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8_murik_8 [283]
3 years ago
12

Express the complex number in trigonometric form.

Mathematics
1 answer:
Maru [420]3 years ago
7 0
-5i can be written as 0 + (-5)i
It is in the form a+bi where a = 0 and b =-5
So the point (a,b) is (0,-5)

The distance from the origin to this point is 5 units, therefore r = 5. This is the magnitude. 

The angle is 270 degrees as shown in the attached image. You start on the positive x axis and rotate until you reach the point (0,-5)

This is why the answer is choice A) 5(cos(270) + i*sin(270))

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Tema [17]

Answer:

I have a lead pencil and only 2 pieces of lead left. One is 5/6 inches long and the other is 1/3 inches long. How many times longer is the 5/6 then the 1/3?

Step-by-step explanation:

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OFFERING 10 POINTS
ELEN [110]

Answer:

  • slope: 0
  • equation: y = -2

Step-by-step explanation:

a) The y-coordinates of points A and B are both -2, so there is no change in the y-value between those points. The x-coordinates differ by 4, so the slope is ...

... slope = (change in y)/(change in x) = 0/4 = 0

b) The y-value is constant at -2 for any value of x, so the equation of the line is ...

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3 0
3 years ago
Tina is finding the quotient of. Is she correct? If not, what changes should be made?
Mice21 [21]

For this case, we must find the quotient of

(15x ^ 3 + 12x ^ 2-9x) divided by3x, to verify if Tina was correct.

So:

\frac {15x ^ 3 + 12x ^ 2-9x} {3x} =\\\frac {15x ^ 3} {3x} + \frac {12x ^ 2} {3x} - \frac {9x} {3x} =\\5x ^ 2 + 4x-3

So, Tina was wrong, she had to divide by 3x.

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Option B


5 0
3 years ago
Two gears are connected and are rotating simultaneously. The smaller gear has a radius of 3 inches, and the larger gear has a ra
Dovator [93]
Circumference of a circle is C = 2πr.

part 1)

so the radius of the smaller gear is 3 inches, so after a full rotation, namely a revolution, the smaller gear has covered an arc of 2π(3), or 6π.

what angle has the larger gear of 7 inches in radius, has it covered with an arc of 6π?

\bf \textit{arc's length}\\\\
s=r\theta ~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad radians\\
------\\
s=6\pi \\
r=7
\end{cases}\implies 6\pi =7\theta \implies \cfrac{6\pi }{7}=\theta



part 2)

since the larger gear has a radius of 7, in a revolution it will have an arc of 2π(7), or 14π.

now, we know the smaller gear does a 6π arc in a revolution, how many revolutions will it do in an arc of 14π?

\bf \begin{array}{ccll}
arc&revolution\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
6\pi &1\\
14\pi &x
\end{array}\implies \cfrac{6\pi }{14\pi }=\cfrac{1}{x}\implies \cfrac{3}{7}=\cfrac{1}{x}\implies x=\cfrac{7}{3}
6 0
3 years ago
How much pure water must be mixed with 10 liters of a 25% acid solution to reduce it to a 10% acid solution?
elena-s [515]

Suppose you add x liters of pure water to the 10 L of 25% acid solution. The new solution's volume is x + 10 L. Each L of pure water contributes no acid, while the starting solution contains 2.5 L of acid. So in the new solution, you end up with a concentration of (2.5 L)/(x + 10 L), and you want this concentration to be 10%. So we have

\dfrac{2.5}{x+10}=0.1\implies25=x+10\implies x=15

and so you would need to add 15 L of pure water to get the desired concentration of acid.

8 0
4 years ago
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