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2 years ago

Find the distance between 2-3i And 9+21i

Mathematics

1 answer:

Goryan [66]2 years ago

3 0

2 - 3i is just another of writing (2, -3) in the cartesian plane, the 2-3i however is using the "imaginary axis" for the imaginary plane, is all however the imaginary axis is simply the equivalent of the y-axis. Likewise 9+21i is just (9,21), so let's just use the distance formula.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{21})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[9-2]^2+[21-(-3)]^2}\implies d=\sqrt{(9-2)^2+(21+3)^2} \\\\\\ d=\sqrt{7^2+24^2}\implies d=\sqrt{49+576}\implies d=\sqrt{625}\implies d=25$

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A garden is in the shape of a square of length 35 2/5 m. find its (i) perimeter and (ii) area.

Crank

Answer:

perimeter = 56 m

area= 196 m^2

Step-by-step explanation:

perimeter = 4 x sides = 4 x 35(2/5) = 4 x 14 = 56 m

area= sides^2 = (35 x $\frac{2}{5} )^{2}$ = 14^2 = 196 m^2

3 0

2 years ago

Suppose that you were not given the sample mean and sample standard deviation and instead you were given a list of data for the

Troyanec [42]

Answer:

So, the sample mean is 31.3.

So, the sample standard deviation is 6.98.

Step-by-step explanation:

We have a list of data for the speeds (in miles per hour) of the 20 vehicles. So, N=20.

We calculate the sample mean :

$\mu=\frac{19 +19 +22 +24 +25 +27 +28+ 37 +35 +30+ 37+ 36+ 39+ 40+ 43+ 30+ 31+ 36+ 33+ 35}{20}\\\\\mu=\frac{626}{20}\\\\\mu=31.3$

So, the sample mean is 31.3.

We use the formula for a sample standard deviation:

$\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\mu)^2}$

Now, we calculate the sum

$\sum_{i=1}^{20}(x_i-31.3)^2=(19-31.3)^2+(19-31.3)^2+(22-31.3)^2+(24-31.3)^2+(25-31.3)^2+(27-31.3)^2+(28-31.3)^2+(37-31.3)^2+(35-31.3)^2+(30-31.3)^2+(37-31.3)^2+(36-31.3)^2+(39-31.3)^2+(40-31.3)^2+(43-31.3)^2+(30-31.3)^2+(31-31.3)^2+(36-31.3)^2+(33-31.3)^2+(35-31.3)^2\\\\\sum_{i=1}^{20}(x_i-31.3})^2=926.2\\$

Therefore, we get

$\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_i-\mu)^2}\\\\\sigma=\sqrt{\frac{1}{19}\cdot926.2}\\\\\sigma=6.98$

So, the sample standard deviation is 6.98.

3 0

2 years ago

Find the value of x.

Serjik [45]

Answer:

x=30

Step-by-step explanation:

a straight line is 180 degrees so to figure out x you would do 180-151 which equals 29 however if u plug 29 in for x it wouldn't work because (29-1) equals 28 and 151+28 do not equal to 180 degrees so x would equal 30 because (30-1) is 29

3 0

2 years ago

Read 2 more answers

A box of colored pencils contains exactly 6 red pencils. The probability of choosing a red pencil from the box is 2/7. How many

ZanzabumX [31]

Answer:

B.21

Step-by-step explanation:

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3 years ago

For which number is this the expanded form? 9 × 10 + 2 × 1 + 3 × (1/10) + 8 × (1/100) Group of answer choices 98.08 93.48 9.238

photoshop1234 [79]

Answer:

Well it is i think

Step-by-step explanation:

98.8 I don't know tho

6 0

2 years ago