Calculate the equation of the line through the points (1, 1), (4,3), (10, 7) and (40, 27).

The angle between the complex numbers 2+2i and -7

anygoal [31]

Answer:Consider the right triangle formed by the complex number in the Argand-Gauss plane and it's projections on the axis. – José Siqueira Nov 12 '13 at 17:21

In particular what is the definition of sine of theta in terms of the known sides of the above mentioned right triangle? – Adam Nov 12 '13 at 17:27

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3 Answers

1

Consider the following Argand-diagram

enter image description here

The y-axis is the imaginary axis and the x-axis is the real one. The complex number in question is

x+yi

To figure out θ, consider the right-triangle formed by the two-coordinates on the plane (illustrated in red). Let θ be the angle formed with the real axis.

tanθ=yx

⟹tan−1(yx)

The hypotenuse of the triangle will be

x2+y2−−−−−−√

Therefore,

Step-by-step explanation:

5 0

2 years ago

Solve the system of linear equations. separate the x- and y- values with a coma.

kobusy [5.1K]

Solve the following system:
{7 x - 3 y = 37 | (equation 1)
{14 x + 11 y = 23 | (equation 2)
Swap equation 1 with equation 2:
{14 x + 11 y = 23 | (equation 1)
{7 x - 3 y = 37 | (equation 2)
Subtract 1/2 × (equation 1) from equation 2:
{14 x + 11 y = 23 | (equation 1)
{0 x - (17 y)/2 = 51/2 | (equation 2)

Multiply equation 2 by 2/17:
{14 x + 11 y = 23 | (equation 1)
{0 x - y = 3 | (equation 2)

Multiply equation 2 by -1:
{14 x + 11 y = 23 | (equation 1)
{0 x+y = -3 | (equation 2)
Subtract 11 × (equation 2) from equation 1:
{14 x+0 y = 56 | (equation 1)
{0 x+y = -3 | (equation 2)

Divide equation 1 by 14:
{x+0 y = 4 | (equation 1)
{0 x+y = -3 | (equation 2)
Collect results:
Answer: {x = 4
{y = -3

4 0

2 years ago

A homes value increases at an average rate of 5.5% each year the current value it is $120,000 what function can be used to find

likoan [24]

Around this time many people find home prices going up dramatically. Let's start with the X factor. If we know the starting is $120,000, the we know the initial velocity. To find the final but the very simple equation one may use is; P=(120000)^x\0.5

Cheers

3 0

2 years ago

What happens if you label the starting number x

tester [92]

You can use any letter but when you label it x you find x

3 0

3 years ago

What is the value of x if 17-3(x+9)=50

Rom4ik [11]

Answer:

-31 1/3

Step-by-step explanation:

17-3(x+9)=50

-17 -17

-3(x+9)=67

divide by -3

x+9=-22 1/3

-9 -9

x=-31 1/3

6 0

3 years ago

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Calculate the equation of the line through the points (1, 1), (4,3), (10, 7) and (40, 27).​

Calculate the equation of the line through the points (1, 1), (4,3), (10, 7) and (40, 27).