 years ago

8 0

The expression that represents the value of z is $\sqrt[3]{3 + i\sqrt 3 }$

<h3>What are complex numbers?</h3>

Complex numbers are numbers that have real and imaginary parts

A complex number (n) is represented as:

$n = a + bi$

From the above expression, we have:

a represents the real part
bi represents the imaginary part

Given that:

$z^3 = 3 + \sqrt 3 i$

Rewrite the above expression as:

$z^3 = 3 + i\sqrt 3$

Take the cube roots of both sides

$z = \sqrt[3]{3 + i\sqrt 3 }$

The letters are not given.

Hence, the expression that represents the value of z is $\sqrt[3]{3 + i\sqrt 3 }$

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Tina's aquarium has a capacity of 40 gallons or water. She plans to stock her aquarium with 0.25 inches of fish per quart of cap

Sonbull [250]

Answer:

The number of mollies fishes in the aquarium is 20 .

Step-by-step explanation:

Given as :

The capacity of aquarium = 40 gallons

∵ 1 gallon = 4 quart

∴ 40 gallons = 4 × 40 = 160 quart

Now, According to question

0.25 inches of fish required 1 quart capacity

I.e for 1 quart capacity , 0.25 inches fish

So. for 160 quart capacity , 0.25 × 160 = 40 inches fishes

Now the size of mollies fish = 2 inches

Then , number of mollies fish = $\dfrac{\textrm total size of fishes}{\textrm size of mollies fish}$

I.e Number of mollies fish = $\frac{40}{2}$ = 20

Hence The number of mollies fishes in the aquarium is 20 . Answer

3 0

3 years ago

Is f(x)=x^2-2x+3 a quadratic function

Sav [38]

Answer:

yes

Step-by-step explanation:

A quadratic function has the general form

fx) = ax² + bx + c ( a ≠ 0 )

f(x) = x² - 2x + 3 ← is in this form and is a quadratic function

6 0

3 years ago

Read 2 more answers

If Free Yer Assets Bank (FYAB) will give you 0.25% compounded quarterly and I.M.A.Q.T.π bank will give you 0.23% interest compou

ivann1987 [24]

Answer:

FYAB gives a better deal.

Step-by-step explanation:

Compound interest:

$A = P(1 + \dfrac{r}{n})^{nt}$

Continuously compounded interest:

$A = Pe^{rt}$

For the quarterly compounded interest, r = 0.25%, and n = 4.

$2P = P(1 + \dfrac{0.0025}{4})^{4t}$

$1.000625^{4t} = 2$

$\log (1.000625^{4t}) = \log 2$

$4t(\log 1.000625) = \log 2$

$t = \dfrac{\log 2}{4\log 1.000625}$

$t = 277$

For the continuously compounded interest, r =0.23%

$A = Pe^{rt}$

$2P = Pe^{0.0023t}$

$2 = e^{0.0023t}$

$\ln 2 = \ln e^{0.0023t}$

$\ln 2 = 0.0023t$

$t = \dfrac {\ln 2}{0.0023}$

$t = 301$

The quarterly compounded doubles in 277 years.

The continuously compounded doubles in 301 years.

Answer: FYAB gives a better deal.

7 0

3 years ago

Solve the equation. 2(y – 4) = 4 SHOW YOUR WORK!

ahrayia [7]

2(y−4)=4

(2)(y)+(2)(−4)=4

2y+−8=4

2y−8=4

2y−8+8=4+8

2y=12

$\frac{2y}{2}=\frac{12}{2}$

y=6 is correct answer.

Hope this helps!

Thanks!

8 0

3 years ago

Seven customers enter a clothing store and are observed to determine if they will make a purchase. The store owner states that t

blondinia [14]

Answer: Mean = 5.25

Variance = 1.3125

Standard deviation = 1.456

Step-by-step explanation:

The mean and variance of a binomial distribution with parameters n (number of trials) and p ( the probability of getting success in each trial) is given by :-

$\text{Mean}=np\\\\\text{Variance}=np(1-p)$

Given : The total number of enter a clothing store : n=7

The probability of a customer making a purchase= 0.75

Now,

$\text{Mean}=7(0.75)=5.25\\\\\text{Variance}=7(0.75)(0.25)=1.3125\\\\\Rightarrow\ \text{Standard deviation}=\sqrt{1.3125}=1.14564392374\approx1.1456$

3 0

3 years ago