Answer:
I couldn't understand question paper plz can u give question with photo too.
If by "coincide", in other words this is also known as intersect, it means that the solution to the system is that intersection point. For instance, if the intersection point of the 2 lines is (5,7) on the graph, it means that in both equations, x = 5 and y = 7. If you mean that the 2 equations result in the same line, it means that the 2 equations were really equal, but that one could be basic to be identical with the other. For example, if you have 2x + 2y = 8 and 4x + 4y = 16, they will give you the same line, and you can see that if you divide that second equation by 2 all the way crossways, it merely shows the first equation.
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
The small dish costs $2 each and the large dish costs $4 each,
2(3)+4(2)=6+8=14
2(4)+4(1)=8+4=12
Answer:
see the angle is more than 90 and it's obtuse in nature so u can find only supplement of that angle
85,106
