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Home » x + y = 24 y x - y = 8. - Ready Digital AB

x + y = 24 y x - y = 8. - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 Factoring out \( 2x \):

📌 2x(x - 2) = 0.

📌 Thus, the points of intersection are \( x = 0 \) and \( x = 2 \).

📌 The area \( A \) between the curves from \( x = 0 \) to \( x = 2 \) is given by:

📌 A = \int_0^2 \left((4x - x^2) - x^2\right) \, dx = \int_0^2 (4x - 2x^2) \, dx.

📌 Evaluating the integral:

📌 A = \left[ 2x^2 - \frac{2}{3}x^3 \right]_0^2 = \left( 2(2)^2 - \frac{2}{3}(2)^3 \right) - \left( 2(0)^2 - \frac{2}{3}(0)^3 \right).

📌 Calculating each term:

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\Rightarrow x^2 - 2x + 1 + y^2 - 2y + 1 + z^2 = 2
\Rightarrow (x^2 + y^2 + z^2) - 2x - 2y + 2 = 2
\Rightarrow 2 - 2x - 2y + 2 = 2 \Rightarrow -2x - 2y = -2 \Rightarrow...
Distance from $(1,0,1)$:
\Rightarrow x^2 - 2x + 1 + y^2 + z^2 - 2z + 1 = 2
\Rightarrow (x^2 + y^2 + z^2) - 2x - 2z + 2 = 2
\Rightarrow 2 - 2x - 2z + 2 = 2 \Rightarrow -2x - 2z = -2 \Rightarrow...
From (2) and (3), we have:
x + y = 1, \quad x + z = 1 \Rightarrow y = z
From the first equation:

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