Fanga ran 28 miles per in 4 hours She ran at a rate of how many miles per hour

Mathematics

2 answers:

Citrus2011 [14]3 years ago

5 0

7 mph. 28 divided by 4 is 7. Or 7 miles in one hour

tekilochka [14]3 years ago

3 0

The answer for this problem is 7

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Express the complex number in trigonometric form. -6 + 6 square root of 3 i ?

bagirrra123 [75]

$\bf \begin{array}{clclll}
-6&+&6\sqrt{3}\ i\\
\uparrow &&\uparrow \\
a&&b
\end{array}\qquad 
\begin{cases}
r=\sqrt{a^2+b^2}\\
\theta =tan^{-1}\left( \frac{b}{a} \right)
\end{cases}\qquad r[cos(\theta )+i\ sin(\theta )]\\\\
-------------------------------\\\\$

$\bf r=\sqrt{(-6)^2+(6\sqrt{3})^2}\implies r=\sqrt{36+(6^2\cdot 3)}\implies r=\sqrt{144}
\\\\\\
r=12\leftarrow 
\\\\\\
\theta =tan^{-1}\left( \frac{6\sqrt{3}}{-6} \right)\implies \theta =tan^{-1}\left( -\sqrt{3}\right)\implies \theta =
\begin{cases}
\frac{2\pi }{3}\leftarrow \\
\frac{5\pi }{3}
\end{cases}$

now, notice, there are two valid angles for such a tangent, however, if we look at the complex pair, the "a" is negative and the "b" is positive, that means, "x" is negative and "y" is positive, and that only occurs in the 2nd quadrant, so the angle is in the second quadrant, not on the fourth quadrant.

thus $\bf 12\left[cos\left( \frac{2\pi }{3} \right) +i\ sin\left( \frac{2\pi }{3} \right) \right]$