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Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite Suppose that $X subset mathbbCP^n$ is a (possibly singular) algebraic curve. Let $H_tau subset mathbbCP^n$ be a family of hyperplanes, with $tau in (-1,1)$. By Bezout's theorem, the count of intersection points (with multiplicity) is independent of $tau$. (Let us assume that $H_tau$ does not contain any irreducible components of $X$, and that $X$ is reduced. This justifies the application of Bezout's theorem). Question: I would like to say that the intersection points vary continuously in $mathbbCP^n$, with respect to the Euclidean topology. Is this statement true, and if so, where can it be found in the literature? complex-analysis algebraic-geometry share | cite | improve this question edited Aug 6 at 20:06 asked Aug 6 at 18:51 user142700 1,190 5 15 1 what is the role of $tau$ here? You might need some kind of "generic" requirement. As in, take...

Clash Royale CLAN TAG #URR8PPP up vote 1 down vote favorite Let k a field. Let $ A = k+ x^2 k[x] $, Show that A is integral domain and finite type. An element of $A$ is $alpha + x^2. f(x) $ where$ fin k[x] $ I know that A is a subalgebra of k[x], Any hint for integral domain abstract-algebra ring-theory share | cite | improve this question edited Aug 6 at 20:15 asked Aug 6 at 19:56 Ali NoumSali Traore 48 6 add a comment  |  up vote 1 down vote favorite Let k a field. Let $ A = k+ x^2 k[x] $, Show that A is integral domain and finite type. An element of $A$ is $alpha + x^2. f(x) $ where$ fin k[x] $ I know that A is a subalgebra of k[x], Any hint for integral domain abstract-algebra ring-theory share | cite | improve this question edited Aug 6 at 20:15 asked Aug 6 at 19:56 Ali NoumSali Traore 48 6 add a comment  |  up vo...

Clash Royale CLAN TAG #URR8PPP up vote 3 down vote favorite I'm working on some summer problems so that I can be more prepared when I go into my class in the fall. I found a website full of problems of the content we will be learning but it doesn't have the answers. I need a little guidance on how to do this problem. The following diagram shows a circle with centre o and radius 5 cm. The points A , B , and C like on the circumference of the circle, and $angle AOC$ = 0.7 radians. a. Find the length of the arc ABC . b. Find the perimeter of the shaded sector. c. Find the area of the shaded sector. For a, the arc length would be the angle multiplied by the radius, correct? l = 5 x 0.7 l = 3.5 cm For b, would it be 2 radii and the length of the arc added together? 5+5+3.5 = 13.5 cm And for c, I’m honestly not too sure. Is it the central angle over 360° = the sector over $πr^2$ circle shar...