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2 years ago

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Counting numbers are to be formed using only the digits 1, 9, 8, 6, 2, 4, and 5. determine the number of different possibilities

for two-digit numbers

1 answer:

MAXImum [283]2 years ago

8 0

Assuming numbers can repeat

$7^2=49$

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The graph of y = 3*:

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2 years ago

Describe the additive inverse of a vector in the vector space.

Step2247 [10]

I dont know what you mean by describe but the inverse is -v

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3 years ago

What is the square root of -2i?

Studentka2010 [4]

Answer:

1-i and -1+i

Step-by-step explanation:

We are to find the square roots of $z=0-2i$ . First, convert from Cartesian to polar form:

$r=\sqrt{a^2+b^2}\\r=\sqrt{0^2+(-2)^2}\\r=\sqrt{0+4}\\r=\sqrt{4}\\r=2$

$\theta=tan^{-1}(\frac{b}{a})\\ \theta=tan^{-1}(\frac{-2}{0})\\\theta=\frac{3\pi}{2}$

$z=2(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2})$

Next, use the formula $\displaystyle \sqrt[n]{r}\biggr[\cis\biggr(\frac{\theta+2\pi k}{n}\biggr)\biggr]$ where $\displaystyle k=0,1,2,...\:,n-1$ to find the square roots:

<u>When k=1</u>

<u /> $\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(1)}{2}\biggr)\biggr]$

$\displaystyle \sqrt{2}\biggr[cis\biggr(\frac{3\pi}{4}+\pi\biggr)\biggr]$

$\sqrt{2}\biggr(cis\frac{7\pi}{4}\biggr)$

$\sqrt{2}(\cos\frac{7\pi}{4}+i\sin\frac{7\pi}{4})\\ \\\sqrt{2}(\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i)\\ \\1-i$

<u>When k=0</u>

<u /> $\displaystyle \sqrt[2]{2}\biggr[cis\biggr(\frac{\frac{3\pi}{2}+2\pi(0)}{2}\biggr)\biggr]$

$\sqrt{2}\biggr(cis\frac{3\pi}{4}\biggr)$

$\sqrt{2}(\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4})\\ \\\sqrt{2}(-\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i)\\ \\-1+i$

Thus, the square roots of -2i are 1-i and -1+i

4 0

1 year ago

Ill brainlist anyone who anwsers this if i havent already

jonny [76]

Answer:

It increases 3cm each minute.

Step-by-step explanation:

4 0

2 years ago

Find the distance between the origin and the point R = (9,7,8). The distance is: Ensure that you use at least 4 decimal place ac

Brrunno [24]

Answer:

Distance between points R=(9,7,8) and origin is,

d = 13.9283 units.

Step-by-step explanation:

We have to calculate the distance between the two points,

Where,

the first point is origin, i.e.

Q = (0,0,0)

and R = (9,7,8)

According to distance formula, the distance between two points can be given by

$d\ =\ \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2)}$

$=\ \sqrt{(0-9)^2+|(0-7)^2+(0-8)^2)}$

$=\ \sqrt{(-9)^2+(-7)^2+(-8)^2)}$

$=\ \sqrt{81+49+64}$

$=\ \sqrt{194}$

= 13.9283

Hence, the distance between two points R=(9,7,8) and origin is 13.9283 units.

5 0

2 years ago