Golden Ellipse Calculus Level 5

Consider an ellipse whose semi-axes have lengths aa and bb, where {a>b}a>b. A chord in this ellipse makes acute angles \alphaα and \betaβ with the ellipse. Let \beta_{\text{min}}β
min
​
denote the minimum possible value of \betaβ, for a given value of \alphaα. Evaluate \beta_{\text{min}}β
min
​
as a function of \alphaα.

Now, take the ratio of the semi-axes of the ellipse to be \varphiφ (the golden ratio), and submit your answer as the value of {\displaystyle\int_{0}^{\frac{\pi}{ 2}}\tan\left(\beta_{\text{min}}\rig ht)\,d\alpha}∫
0
2
π
​

​
tan(β
min
​
)dα.

vwhat effect does the word head have on the meaning of this passage?

a. it demonstrates how intelligent he was.

b. it shows he was a favorite of the teachers.

c. it indicates he would be a good preacher.

d. it reveals how self-important he was.

how does the choice of the word head contribute to the passage’s tone?

a. it offers a sense of entitlement.

step-by-step explanation:

this is a math question that is a riddle in which you can only discover the answer by cracking the given equations and each answer has the corresponding letters. nonetheless, the solution to this is the scientist created  an exact duplicate of himself because he was just cloning around.

both.

step-by-step explanation:

algebra is a fundamental math skill you need in order to go forward in math. without it, geometry will be harder for you. if you don't learn algebra, it will be hard when your in geometry.