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liberstina [14]

2 years ago

10

Find all the cube roots of cube roots

le="2 {e}^{2i\pi} " alt="2 {e}^{2i\pi} " align="absmiddle" class="latex-formula">

1 answer:

DochEvi [55]2 years ago

7 0

Answer:

It is

$1.26{e}^{ \frac{2i\pi}{3}}$

Step-by-step explanation:

$2 {e}^{2i\pi}$

cube root:

$= \sqrt[3]{2 {e}^{2i\pi}} \\ = ( {2 {e}^{2i\pi})}^{ \frac{1}{3} } \\ = {2}^{ \frac{1}{3} } ( {e}^{ \frac{2i\pi}{3} } ) \\ = 1.26{e}^{ \frac{2i\pi}{3}}$

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Find S12 for geometric series: (-7.5) + 15 + (-30) + ...

kolezko [41]

Answer:

S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5

Step-by-step explanation:

Given the sequence to find the sum up-to 12 terms

$(-7.5) + 15 + (-30) + ...$

As we know that

A geometric sequence has a constant ratio 'r' and is defined by

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Compute\:the\:ratios\:of\:all\:the\:adjacent\:terms}:\quad \:r=\frac{a_{n+1}}{a_n}$

$\frac{15}{\left(-7.5\right)}=-2,\:\quad \frac{\left(-30\right)}{15}=-2$

$\mathrm{The\:ratio\:of\:all\:the\:adjacent\:terms\:is\:the\:same\:and\:equal\:to}$

$r=-2$

$\mathrm{The\:first\:element\:of\:the\:sequence\:is}$

$a_1=\left(-7.5\right)$

$a_n=a_1\cdot r^{n-1}$

$\mathrm{Therefore,\:the\:}n\mathrm{th\:term\:is\:computed\:by}\:$

$a_n=\left(-7.5\right)\left(-2\right)^{n-1}$

$a_n=-\left(-2\right)^{n-1}\cdot \:7.5$

$\mathrm{Geometric\:sequence\:sum\:formula:}$

$a_1\frac{1-r^n}{1-r}$

$\mathrm{Plug\:in\:the\:values:}$

$n=12,\:\spacea_1=\left(-7.5\right),\:\spacer=-2$

$=\left(-7.5\right)\frac{1-\left(-2\right)^{12}}{1-\left(-2\right)}$

$=-7.5\cdot \frac{1-\left(-2\right)^{12}}{1+2}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=-\frac{-30712.5}{1+2}$ ∵ $\left(1-\left(-2\right)^{12}\right)\cdot \:7.5=-30712.5$

$=-\frac{-30712.5}{3}$

$=\frac{30712.5}{3}$

$=10237.5$

Thus, S12 for geometric series: (-7.5) + 15 + (-30) + ... would be: 10237.5

5 0

2 years ago

I am confused on how to get the answer

Ksju [112]

Answer:

try using this

Step-by-step explanation:

multiply π which = 3.14 by the diamiter so it would be 3.14 x 6.5 = 20.41

4 0

2 years ago

Read 2 more answers

4vir4ik [10]

Answer:

1. 45

2. 24

3. 32

Step-by-step explanation:

One

Ashley= 3/4 * Steve

Ashley= 3/4 * 60

Ashley = 180/4

Ashley = 45

Two

60% of 40

60/100 * 40

2400/100 = 24

Three

40% 80 = 40/100 * 80 = 3200 / 100 = 32

5 0

2 years ago

What are the next three numbers of the pattern? Plz answer quick and btw u will be marked brainliest

dimulka [17.4K]

1, 4, 9, 16, 25,... $n^{2}$

5 0

2 years ago

Read 2 more answers

Please help with an explanation

Vsevolod [243]

Answer:

the answer is incorrect though the first step is correct but the second step is wrong and so is the answer. the correct answer would be x raise to the power of 2by 5

Step-by-step explanation:

{x⁶/⁵⁻²/⁵} ¹/²= {x⁴/⁵}¹/²= x²/⁵

in the second step the power of the denominator must be subtracted from the power of the numerator using the law of indices then we would get the correct answer

8 0

2 years ago