(See Solution) Suppose a,b and c are positive real numbers so that the point (a, b, c) is on the surface √x+√y+√z=1. Prove that the sum
Question: Suppose \(a,b\) and \(c\) are positive real numbers so that the point \((a, b, c)\) is on the surface \(\sqrt{x}+\sqrt{y}+\sqrt{z}=1\). Prove that the sum of the \(x\) -intercept, the \(y\) -intercept, and the \(z\) -intercept of the tangent plane to \(\sqrt{x}+\sqrt{y}+\sqrt{z}=1\) at \((a, b, c)\) is a constant and does not depend on a, b, or c.
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![[Steps Shown] The point P=(-2,1,1) satisfies the](/images/solutions/MC-solution-library-70558.jpg "[Steps Shown] The point P=(-2,1,1) satisfies the equation z^3+x y^2")
[Steps Shown] The point P=(-2,1,1) satisfies the equation z^3+x y^2
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(Solution Library) Compute the triple integral of the function e^-(x^2+y^2)
![[Solution Library] Consider a variable with unknown](/images/solutions/MC-solution-library-70561.jpg "[Solution Library] Consider a variable with unknown mean μ")
[Solution Library] Consider a variable with unknown mean μ
(See Steps) (a) Let X_1, X_2 ... be a sequence of independent
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