(04.04 MC) A designer wants to create a whisper chamber in the shape of an ellipse. He has a warehouse space with a longest length of 30 ft, which he decides will be the major axis of his elliptical chamber. He determines the best spots for his guests to stand to experience his whisper chamber will be 4 ft from the center of the warehouse space, which will act as the foci. How far out from the center, along the minor axis, should he build his whisper chamber?

(04.04 MC) Given the directrix of y = 4 and focus of (0, 2), which is the equation of the parabola?

What type of joint can be found in the coronal suture of the skull?

Find the interval of convergence for the following series. Make sure to test the endpoints of your interval. ∑ n = 1 ∞ ( − 1 ) n x n n + 3 {“version”:”1.1″,”math”:”\sum\limits_{n=1}^\infty (-1)^n \frac{x^n}{\sqrt{n+3}}”}

Consider the sequence defined bya1=1an+1=2an−4Find the next three terms (a2, a3, a4) of the sequence.

Consider the sequence defined bya1=1an+1=2an−4Find the next three terms (a2, a3, a4) of the sequence.

Categorize the following plant organ modifications with the matching organ.

(10 points) Evaluate the following integral by using integration by parts (IBP).    

First, prove that the following series converges. Second, calculate the number of terms n that must be added in order to find the sum to within 0.01 and type your answer into the answer box. ∑ n = 1 ∞ ( − 1 ) n 4 n 2 {“version”:”1.1″,”math”:”\sum\limits_{n=1}^\infty (-1)^n \frac{4}{n^2}”}

First, prove that the following series converges. Second, calculate the number of terms n that must be added in order to find the sum to within 0.01 and type your answer into the answer box. ∑ n = 1 ∞ ( − 1 ) n 4 n 2 {“version”:”1.1″,”math”:”\sum\limits_{n=1}^\infty (-1)^n \frac{4}{n^2}”}