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2 years ago

What is the absolute value of the complex number -4 -square root of 2i

Mathematics

2 answers:

kati45 [8]2 years ago

4 0

Answer:

Step-by-step explanation:

The i is not under the square root.

balu736 [363]2 years ago

3 0

Absolute value is the same as modulus, thus
|-4 -sqrt(2) i |
=sqrt((-4)^2+(-sqrt(2))^2|
=sqrt(16+2)
=sqrt(18) = 4.243 (approx.)

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Please help me!!!!!!!!!!

bezimeni [28]

9.2 x 13.8 = 126.96, now usually to get the area of a triangle we would half this but because we have two of the same triangle we would then have to double it again so they cancel each other out. We then do 6.9 x 9.2 which equals 63.48 and again we have two of the same triangle so no need to half it. So we add the two totals of 126.96 and 63.48 together to get 190.44.

4 0

1 year ago

One of the vertices of △PQR is P(2, −1). The midpoint of PQ is M(3, 0). The midpoint of QR is N(5, 3). Show that MN || PR and MN

VLD [36.1K]

Answer:

See the proof below

Step-by-step explanation:

Given the following coordinates

P(2, −1)

Midpoint of PQ M(3, 0)

We can get the coordinate point Q using the midpoint formula;

M(X,Y) = (x1+x2/2, y1+y2/2)

X = x1+x2/2

3 = 2+x2/2

6 = 2+x2

x2 = 6-2

x2 = 4

Y = y1+y2/2

0 = -1+y2/2

0 = -1 + y2

y2 = 0+1

y2 = 1

Hence the coordinate of Q is (4, 1)

Next is to get the coordinate of R

Given the midpoint of QR to be N(5, 3)

(5,3) = (4+x2/2, 1+y2/2)

5 = 4+x2/2

10 = 4+x2

x2 = 10-4

x2 = 6

1+y2/2 = 3

1+y2 = 6

y2 = 6-1

y2 = 5

Hence the coordinate of R is (6,5)

Given the coordinates M(3, 0) and N(5, 3)

Slope is expressed as:

m = y2-y1/x2-x1

m = 3-0/5-3

m = 3/2

Slope of MN = 3/2

Get the slope of PR

Given the coordinates P(2, −1) and R (6,5)

Slope of PR = 5-(-1)/6-2

Slope of PR = 5+1/4

Slope of PR = 6/4 = 3/2

Since the slope of MN is equal to that of PR, hence MN is parallel to PR i.e MN || PR

To show that MN = 1/2PR, we will have to take the distance between M and N and also P and R first as shown:

For MN with coordinates M(3, 0) and N(5, 3)

MN = √(x2-x1)²+(y2-y1)²

MN = √(5-3)²+(3-0)²

MN = √2²+3²

MN = √13

Get the length of PR where P(2, −1) and R (6,5)

PR = √(6-2)²+(5+1)²

PR = √4²+6²

PR = √16+36

PR = √52

PR = √4*13

PR = √4*√13

PR = 2√13

Since MN = √13

PR = 2MN

Divide both sides by 2

PR/2 = 2MN/2

PR/2 = MN

Hence MN = 1/2 PR (Proved!)

8 0

1 year ago

In the Fall STA 2023 Beginning of the Semester Survey, students were asked how many parties they attended every week and how man

Shtirlitz [24]

Answer:

-95.78

Step-by-step explanation:

As the researcher decided to make the number of parties attended per week the explanatory variable, this would be variable x in the regression line, and of course, the variable y would be the number of text messages sent per day.

After constructing the linear regression equation, the researcher found that an approximate value $\hat y$ for the actual value of y could be represented by the line

$\hat y=64.96+25.41x$

Since this is an approximate value, it is not expected that it coincides with the actual value of y. We define then the residual for each value of x as the difference between the actual value of y and the approximation for the given x.

For the value x = 2 (the student attended 2 parties that week) the actual value of y is 20 (the student sent 20 text messages per day that week).

The approximate value of y would be according to the regression line

$\hat y(2)=64.96+25.41(2)=64.96+50.82=115.78$

Hence, the residual value for x=2 would be

$y_{real}-\hat y=20-115.78=-95.78$

5 0

2 years ago

Line l has a slope of 2. The line through which of the following pair of points is perpendicular to l?

djverab [1.8K]

Answer:

Step-by-step explanation:

If two lines are perpendicular, the products of their slopes will be -1. Therefore, we're looking for a line with slope of -1/2. Let's check each answer:

A: 5 - 3 / (-2 - 3) = 2 / -5

B: 6 - 5 / 6 - 5 = 1

C: 5 - 3 / 4 - 3 = 2

D: 4 - 3 / 3 - 5 = -1/2

The answer is D.

8 0

2 years ago

Read 2 more answers

Researchers want to determine if caffeine affects reaction time. They divide a sample of 150 people into 3 groups. Group 1 gets

11111nata11111 [884]

Answer:

One-way ANOVA

Step-by-step explanation:

One-way ANOVA(analysis of variance) a testing method in statistics that is used to compare the means of two or more independent samples, to check if the differences are statistically significant.

In this case, we have three groups which their various reaction time to caffeine is to be tested using the same testing method (amount of caffeine). Hence the appropriate test to use here is the one-way ANOVA

7 0

2 years ago