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Vsevolod [243]
2 years ago
5

In which quadrant is the number –14 – 5i located on the complex plane?

Mathematics
1 answer:
loris [4]2 years ago
5 0

Answer:

The complex number r = -14 - i\,5 belongs to the third quadrant of the complex plane.

Step-by-step explanation:

Let be r = -14 - i\,5. In the complex plane, if \Re (r) < 0 (real component) and \Im (r) < 0 (imaginary component), the number belongs to the third quadrant of the complex plane. The complex number r = -14 - i\,5 belongs to the third quadrant of the complex plane.

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HELP me with this question PLEASE
Anuta_ua [19.1K]

Answer:

YES

Step-by-step explanation:

Why is the classmate correct?

The reason why the classmate is correct is that everything can turn 360 degrees. This means that a square, has to turn 360 degrees, and it does that by doing 90x4. This means that it has 90-degree angles, which turn 4 times. And that makes 360. That's how this is also correct. Because this classmate turned a figure 270 degrees clockwise, and also, 360-270=90, which means that turning that figure 90 degrees counter-clockwise will make it in that same position.

To check whether this is right or not, take an object, probably like a book. Then turn it 90 degrees to counter-clockwise, and note down the position, that the front of the book is now facing left, and the back of the book is now facing right. Then, turn it back to normal position, (back of the book facing you), then, turn it 3 times 90 degrees towards Clockwise, in that way, you can see, that the book turns in the same way it did when you did 90 degrees counter-clockwise!

<h2>I checked this, it's 176 words long.</h2>

Thanks!

Answered by: FieryAnswererGT

#learnwithbrainly

8 0
2 years ago
Read 2 more answers
Calculus 3 help please.​
Reptile [31]

I assume each path C is oriented positively/counterclockwise.

(a) Parameterize C by

\begin{cases} x(t) = 4\cos(t) \\ y(t) = 4\sin(t)\end{cases} \implies \begin{cases} x'(t) = -4\sin(t) \\ y'(t) = 4\cos(t) \end{cases}

with -\frac\pi2\le t\le\frac\pi2. Then the line element is

ds = \sqrt{x'(t)^2 + y'(t)^2} \, dt = \sqrt{16(\sin^2(t)+\cos^2(t))} \, dt = 4\,dt

and the integral reduces to

\displaystyle \int_C xy^4 \, ds = \int_{-\pi/2}^{\pi/2} (4\cos(t)) (4\sin(t))^4 (4\,dt) = 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt

The integrand is symmetric about t=0, so

\displaystyle 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \,dt

Substitute u=\sin(t) and du=\cos(t)\,dt. Then we get

\displaystyle 2^{13} \int_0^{\pi/2} \cos(t) \sin^4(t) \, dt = 2^{13} \int_0^1 u^4 \, du = \frac{2^{13}}5 (1^5 - 0^5) = \boxed{\frac{8192}5}

(b) Parameterize C by

\begin{cases} x(t) = 2(1-t) + 5t = 3t - 2 \\ y(t) = 0(1-t) + 4t = 4t \end{cases} \implies \begin{cases} x'(t) = 3 \\ y'(t) = 4 \end{cases}

with 0\le t\le1. Then

ds = \sqrt{3^2+4^2} \, dt = 5\,dt

and

\displaystyle \int_C x e^y \, ds = \int_0^1 (3t-2) e^{4t} (5\,dt) = 5 \int_0^1 (3t - 2) e^{4t} \, dt

Integrate by parts with

u = 3t-2 \implies du = 3\,dt \\\\ dv = e^{4t} \, dt \implies v = \frac14 e^{4t}

\displaystyle \int u\,dv = uv - \int v\,du

\implies \displaystyle 5 \int_0^1 (3t-2) e^{4t} \,dt = \frac54 (3t-2) e^{4t} \bigg|_{t=0}^{t=1} - \frac{15}4 \int_0^1 e^{4t} \,dt \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} e^{4t} \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \frac54 (e^4 + 2) - \frac{15}{16} (e^4 - 1) = \boxed{\frac{5e^4 + 55}{16}}

(c) Parameterize C by

\begin{cases} x(t) = 3(1-t)+t = -2t+3 \\ y(t) = (1-t)+2t = t+1 \\ z(t) = 2(1-t)+5t = 3t+2 \end{cases} \implies \begin{cases} x'(t) = -2 \\ y'(t) = 1 \\ z'(t) = 3 \end{cases}

with 0\le t\le1. Then

ds = \sqrt{(-2)^2 + 1^2 + 3^2} \, dt = \sqrt{14} \, dt

and

\displaystyle \int_C y^2 z \, ds = \int_0^1 (t+1)^2 (3t+2) \left(\sqrt{14}\,ds\right) \\\\ ~~~~~~~~ = \sqrt{14} \int_0^1 \left(3t^3 + 8t^2 + 7t + 2\right) \, dt \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 t^4 + \frac83 t^3 + \frac72 t^2 + 2t\right) \bigg|_{t=0}^{t=1} \\\\ ~~~~~~~~ = \sqrt{14} \left(\frac34 + \frac83 + \frac72 + 2\right) = \boxed{\frac{107\sqrt{14}}{12}}

8 0
1 year ago
Ruby red paint costs $0.50 per square inch. A ball is painted ruby red and costs $100.00 to paint. What is the diameter of the b
8090 [49]
The diameter can be obtained by the formula A = pi*r^2

First, multiply 0.50 * 100 to obtain the area of the ball, then simplify and solve for the radius. Doubling the radius would yield the diameter. This is shown below:

Area of the ball = 0.50 * 100 = 50 in^2
<span>A = pi*r^2
</span>50 = (3.14)*r^2
r = 3.99 = approx. 4
diameter = 2r
Diameter = 8 inches.

Among the choices, the correct answer is C. 8.0 in. 

6 0
3 years ago
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No they wont have the same amount of money ana has more than jose and he’s spending more and wont have enough for the whole week, while ana will have enough and she’s only wasting 4$....
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12 sec..............
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