Answer:
72+ 48i
Step-by-step explanation:
Answer:
Step-by-step explanation:
We are given the equation of the curve:
(1)
And the equation of the line that is normal (perpendicular to that curve) in the point :
(2)
Note this equation has the form , where is the slope of the line that es normal to the curve and the intersection of that line with the y-axis.
Well, let’s begin by finding the slope of the line that is tangent to the curve by differentiating the equation (1):
(3)
Then, we have to evaluate that when (remember we are given the point ):
(4) This is the slope of the line that is tangent to the curve
And the slope of the line that is perpendicular to that tangent line is its negative reciprocal. Hence:
(5) This is the slope of the line normal to the curve
Then:
(6)
Rewritting (2):
(7)
Evaluating in the point :
(8)
Finding :
(9) This is the value of
Substituting (9) in (6):
(10)
(11) This is the value of
Answer:
x = -3
y = -15
Step-by-step explanation:
9x - 2y = 3
3x - 6 = y
Since the equation 3x - 6 is equal to y then you can plug in that equation in the other equation.
9x - 2(3x - 6) = 3
Solve for x
9x - 2(3x - 6) = 3
9x - 6x + 12 = 3
3x + 12 =3
3x = -9
x = -3
Now plug in x to find y
3(-3) -6 = y
-9 - 6 = y
-15 = y
plug it back in to double check your answer
9(-3) - 2(-15) = 3
-27 + 30 =3
3 = 3
hope this helps
When yi calculate 1 by 1 by 1 by 1 by 1 by 1 you gets 2qu2y458yq4t5uhq35th
4x = -60 - 19y
-7x = -48 - 19y
Subtract the bottom equation from the top:
4x + 7x = -60 + 48 - 19y + 19y
Simplify:
11x = -12 -0y
11x = -12
Divide both sides by 11:
11x/11 = -12/11
Simplify:
x = -12/11
Then plug in x to solve for y:
4(-12/11) = -60 - 19y
Simplify:
-48/11 = -60 - 19y
Add 60 to both sides (keep in mind 60 = 660/11):
-48/11 + 660/11 = -60 + 60 - 19y
Simplify:
612/11 = 0 - 19y
612/11 = -19y
Divide both sides by -19 (keep in mind that dividing by -19 is the same as multiplying by -1/19):
612/11 • -1/19 = -19y/-19
Simplify:
-612/209 = y
y = -612/209
So, the answer is: (-12/11, -612/209)