We have the following region of integrate in image. Make orthogonal change of variables, where the line "u=\\frac{169v}{100}" will be the axis "u'" and orthogonal line "u=-\\frac{100}{169}v" will be axis "v'" .
So "\\begin{pmatrix}\n v \\\\\n u\n\\end{pmatrix}=\n\\begin{pmatrix}\n \\cos\\alpha & -\\sin\\alpha \\\\\n \\sin\\alpha & \\cos\\alpha\n\\end{pmatrix}\n\\begin{pmatrix}\n v' \\\\\n u'\n\\end{pmatrix}" , where "\\tan\\alpha=-\\frac{100}{169}" , that is "\\cos\\alpha=\\frac{169}{\\sqrt{38561}}" and "\\sin\\alpha=-\\frac{100}{\\sqrt{38561}}" .
We obtain that line "u=\\frac{169v-2}{100}" will be transformed into "-\\frac{100}{\\sqrt{38561}}v'+\\frac{169}{\\sqrt{38561}}u'=\\frac{169}{100}\\bigl(\\frac{169}{\\sqrt{38561}}v'+\\frac{100}{\\sqrt{38561}}u'\\bigr)-\\frac{1}{50}" or "v'=\\frac{2}{\\sqrt{38561}}"
Line "u=-\\frac{100}{169}v" will be transformed into "u'=0".
We obtain the new region of integration "\\bigl\\{(u',v'): v'\\ge\\frac{2}{\\sqrt{38561}}\\bigr\\}"
Jacobian of our transformation is "J=\\bigl|\\begin{pmatrix}\n \\cos\\alpha & -\\sin\\alpha \\\\\n \\sin\\alpha & \\cos\\alpha\n\\end{pmatrix}\\bigr|=1"
Since our transformation is orthogonal, we have "u^2+v^2=(u')^2+(v')^2" , so "\\frac{1}{\\sqrt{2\\pi}}\\frac{1}{\\sqrt{2\\pi}}\\int\\limits_{-\\infty}^{+\\infty}\\int\\limits_{-\\infty}^{\\frac{169v-2}{100}}e^{-\\frac{u^2}{2}}e^{-\\frac{v^2}{2}}dudv="
https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf - Normal Disribution Table
Since "\\frac{2}{\\sqrt{38561}}\\approx 0.01" , from table we see that "\\Phi\\bigl(\\frac{2}{\\sqrt{38561}}\\bigr)\\approx\\Phi(0.01)\\approx 0.50399" , so "1-\\Phi\\bigl(\\frac{2}{\\sqrt{38561}}\\bigr)\\approx 0.49601"
Answer: "0.49601"
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