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Anestetic [448]

3 years ago

16

What are the x- and y- coordinates of point P on the directed line segment from A to B such that P is Two-thirds the length of t

he line segment from A to B? (2, –1) (4, –3) (–1, 2) (3, –2)

1 answer:

Maslowich3 years ago

7 0

Answer: (4,-3) B

Step-by-step explanation:

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Identify the like terms.

Aloiza [94]

The correct answer is C: -3b and 4b.

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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

1 year ago

Nth term of 1 8 15 22 29

k0ka [10]

This is an arithmetic sequence because each term is 7 greater than the previous term, so 7 is what is called the common difference...

Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=first term, d=common difference, n=term number.

We know a=1 and d=7 so:

a(n)=1+7(n-1)

a(n)=1+7n-7

a(n)=7n-6

The above is the "rule" for the nth term.

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Pooky eats three cans of cat food each day. How long will 27 cans of food last?

wlad13 [49]

Answer: 9 days.

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2b−6= −4 what is b

gogolik [260]

2b - 6 = -4

2b = -4 + 6

2b = 2

b = 2/2

b = 1

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3 years ago

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