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3 years ago

Solve Y=3/2cot(1/2x)

Mathematics

1 answer:

Galina-37 [17]3 years ago

3 0

So basically the x will want to be singled out and 3/2-y=the variable

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What is the simplified form of the expression k^3(K^7/5)^-5

Vladimir79 [104]

$\bf k^3\left( \cfrac{k^7}{5} \right)^{-5}\implies k^3\left( \cfrac{5}{k^7} \right)^5\implies k^3\left( \cfrac{5^5}{k^{7\cdot 5}} \right)\implies k^3\cdot \cfrac{5^5}{k^{35}}
\\\\\\
k^3\cdot 5^5\cdot k^{-35}\implies 5^5\cdot k^{3-35}\implies 5^5k^{-32}\implies \cfrac{5^5}{k^{32}}\implies \cfrac{3125}{k^{32}}$

3 0

4 years ago

30PTS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1

Yuliya22 [10]

P = 1500, r = 4% = 0.04, n = 5

$A = 1500 (1+0.04)^5= 1824.98$

He shall have $1824.98 in his account after 5 years

Here P = 1500 , r = 4% = 0.04, n = 5 but simple interest

$I=PRn= 1500(.04)(5)=300$

Interest = $300

Amount in his account after 5 years = 1500 + 300 = $1800

First one shall yield a better income and by 1824.98-1800 = $24.98

P= $2000, r = 8% = 0.08 so quaterly = 0.08/4 = 0.02, n = 1 year

$A = P(1+r)^{4n} =2000(1+0.02)^4 =2164.86$

There shall be $2164.86 after 1 year

P = 2000, r= 8%=0.08 and n = 1 for simple interest

$I=PRn = 2000(0.08)(1)=160$

Amount after 1 year shall be 2000 + 160= $2160

First option is a better option.

The difference is 2164.86 - 2160 = $4.86

Bank A

P= 3200, r = 3.5%= 0.035, n = 3 years for simple interest

$I =3200(0.035)(3)=336$

Interest earned in Bank A = $336

Bank B

P = 3200, r = 3.4% = 0.034, n= 3

$A= P(1+r)^n=3200(1+0.034)^3=3537.62$

Interest earned = 3537.62 - 3200 = $337.62

Tyler must choose Bank B as it fetches greater interest

The difference in interest = 337.62 - 336 = $1.62

4 0

3 years ago

Using the factorised trinomial <img src="https://tex.z-dn.net/?f=%28n-2%29%284n-7%29" id="TexFormula1" title="(n-2)(4n-7)" alt="

andrew-mc [135]

4n² - 15n + 14 is always the product of two numbers, for it to be prime number, one of these factors must be either 1 or -1.

Case n - 2 = 1
That would be n = 3
Then 4n² - 15n + 14 = 5 , which is prime.

Case n - 2 = -1
That would be n = 1
Then 4n² - 15n + 14 = 3, which is also prime.

Case 4n - 7 = 1
That would be n = 2 and that makes other factor (n-2) zero so it's not prime

Case 4n-7 = -1
That would be n = 3/2 which is not integer, so 4n² - 15n + 14 will not be interger.

For any other n values, 4n² - 15n + 14 will be composite number since it is product of two factors.

Therefore we are left with n = 1 and n = 3; only two values of n.

5 0

3 years ago

Which expression is a fourth root of -1+isqrt3?

aleksklad [387]

Answer:

Step-by-step explanation:

$\sf n^{th}$ roots of a complex number is given by DeMoivre's formula.

$\sf \boxed{\bf r^{\frac{1}{n}}\left[Cos \dfrac{\theta + 2\pi k}{n}+i \ Sin \ \dfrac{\theta+2\pi k}{n}\right]}$

Here, k lies between 0 and (n -1) ; n is the exponent.

$\sf -1 + i\sqrt{3}$

a = -1 and b = √3

$\sf \boxed{r=\sqrt{a^2+b^2}} \ and \ \boxed{\theta = Tan^{-1} \ \dfrac{b}{a}}$

$\sf r = \sqrt{(-1)^2 + 3^2}\\\\ = \sqrt{1+9}\\\\=\sqrt{10}$

$\sf \theta = tan^{-1} \ \dfrac{\sqrt{3}}{-1}\\\\ = tan^{-1} \ (-\sqrt{3})$

$\sf = \dfrac{-\pi }{3}$

n = 4

For k = 0,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{\dfrac{-\pi}{3} +0}{4}+iSin \ \dfrac{\dfrac{-\pi}{3}+0}{4}\right] \\\\\\z= \sqrt[4]{10} \left[Cos \ \dfrac{ -\pi }{12}+iSin \ \dfrac{-\pi}{12}\right]\\\\\\z = \sqrt[4]{10}\left[-Cos \ \dfrac{\pi}{12}-i \ Sin \ \dfrac{\pi}{12}\right]$

For k =1,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{5\pi}{12}+i \ Sin \ \dfrac{5\pi}{12}\right]$

For k =2,

$z = \sqrt[4]{10}\left[Cos \ \dfrac{11\pi}{12}+i \ Sin \ \dfrac{11\pi}{12}\right]$

For k = 3,

$\sf z = \sqrt[4]{10}\left[Cos \ \dfrac{17\pi}{12}+i \ Sin \ \dfrac{17\pi}{12}\right]$

For k = 4,

$\sf z =\sqrt[4]{10}\left[Cos \ \dfrac{23\pi}{12}+i \ Sin \ \dfrac{23\pi}{12}\right]$

4 0

2 years ago

How do you answer this

Elanso [62]

Okay so you take the 12 feet I'm pretty sure you multiply 12 and 30 and then that's one of your answers and then the 12 and a 75 you must put those to together and that's an answer and you subtract your 12 x 30 and you're 12 x 75 and that's how you get your answer I am pretty sure that's how you and that's how you get your answer I am pretty sure that's how you do it

5 0

3 years ago