Aplane intersects a double-napped cone only at the cone's vertex. which terms describe the degenerate conic section that is formed? select each correct answer. degenerate parabola degenerate ellipse line degenerate hyperbola point pair of intersecting lines

In addition to ...

 degenerate ellipse

 point

it is also a degenerate circle (special case of ellipse).

___

The vertex of a double-napped cone is a point. So, the intersection of only the vertex with a plane is a point, not a degenerate parabola (a line) or degenerate hyperbola (pair of crossing lines).

Essentially, the plane must intersect at an angle greater than the angle of the edge of the cone with the axis of the cone. If the plane is not at the vertex, such an intersection angle will result in a circle or ellipse. As the plane gets closer to the vertex, the ellipse gets smaller, degenerating to a single point.

The answer is:

        Degenerate ellipse.

         Point.

Step-by-step explanation:

We know that when a plane intersects a double-napped cone only at the cone's vertex then the cross-section that is obtained is the point.

Also we know that a point is also considered as a circle with radius 0.

and a circle is also a kind of a ellipse when the length of both the transverse and conjugate axis are equal.

Hence, the term that best describe the degenerate conic section that is formed is:

degenerate ellipse

point

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places