What number is 16% of 60

Simplify: 1 + i + i^2 + i^3 +i^4 +i^5 if i^2 =-1.

Vika [28.1K]

1 + i + i ² + i ³ + i ⁴ + i ⁵ = 1 + i + i ² (1 + i + i ² + i ³)

… = 1 + i + i ² (1 + i + i ² (1 + i ))

… = 1 + i + (-1) (1 + i + (-1) (1 + i ))

… = 1 + i + (-1) (1 + i - 1 - i )

… = 1 + i

Alternatively, notice that

1 - i ⁶ = (1 - i ) (1 + i + i ² + i ³ + i ⁴ + i ⁵)

so that

1 + i + i ² + i ³ + i ⁴ + i ⁵ = (1 - i ⁶) / (1 - i )

Now, i ⁶ = (i ²)³ = (-1)³ = -1, so

1 + i + i ² + i ³ + i ⁴ + i ⁵ = (1 - (-1)) / (1 - i )

… = 2 / (1 - i )

Multiply the numerator and denominator by the conjugate of 1 - i :

… = 2 (1 + i ) / ((1 - i ) (1 + i ))

… = 2 (1 + i ) / (1² - i ²)

… = 2 (1 + i ) / (1 + 1)

… = 1 + i

3 0

3 years ago

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suppose labor productivity in the united states was $100,000 per worker in 2015. calculate the value of labor productivity in 20

sukhopar [10]

a. U.S labor productivity in 2035 would be $206,800 per worker.

b. U.S labor productivity in 2035 would be $68,100 per worker.

c. Labor productivity per worker in 2035 with the higher growth rate is 3.04

a. Calculation to determine what the U.S labor productivity in 2035 would be $ per worker assuming productivity grows by 3.7 percent per year

Given:

Labor Productivity in 2015 = $100,000

Growth rate = 3.7%pa or 0.037

Using this formula

Future value = Present value*(1+Growth rate)^Number of years

Let plug in the formula

2035 labor productivity per worker=100,000(1 + 0.037)^20

2035 labor productivity per worker= $206,811.71

2035 labor productivity per worker= $206,800

( rounded to nearest $100)

b.Calculation to determine what the U.S labor productivity in 2035 would be $ per worker assuming productivity falls to 1.9 percent per year

Given:

Labor Productivity in 2015 = $100,000

Growth rate = -1.9%pa or -0.019

Using this formula

Future value = Present value*(1+Growth rate)^Number of years

Let plug in the formula

2035 labor productivity per worker= 100,000(1-0.019)^20

2035 labor productivity per worker= $68,136.55

2035 labor productivity per worker= $ 68,100

( rounded to nearest $100)

c. Calculation to determine How much larger would labor productivity per worker be in 2035 with the higher growth rate

2035 labor productivity per worker=($206,811.711/$68,136.55121)

2035 labor productivity per worker= 3.04 times

Inconclusion:

a. U.S labor productivity in 2035 would be $206,800 per worker.

b. U.S labor productivity in 2035 would be $68,100 per worker.

c. Labor productivity per worker in 2035 with the higher growth rate is 3.04

Learn more here:

brainly.com/question/14174963

6 0

2 years ago

When making lemonade, 1 over 4 cup of sugar will make 5 glasses of lemonade. How many cups of sugar would be needed to make 22 g

olga_2 [115]

Answer:

1/4 sugar = 5 glasses

1/4 x 22/5 sugar = 5 x 22/5 glasses

22/20 sugar = 22 glasses

1 1/10 cup of sugar = 22 glasses lemonade

4 0

2 years ago

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what does On May 17, 1954, Chief Justice Earl Warren issued the Supreme Court’s unanimous decision in Brown v. Board of Educatio

S_A_V [24]

Answer:

<h3>Plessy v. Ferguson case.</h3>

Explanation:

The Plessy v. Ferguson case of 1896 ruled out that segregation was constitutional as long as both blacks and whites enjoyed opportunities that were separate but equal.

However, the Supreme Court's verdict in the Plessy v. Ferguson case of 1896 was challenged by Justice Earl Warren stating that the idea of ‘separate but equal’ in public school was unconstitutional and inherently unequal.

Thus, Chief Justice Earl Warren issued the Supreme Court’s unanimous decision in Brown v. Board of Education, ruling that racial segregation in public schools violated the "Equal Protection Clause” of the 14th Amendment.

4 0

4 years ago

PLEASE READ:

Rashid [163]

Answer:

trivia considerations, or pieces of information of little importance or value.

let me help u in ur questions

3 0

3 years ago

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