Step-by-step explanation:
![\beta](https://tex.z-dn.net/?f=%20%5Cbeta%20)
is a root of the quadratic
![4 {x}^{2} - 10x + 5](https://tex.z-dn.net/?f=4%20%7Bx%7D%5E%7B2%7D%20%20-%2010x%20%2B%205)
This quadratic isn't factorable so use the quadratic formula
![- b + - \sqrt{ \frac{b {}^{2} - 4ac }{2a} }](https://tex.z-dn.net/?f=%20-%20b%20%2B%20%20-%20%20%5Csqrt%7B%20%5Cfrac%7Bb%20%7B%7D%5E%7B2%7D%20%20-%204ac%20%7D%7B2a%7D%20%7D%20)
The plus and minus sign after b means we going to have two roots.
The roots are
![\frac{5 + \sqrt{5} }{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%20%2B%20%20%5Csqrt%7B5%7D%20%7D%7B4%7D%20)
and
![\frac{5 - \sqrt{5} }{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%20-%20%20%5Csqrt%7B5%7D%20%7D%7B4%7D%20)
We subsitue those values for Beta.
27a.
![\frac{5}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B2%7D%20)
27b.
25
Answer:
The cross section will be an isosceles triangle
Step-by-step explanation:
The picture of the question in the attached figure N 1
we know that
If a plane passes through the axis of rotation of the cone, then the resultant cross-section will be a triangle with one vertex as the vertex of the cone and the two sides of the triangle through the vertex A will be equal.
Where the base of the triangle will be equal to the diameter of the circular base of cone and the two congruent sides of triangle will be equal to the slant height of the cone
therefore
The cross section will be an isosceles triangle
Answer in decimal form: 37.69911184