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Mathematics

1 answer:

Elza [17]3 years ago

4 0

Answer:

4/10 + 3/100 in each of his groups = .43

.43 * 3 = 1.29

his model is short

he should have 1.38

1.38/3 = .46

Step-by-step explanation:

4/10 + 3/100 in each of his groups = .43

.43 * 3 = 1.29

his model is short

he should have 1.38

1.38/3 = .46

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A bus driver drives 147 miles on her route each day. She drove the bus 23 days last month. How many miles did the bus driver dri

elena-s [515]

Answer:

Step-by-step explanation:

147 x 23 = 3381

5 0

3 years ago

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Veronica has been saving dimes and quarters. She has 94 coins in all and the total value is $19.30. How many dimes and how many

Stolb23 [73]

Answer:

Step-by-step explanation:

d + q = 94.....d = 94 - q

0.10d + 0.25q = 19.30

0.10(94 - q) + 0.25q = 19.30

9.4 - 0.10q + 0.25q = 19.30

-0.10q + 0.25q = 19.30 - 9.40

0.15q = 9.90

q = 9.90/0.15

q = 66 <===== there are 66 quarters

d + q = 94

d + 66 = 94

d = 94 - 66

d = 28 <==== there are 28 dimes

3 0

3 years ago

If z1= 3+3i and z2=7(cos(5pi/9) + i sin (5pi/9)), then z1/z2= blank

mixas84 [53]

$z1=\stackrel{a}{3}+\stackrel{b}{3}i~~ \begin{cases} r = \sqrt{a^2+b^2}\\ r = \sqrt{18}\\[-0.5em] \hrulefill\\ \theta =\tan^{-1}\left( \frac{b}{a} \right)\\ \theta =\frac{\pi }{4} \end{cases}~\hfill z1=\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right] \\\\[-0.35em] ~\dotfill$

$\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}\left[\cos\left( \frac{\pi }{4} \right) i\sin\left( \frac{\pi }{4} \right) \right]} {7\left[\cos\left( \frac{5\pi }{9} \right) i\sin\left( \frac{5\pi }{9} \right) \right]} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{division of two complex numbers} \\\\ \cfrac{r_1[\cos(\alpha)+i\sin(\alpha)]}{r_2[\cos(\beta)+i\sin(\beta)]}\implies \cfrac{r_1}{r_2}[\cos(\alpha - \beta)+i\sin(\alpha - \beta)] \\\\[-0.35em] ~\dotfill$

$\cfrac{z1}{z2}\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{\pi }{4}-\frac{5\pi }{9} \right)+i\sin\left( \frac{\pi }{4}-\frac{5\pi }{9} \right) \right] \\\\\\ \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{-11\pi }{36} \right) +i\sin\left( \frac{-11\pi }{36} \right) \right]\implies \cfrac{\sqrt{18}}{7}\left[\cos\left( \frac{83\pi }{36} \right) +i\sin\left( \frac{83\pi }{36} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{z1}{z2}\approx 0.348~~ + ~~0.496i~\hfill$