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3 years ago

Simplify 4 over quantity 2 plus 7 i.

Mathematics

2 answers:

alexandr1967 [171]3 years ago

5 0

Answer:

(8-28i)/53

hope it helps!

spayn [35]3 years ago

3 0

To simplify 4/(2+7i), we multiply it by a fraction equal to one that removes the i value in the denominator. The best value to do this is the complex conjugate divided by itself, so we have 4(2-7i)/((2+7i)(2-7i)). Simplifying, we have (8-28i)/(4-(-49))=(8-28i)/53, which is a completely simplified fraction since 8 and 53 are relatively prime (or coprime), and there are no radicals in the denominator.

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Step-by-step explanation:

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3 years ago

World population is approximately upper p equals 6.4 left-parenthesis 1.0126 right-parenthesis superscript t, with upper p in bi

Leviafan [203]

Given equation is

$P=6.4(1.0126)^t$

It gives approx world population in billions for t years since 2004.

Answer(a):

Compare with growth formula P=a(b)^t, we get:

growth factor b = 1.0126

We know that if r is the percent rate of growth then

1+r=b

1+r=1.0126

r=0.0126

Hence the yearly percent rate of growth of the world population is 0.0126 or 1.26%.

Answer(b):

To find worlds population in 2004, plug t=0 because year is counted from 2004.

$P=6.4(1.0126)^0 = 6.4*1 = 6.40$

Hence answer is 6.40 billion.

To find worlds population in 2018, plug t=2018-2004=14 because year is counted from 2004.

$P=6.4(1.0126)^{14} = 6.4*1.19160117479 = 7.62624751867$

Hence answer is approx 7.63 billion.

Answer(c):

Average rate of change of the world population between 2004 and 2018 is given by:

$\frac{P\left(Year_{2018}\right)-P\left(year_{2004}\right)}{2018-2004}$

$=\frac{P\left(14\right)-P\left(0\right)}{14-0}$

$=\frac{7.63-6.40}{14}$

$=0.0878571428571$

Hence answer is approx 0.0878571428571 billion per year.

To convert it into millions, multiply by 1000

So we get 0.0878571428571*1000 = 87.8571428571

Which is approx 88 to the nearest integer

Hence final answer is approx 88 millions per year.

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skelet666 [1.2K]

I think it's D, because 3/4 x 2 = - 3/2
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3 years ago