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 answer is b. Hope this helps!!
Answer:
5. R = 6
6. D = 22
Step-by-step explanation:
5. The area formula is πr2.
If πr2=36π,
π can be canceled out from both sides.
Then, it is r2=36.
If we square root both sides, we get:
r=6 .
Therefore, the radius of your circle is 6.
6.A = 121 π
A = r² π
r² π = 121 π
r = √ 121 = 11
The diameter: d = 2 r = 2 * 11 = 22 units
Answer:
simplifying
Step-by-step explanation:
