Answer:
<u><em>For x - y = 2</em></u>
You need to find x or y in one of the equations and then substitute that into the other.
So we have;
x-y=2
4x-3y=11
We will take the first equation and find x;
x-y=2
add y to both sides;
x-y+y=2+y
x=2+y
Now we take that answer and substitute it forx in the other equation;
4(2+y)-3y=11
8+4y-3y=11
8+y=11
y=3
Now we have what y equals, so we use it in the first equation to find x;
x-3=2
x=5
So we have;
x=5; y=3
Hope you understand!
=)
<u><em>And for 4x – 3y = 11</em></u>
Multiply the first equation by 2 and the second by 3 so that there are the same number of y's in each:
8x - 6y = 22 ...(3)
30x + 6y = -3 ...(4)
Now add (3) and (4) term by term:
38x + 0 = 19
or
38x = 19
or x = 1/2
Put this back into equation (1)
4*(1/2) - 3y = 11
or
2 - 3y = 11
Subtract 2 from both sides:
-3y = 9
Divide both sides by -3
y = -3
9514 1404 393
Answer:
2nd quadrant
Step-by-step explanation:
Reversing the signs of both coordinates reflects the point across the origin. The quadrant diagonally opposite quadrant 4 is quadrant 2.
_____
You recall that quadrants are numbered 1 to 4 counterclockwise, starting from upper right.
I'll explain how to do the first one:-
y = cos-1(x2)
This can be described as ' a function of a function' x^2 is a function of x and cos-1(x^2) is a function of x^2.
We need to apply the chain rule.
Personally I find this easier to understand if i let u = x^2, so
If y = f(u) and u is a function of x then
dy/dx = dy/ du * du/dx
Here u = x^2 and y = cos-1(u)
du/dx = 2x
so dy/dx = d(cos-1(x^2) dx = dy/du * du/dx
= -1 / √(1 - u^2) * 2x
= -2x / √(1 - u^2)
= -2x / √(1 - (x^2)^2)
= -2x / √(1 - x^4)
I hope this helps. but if not. you might like to employ the formulae in the question - The square boxes contain the 'u' s in my answer. These formulae are equivalent to my explanation.
