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3 years ago

Find all the complex square roots of w= 36(cos60°+ isin60°). Write the roots in polar form with θ in degrees.

Mathematics

1 answer:

DochEvi [55]3 years ago

4 0

Answer:

3√3+i3

Step-by-step explanation:

w= 36(cos60°+ isin60°)

√w = $w^{1/2}$ =√36(cos60°+ isin60°)

=6√(cos60°+ isin60°)

now using DeMoivre's theorem

=(cos60°+ isin60°)^{1/2}

=(cos60°/2+ isin60°/2)=(cos30°+ isin30°)

w^{1/2}=6(cos30°+ isin30°)

=6(sqrt3/2+i1/2) $\sqrt{frac{3}{2} }$

=3√3+i3

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wyatt opend a savings account 4 years ago. the account earns 4%interest compounded quarterly if the current balance is $1,000.00

Doss [256]

Answer:

He deposited initially $852.82

Step-by-step explanation:

The rule of the compound interest is $A=P(1+\frac{r}{n})^{nt}$ , where

A is the new amount

P is the initial amount

r is the rate in decimal

n is the period of the time

t is the time

∵ Wyatt opened a savings account 4 years ago

∴ t = 4

∵ The account earns 4% interest compounded quarterly

∴ r = 4% = 4 ÷ 100 = 0.04

∴ n = 4 ⇒ compounded quarterly

∵ The current balance is $1,000.00

∴ A = 1,000

→ Substitute these values in the rule above to find P

∵ 1,000 = $P(1+\frac{0.04}{4})^{4(4)}$

∴ 1,000 = $P(1+0.01)^{16}$

∴ 1,000 = $P(1.01)^{16}$

→ Divide both sides by $(1.01)^{16}$

∴ 852.8212622 = P

→ Round it to the nearest cent (2d.p)

∴ P = 852.82

∴ He deposited initially $852.82

4 0

3 years ago

Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal:

DochEvi [55]

We are given

$\frac{(4.1\times 10^{3})(2.8\times 10^{-7})}{(3.1\times 10^{-5})}$

We can move like terms altogether

$\frac{(4.1\times 10^{3})(2.8\times 10^{-7})}{(3.1\times 10^{-5})}=\frac{4.1\times 2.8}{3.1}\times \frac{10^{3}\times 10^{-7}}{10^{-5}}$

now, we can use property of exponent

$a^m\times a^n=a^{m+n}$

$=\frac{4.1\times 2.8}{3.1}\times \frac{10^{3-7}}{10^{-5}}$

We can use another exponent property

$\frac{a^m}{a^n} =a^{m-n}$

so, we get

$=\frac{4.1\times 2.8}{3.1}\times 10^{3-7+5}$

$=\frac{4.1\times 2.8}{3.1}\times 10^{1}$

$=3.70323\times 10^{1}$

So, the result in scientific notation is

$=3.70323\times 10^{1}$ ..........Answer

So, the result as a decimal is

$=37.0323$ .............Answer

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4 years ago

Brittney sewed together fabric triangles to make the quilt square shown below.

Snezhnost [94]

Answer:

6 in. per triangle & 24 in total (white squares only)

Step-by-step explanation:

So, one side is 12 inches and each side is made up of one blue and one white. With this you can just divide each side by 2, getting 6. There are 4 sides so,

4 sides X 6 in. per each square= 24

Therefore, she used <u><em>24 in. in total</em></u> and 6 for each triangle.

Hoped this helped!

6 0

3 years ago

Without doing the math, determine which is greater, 40 . 1/4 or 40/14. explain your reasoning

BARSIC [14]

40 is greater because we can easily see that 1/4 is not a whole number that is less than 40 and the 40/14 will be changed into a lesser mixed number which again, is less than 40.

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3 years ago

During a sale, Cindy found boxes of dog biscuits on sale for $0.69 that had previously cost $2.23. What percentage is the discou

N76 [4]

Answer:

The dog biscuits are approximately 69% off.

Step-by-step explanation:

(1 - 0.69/2.23) * 100

(223/223 - 69/223) * 100

154/223 * 100 = 69%

7 0

3 years ago