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devlian [24]
3 years ago
8

Please help! thank you. ​

Mathematics
1 answer:
V125BC [204]3 years ago
4 0

Answer:

The first one is right

Step-by-step explanation:

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3 years ago
If 5-y^2=x^2 then find d^2y/dx^2 at the point (2, 1) in simplest form. ​
ratelena [41]

Answer:

y"(2, 1) = -5

Step-by-step explanation:

Step 1: Define implicit differentiation

5 - y² = x²

Step 2: Find dy/dx

  1. Take implicit differentiation: -2yy' = 2x
  2. Isolate y': y' = 2x/-2y
  3. Isolate y': y' = -x/y

Step 3: Find d²y/dx²

  1. Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
  2. Substitute y': y" = [-y - (-x/y)(-x)] / y²
  3. Simplify: y" = [-y - x²/y] / y²
  4. Multiply top/bottom by y: y" = (-y² - x²) / y³
  5. 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

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Event\ A\ and\ event\ B\ are\  independent\\\\ \ \Leftrightarrow\ \ \ \ P(A\ \cap\ B)=P(A)\ \cdot\ P(B)\\---------------------\\\\P(A)=0.78\ \ \ and\ \ \ P(B)=0.58\ \ \ and\ \ \ P(A\ \cap\ B)=0.58\\\\P(A)\cdot P(B)=0.78\cdot0.58\  \neq \ 0.58\\\\\Rightarrow\ \ \ Event\ A\ and\ event\ B\ are\  dependent\ \ \ \Rightarrow\ \ \ Ans.\ (?)
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2 years ago
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