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Talja [164]
3 years ago
8

Help!!!!!!!!!!! please!!!!!!!!!

Mathematics
1 answer:
ohaa [14]3 years ago
3 0

Answer: The first one is not a function the second is a function the third one is not one and the fourth one is

Step-by-step explanation:

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Find the real numbers x and y if -3+ix^2y and x^2+y+4i are conjugate of each other. Pls solve with the steps
Firdavs [7]
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions. 

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the 

   x²y = -4 ... (I)

Condition 2: Real parts are the same

   x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

   x²y = -4 ... (I)
   x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

   y = -3 - x² ... (II)

Substituting into equation (I)

   x²y = -4 ... (I)
   x²(-3 - x²) = -4
   -3x² - x⁴ = -4
   x⁴ + 3x² - 4 = 0
   (x² + 4)(x² - 1) = 0
   (x² + 4)(x-1)(x+1) = 0

Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

   y = -3 - x² ... (II)
   y = -3 - (±1)²
   y = -3 - 1
   y = -4

So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

   -3 + ix²y 
   = -3 + i(±1)²(-4)
   = -3 - 4i

   x² + y + 4i
   = (±1)² - 4 + 4i
   = 1 - 4 + 4i
   = -3 + 4i

They result in conjugates
4 0
3 years ago
Read 2 more answers
Plz help me out quick​
natima [27]

Answer: 6:5

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Find the area of the rhombus.
Archy [21]
The answer is c
the rhombus above is formed by 4 triangles
area of one triangle= 9*13.5*0.5=60.75
area of 4 triangles = 4*60.75=243
6 0
3 years ago
Read 2 more answers
A college-entrance exam is designed so that scores are normally distributed with a mean of 500 and a standard deviation of 100.
yawa3891 [41]

Answer:

The probability is  0.003

Step-by-step explanation:

We know that the average \mu is:

\mu=500

The standard deviation \sigma is:

\sigma=100

The Z-score is:

Z=\frac{x-\mu}{\sigma}

We seek to find

P(x800)

For P(x>800) The Z-score is:

Z=\frac{x-\mu}{\sigma}

Z=\frac{800-500}{100}

Z=3

The score of Z = 3 means that 800 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

So

P(x>800)=0.15\%

For P(x<200) The Z-score is:

Z=\frac{x-\mu}{\sigma}

Z=\frac{200-500}{100}

Z=-3

The score of Z = -3 means that 200 is 3 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the conficion of 3 deviations from the mean has percentage of 0.15%

So

P(x

Therefore

P(x800)=P(x800)

P(x800)=0.0015 + 0.0015

P(x800)=0.003

6 0
3 years ago
The graph of a function f is shown below.<br> Find f (2)
liberstina [14]

Answer:  f(2) is 3.

Step-by-step explanation:

f(2) just means "what is the vale of the function, f, when x = 2?  Look for x=2 and read the y value where the line crosses x=2, in this case, the y value is 3.  So f(2) = 3.

======

[One could also determine the equation for the line.  Provided below.]  

The slope is -(1/2) and the y-intercept is 4:

y = -(1/2)x + 4

For x=2,

y = -(1/2)*(2) + 4

y = 3  

y(2) = 3  

4 0
3 years ago
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