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3 years ago

3+5i/-2+3i perform operation

Mathematics

1 answer:

melisa1 [442]3 years ago

4 0

Answer:

$\dfrac{9}{13}-\dfrac{19}{13}i$

Step-by-step explanation:

Remember $i^2=-1$

You are given the fraction $\dfrac{3+5i}{-2+3i}$

First, multiply the numerator and the denominator by -2-3i:

$\dfrac{3+5i}{-2+3i}=\dfrac{(3+5i)(-2-3i)}{(-2+3i)(-2-3i)}=\dfrac{(3+5i)(-2-3i)}{(-2)^2-(3i)^2}=\dfrac{(3+5i)(-2-3i)}{4-9i^2}=\dfrac{(3+5i)(-2-3i)}{4+9}$

This gives you 13 in denominator, now multiply two complex numbers in numerator:

$(3+5i)(-2-3i)=-6-9i-10i-15i^2=-6-19i+15=9-19i$

Thus, the initial fraction is

$\dfrac{9-19i}{13}=\dfrac{9}{13}-\dfrac{19}{13}i$

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It was estimated that because of people switching to Metro trains about 33000 of CNG 3300 tons of diesel and 21000 tons of petro

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The question is incomplete. Here is the complete question

It was estimated that because of people switching to Metro trains about 33000 of CNG 3300 tons of diesel and 21000 tons of petrol was saved by the end of year 2007 (I) find a fraction of the quantity of diesel saved to the quantity of petrol saved (ii) find the quantity of cng to the quantity of diesel saved

Answer:

(I) 11/70

(II) 1/10

Step-by-step explanation:

Metro trains contain 330,000 tons of CNG

3300 tons of diesel was saved

21000 tons of petrol was saved at the end of 2007

(I) The fraction of the quantity of diesel saved to the quantity of petrol saved can be calculated as follows

= 3300/21000

= 11/70

(II) The fraction of the quantity of CNG saved to the quantity of diesel can be calculated as follows

= 3300/33000

= 1/10

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3 years ago

While shopping, Dawn finds a backpack that she likes on the sale rack. Its original price is $60,

Nadya [2.5K]

No. Because 33 $ is the money deducted from the 60 $. Dawn bought everything for less than 60 $.

So, if Dawn purchases everything on the rack with a 30% discount and 15% coupon the total will indeed make 45%.

We have to take 100% - 45%= 55% to know the reduction number. Let's proceed to the calculations now.

100%= 60 $

1%=60/100

55%= 60/100 × 55 = 33 $

Now NOTE; 33 $ is the money reduced from the 60 $. So, logically, 33 $ isn't the amount which Dawn purchased the whole rack. 

To find the amount at which she purchased everything, we need to do,

60 $ - 33 $ = 27 $

6 0

3 years ago

3 times a number is 54 less than the square of that number. Find the negative solution.

son4ous [18]

Answer:

-6

Step-by-step explanation:

3n = n² - 54

n² - 3n - 54 = 0

n² - 9n + 6n - 54 = 0

n(n - 9) + 6(n - 9) = 0

(n - 9)(n + 6) = 0

n = 9 , -6

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3 years ago

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Laurel needs 210.5 feet of fence

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3 years ago

Hildy had 2.5 oz of liquid for a science experiment. the instructions said that the experiment needed 3 oz of liquid. she went t

solmaris [256]

For this case we have the following amount of liquid:
2.5 oz.
The amount of liquid needed is:
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Therefore, the amount of fluid needed is:
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Answer:
b. no, hildy did not get a reasonable amount of liquid because she only needed 0.5 oz (3 - 2.5 = 0.5).

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3 years ago

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