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AlekseyPX
2 years ago
8

Make x the subject in the relation

Mathematics
1 answer:
tatyana61 [14]2 years ago
7 0
Cant read your writing-
You might be interested in
Describe the set of points z in the complex plane that satisfy the given equation; |z-2|=Re(z).
OLEGan [10]

Answer:

Parabola with vertex at point (1,0) that goes to the right (see attached diagram).

Step-by-step explanation:

Let the complex number z be

z=x+iy,

then

z-2=x+iy-2=(x-2)+iy\\ \\Re\ (z-2)=x-2\\ \\Im\ (z-2)=y\\ \\|z-2|=\sqrt{Re^2\ (z-2)+Im^2\ (z-2)}=\sqrt{(x-2)^2+y^2}

and

Re\ z=x

Thus,

\sqrt{(x-2)^2+y^2}=x

Square it:

(x-2)^2+y^2=x^2\\ \\x^2-4x+4+y^2=x^2\\ \\-4x+4+y^2=0\\ \\y^2=4x-4\\ \\y^2=4(x-1)

This is the equation of parabola with vertex at point (1,0) that goes to the right.

3 0
2 years ago
point k is between points j and l if jk=xsquared -4x, kl= 3x-2, and jl= 28, write and solve an equation to find the lengths of j
nadya68 [22]
Jk= 18
Kl= 10

3x - 2 = 28
+2. +2
3x / 3 and 30 / 3 = 10
28-10 = 18
8 0
3 years ago
Can someone please tell me what 2 - 1 1/2 equals? Please answer quickly !!!
sergeinik [125]

the answer is 3/2 to this question

7 0
3 years ago
Read 2 more answers
A RIGHT triangle has two other angles measuring x and 2x. What does x equal?
Marianna [84]

Answer:

x = 30

Step-by-step explanation:

because the interior angles of a triangle = 180° so if you subtract 90° you get 90. in order to get 90 you can use the equation x + 2x = 90 which you will then get x = 30

5 0
3 years ago
Consider the function on the interval (0, 2π). f(x) = sin x + cos x (a) Find the open intervals on which the function is increas
Annette [7]

Answer:Increasing in x∈(0,π/4)∪(5π/4,2π) decreasing in(π/4,5π/4)

Step-by-step explanation:

given f(x) = sin(x) + cos(x)

f(x) can be rewritten as \sqrt{2} [\frac{sin(x)}{\sqrt{2} }+\frac{cos(x)}{\sqrt{2} }  ]..................(a)\\\\\ \frac{1}{\sqrt{2} } = cos(45) = sin(45)\\\\

Using these result in equation a we get

f(x) = \sqrt{2} [ cos(45)sin(x)+sin(45)cos(x)]\\\\= \sqrt{2} [sin(45+x)]..........(b)

Now we know that for derivative with respect to dependent variable is positive for an increasing function

Differentiating b on both sides with respect to x we get

f '(x) = f '(x)=\sqrt{2}  \frac{dsin(45+x)}{dx}\\ \\f'(x)=\sqrt{2} cos(45+x)\\\\f'(x)>0=>\sqrt{2} cos(45+x)>0

where x∈(0,2π)

we know that cox(x) > 0 for x∈[0,π/2]∪[3π/2,2π]

Thus for cos(π/4+x)>0 we should have

1) π/4 + x < π/2  => x<π/4  => x∈[0,π/4]

2) π/4 + x > 3π/2  => x > 5π/4  => x∈[5π/4,2π]

from conditions 1 and 2 we have  x∈(0,π/4)∪(5π/4,2π)

Thus the function is decreasing in x∈(π/4,5π/4)

5 0
2 years ago
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