Answer:
y"(2, 1) = -5
Step-by-step explanation:
Step 1: Define implicit differentiation
5 - y² = x²
Step 2: Find dy/dx
- Take implicit differentiation: -2yy' = 2x
- Isolate y': y' = 2x/-2y
- Isolate y': y' = -x/y
Step 3: Find d²y/dx²
- Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
- Substitute y': y" = [-y - (-x/y)(-x)] / y²
- Simplify: y" = [-y - x²/y] / y²
- Multiply top/bottom by y: y" = (-y² - x²) / y³
- Factor negative: y" = -(y² + x²) / y³
Step 4: Substitute and Evaluate
y"(2, 1) = -(1² + 2²) / 1³
y"(2, 1) = -(1 + 4) / 1
y"(2, 1) = -5/1
y"(2, 1) = -5
The solution is:
y = 3
and
x = 5
Answer:
(3,1)
Step-by-step explanation:
Multiplying the second equation by 3, we get
-12x-6y=-42.
Now, adding this to the first equation, we get
-13x=-39
Therefore, x=3
plugging in x=3 to the first equation, we get that
-3+6y=3
adding 3 to both sides,
6y=6
therefore, y=1
Answer:
23
Step-by-step explanation:
According to the diagram, two sum of <1 and <2 is 180 degrees
Hence 3x+30+81 = 180
3x+111 = 180
3x =180-111
3x = 69
x = 69/3
x = 23
Answer:
He's incorrect
Step-by-step explanation:
lf you put -(5/12) you get -2 1/2 and 5/-12 is -0.4166 and so forth. You can tell these number's aren't the same, so always check with a culculator to make sure. In this case he is wrong.
