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 Mar12 asked Thermodynamics: find exit temp and velocity of air out of a nozzle? Feb8 awarded Popular Question Nov5 awarded Popular Question Oct9 awarded Popular Question Sep24 awarded Autobiographer Jul2 awarded Curious Jun16 awarded Popular Question Apr29 comment show that a cone is a ruled surface thank you for the help Apr29 comment show that a cone is a ruled surface Never mind I figured it out. Thanks for the help. Apr29 asked Show that product of x, y, and z intercents of tangent plane to surface xyz=1 is a constant Apr29 comment show that a cone is a ruled surface I appreciate the detailed answer but I am still confused. We didn't cover this topic in the course and I just wrote the practice final and again another question about this topic was on it. This time the question was: The hyperboloid of one sheet $x^2+y^2-z^2 = 1$ is called a ruled surface, which is to say that it is made up of straight lines. Prove this by showing that for any $\theta$, the line $$\frac{x - cos\theta}{sin\theta} = \frac{y-sin\theta}{-cos\theta} = z/1$$ lies entirely on the surface... I would really appreciate more help if you don't mind. Apr29 comment Find integral of a polar function $h(r,\theta)$ over a circle The question I originally asked was copied word for word from our review sheet. Apr28 comment Find integral of a polar function $h(r,\theta)$ over a circle So would the integral then be: $\int_0^{2\pi} \int_0^{2acos\theta} rcos\theta rdrd\theta$ ?? Apr28 asked Find integral of a polar function $h(r,\theta)$ over a circle Apr27 revised show that a cone is a ruled surface edited body Apr27 asked show that a cone is a ruled surface Apr26 asked How to find points in space where the gradient vector is parallel to another vector Apr25 comment tricky surface integral How did you go from the first line of your integral to the second line with the substitution $x=\frac{1}{\sqrt{2}} tan(t)$. I did the substitution but it brought me to the integral $\sqrt{2} \int_0^1 sec(t) dx$ Apr25 comment tricky surface integral Ok. I was also looking online... Could I also use the formula for $\int \sqrt{a^2 +x^2} dx = \frac x2 \sqrt{a^2+x^2} + \frac{a^2}2 ln|x+\sqrt{a^2+x^2}|$ using $a=\sqrt{2}$ and $x=2x$ to get the final answer??? Apr25 asked tricky surface integral