A cone is sliced so the cross section is perpendicular to its base and passes through its vertex.

Mathematics

2 answers:

WARRIOR [948]3 years ago

8 0

The shape of the cross-section formed is a triangle, when a cone is cut in such a way that the cross-section is perpendicular to the base and it passes through the vertex.

Say, we have a cone as shown below. In the figure, the cone is sliced such that the cut passes the vertex of the cone and is perpendicular to the base of the cone (as shown by the dashed line). The figure thus formed after cutting is in the shape of a triangle.

Sladkaya [172]3 years ago

8 0

A triangle because a true cone coming to a discrete point at the apex or vertex and with a plane slicing it perpendicular to the base and through the vertex would have to have the shape of a triangle by construction

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If f(x) and it's inverse function, f^1(x) are both plotted on the same coordinates plane what is their point of intersection

svet-max [94.6K]

The answer is an equation, a condition:

f(x) = f^(-1)(x), then apply f(x) again: f(f(x) ) = f(f^-1(x)) = x,

f(f(x)) =x, that means that:

The point of intersection is the point where applying f(x) twice it results in the identity. A similar argument takes you to f^(-1)(f^(-1)(x)) = x.

Furthermore, the final answer is the point where f(x)=x (which coincides with f^(-1)(x)=x). That is the value of x where the function crosses the line y=x. If there is no such point, then f(x) and f^(-1)(x) will never cross each other.

I can see the proof graphically, so I can't post it.

For a line, it always works:

f(x) = ax+b, f^(-1)(x) = (x-b)/a, ax+b = (x-b)/a --> a^2x+ab=x-b,

x = -(a+1)*b/(a^2-1) = -b/(a-1). Which is indeed where f(x)=x.

7 0

3 years ago

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ra1l [238]

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