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Vedmedyk [2.9K]
4 years ago
6

How can we eliminate an imaginary from the denominator? Simplify 2/(3+5i) to demonstrate.

Mathematics
2 answers:
solmaris [256]4 years ago
8 0
Sure multiple by (3-5i)/(3-5i). Keep in mind i^2 is equal to -1. can you do the rest? 

leva [86]4 years ago
8 0
You can. first multiply both sides of the fraction by (3+5i).
2*(3+5i)/(3+5i)*(3+5i)

(3+5i)*(3+5i)=34

2*(3+5i)/34 divide each side by 2 
(3+5i)/17
\frac{3}{17} - \frac{5i}{17}

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asambeis [7]
Does this help you at all?

3 0
4 years ago
PLEASE HELP‼️‼️Drag the expression that is the most reasonable measurement for each object.
Afina-wow [57]

Answer:

<em>A. Length of a Tour Bus                       ↔     #2.      1.1 × 10¹ meters</em>

<em />

<em>B. Width of an apple                             ↔      #3.     4 × 10⁰ centimeters</em>

<em />

<em>C. Distance from Earth to a Satellite    ↔    #6.     8 × 10² kilometers</em>

<em />

<em>D. Thickness of a human hair               ↔     #5.      9 × 10¹ micrometers</em>

Explanation:

<u><em>A. Length of a tour bus.</em></u>

The length of a tour bus should be measured in meters. It sure is way less than 1 kilometer and way more than a few centimeters. It could be about some meters, more than 5 meters, may be between 10 meters and 15 meters.

The measurement in the box # 2. is 1.1 × 10¹ meters, which is equivalent to 1.1 × 10meters = 11 meters. Thus, this is a reasonable length.

<u><em>B. Width of an apple.</em></u>

The most appropiate unit to measure the width of an apple should be centimer. It certanly is shorter than 1 meter and bigger than 1 mm.

The width of an apple could be, more or less, around 8 centimeters. The only measurement in the boxes that is in that order is that in the box #3., 4 × 10⁰ centimeters, because 10⁰ = 1, so 4 × 10⁰ = 4 × 1 = 4centimeters.

<u><em>C. Distance from Earth to a Satellite</em></u>

The distance from Earth to a satellite should be measured in kilometers.

You can find in the internet that the distances of the satellites are between 700 kilometers and 36,000 kilometers.

The number in the box #1 is too big, in the order of ten trillions of kilometers, because one trillion is 10¹²; thus that is notreasonalbe (too big).

The number in the box #6 is  8 × 10² kilometers, which is equal to 8 × 100 = 800 kilometers.

Thus,  8 × 10² kilometers (box #6) is the most reasonable measurement for the distance from Earth to a Satellite

<u><em></em></u>

<u><em>D. Thickness of a human hair</em></u>

Of course, kilometers, meters, centimeters and even milimeters are units too big to measure the thickness of a human hair.

One micrometer is 10⁻⁶ meters or 10⁻³ milimeters.

In the internet you can find that diameter of the humar hairis in the range from 17 micrometers to 181 micrometers.

The measurement in the box #5. is 9 × 10¹ micrometers, which is equivalent to 9 × 10 = 90 micrometers.

Thus, 9 × 10¹ micrometers is the most reasonable measurement fot the thickness of a human hair.

7 0
3 years ago
NEED ANSWERED ASAP!!!!!!!
Igoryamba

Answer:

5.25 is the lenght of the arc AB.

Step-by-step explanation:

First, since we are told the answer should be expressed in radians, we need to convert the arc angle into radians, we do that by multiplying the angle by π and dividing by 180.

60° * π/180 = 1.05rad

Now, there is a simple formula to calculate the arc lenght, A = Ф*r, where:

A = arc lenght

Ф = arc angle (60°=1.05rad)

r = radius (5cm)

A = 1.05*5cm

A = 5.25cm

5 0
3 years ago
In the expression a=k over b, what is k ?
andreyandreev [35.5K]

Answer: k=ab

Step-by-step explanation:

a=\frac{k}{b}

ab=k

8 0
3 years ago
Arectangularplotoflandistobefencedinusingtwokinds of fencing. Two opposite sides will use heavy-duty fencing selling for $3 a fo
svlad2 [7]

Answer:

Dimensions of the rectangular plot will be 500 ft by 750 ft.

Step-by-step explanation:

Let the length of the rectangular plot = x ft.

and the width of the plot = y ft.

Cost to fence the length at the cost $3.00 per feet = 3x

Cost to fence the width of the cost $2.00 per feet = 2y

Total cost to fence all sides of rectangular plot = 2(3x + 2y)

2(3x + 2y) = 6,000

3x + 2y = 3,000 ----------(1)

3x + 2y = 3000

      2y = 3000 - 3x

      y = \frac{1}{2}[3000-3x]

      y = 1500 - \frac{3x}{2}

Now area of the rectangle A = xy square feet

A = x[1500-\frac{3x}{2}]

For maximum area \frac{dA}{dx}=0

A' = \frac{d}{dx}(1500x-\frac{3}{2}x^{2}) = 0

1500 - 3x = 0

3x = 1500

x = 500 ft

From equation (1),

y = 1500 - \frac{3}{2}\times 500

y = 1500 - 750

y = 750 ft

Therefore, for the maximum area of the rectangular plot will be 500 ft × 750 ft.

two fencing 3(500+500) = $3000

other two fencing 2(750+750) = $3000

8 0
4 years ago
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