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marusya05 [52]
3 years ago
13

Rounding or compatible numbers to estimate the difference. 762-332

Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
4 0
Rounding to the nearest ten 760-330
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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
Which of these are duties of the SEC? Check all that apply.
DaniilM [7]
 <span>overseeing the actions of brokers and financial advisers
</span><span> ensuring the security and fairness of mutual funds and exchanges
</span><span>bringing suits against businesses that are not following securities laws</span>
5 0
3 years ago
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Bennett tried to solve exercise 1 a few different ways. Which of his methods are correct? Of the other methods, which makes the
nasty-shy [4]
The answer is e beac=use it fits

4 0
3 years ago
Can anyone pls help. If in you don't know pls don't answer it there is some people doing it to me pls don't I just need help wit
Dennis_Churaev [7]

Answer:

2500m2

Step-by-step explanation:

A square has four sides and the area is 10,000 m^2. Area is determined by multiplying two sides. In this case, you can divide by two to get 5000, then again by 2 to get 2500.  Each side/dimensions are 2500m^2

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The image of a parabolic lens is traced onto a graph. The function f(x) = (x + 8)(x – 4) represents the image. At which points d
alexandr402 [8]

Answer:

x = -8 and x = 4

Step-by-step explanation:

given

f(x) = (x+8) (x - 4)

recall that at any point on the x-axis, y = 0 [i.e f(x) = 0]

hence to find where the graph crosses the x-axis, we simply substitue f(x) = 0 into the equation and solve for x

f(x) = (x+8) (x - 4)

0 = (x+8) (x - 4)

Hence

either,

(x+8) = 0 ----> x = -8  (first crossing point)

or

(x-4) = 0 ------> x = 4 (second crossing point)

Hence the graph crosses the x-axis at x = -8 and x = 4

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