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I've solved this now!

Consider the spherical triangle $\mathcal{P}$ with vertices $P_1 = (1,0,0)$, $P_2 = (0,1,0)$ and $P_3 = (1/\sqrt{3}, 1/\sqrt{3},1/\sqrt{3})$. Find the angles $\phi_1, \phi_2, \phi_3$ of $\mathcal{P}$ at $P_1, P_2, P_3$ respectively. I know the cosine angles are $\cos(\theta_1) = 0$...

Thank you very much!

Thank you. Is it technically correct to say that $(1, 2)^t$ is a solution to the differential equation? This question was a multiple choice, and the only answer that fits is $(1,2)^t$. I think this is the correct answer because $c_1 (1,2)^t+c_2(-2,1)^te^{5t} = (1,2)^t$ for $c_1 = 1, c_2 = 0$.

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Suppose $\displaystyle f = e^{(x^2+y^2+z^2)^{3/2}}$. We want to find the integral of $f$ in the region $R = \left\{x \ge 0, y \ge 0, z \ge 0, x^2+y^2+z^2 \le 1\right\}$. Could someone tell me how we quickly determine that $R$ can be written as: $R = \left\{\theta \in [0, \pi/2], \phi \in [0...