Question

answer questions 3,4,5 please

the questions are more visible in second picture

Choose File No file chosen upload your Exercise 14: (Optional:for extra credit) The radius r of the smallest circular paper plate that holds a pizza of a given radius R-5 inches and central angle 9, 0 c ess, is given by the function rafte) where Elouce Following sketches to be done by hand: 1. Sketch the pizza in its plate for e s/6 (a 30 deqree wedge). Find r for e n/6 2. Sketch the pizza in its plate for x (half the pizza). Find r for 3. Determine the function e) for the domain x ses 2 4. Explain how to obtain the formula above for the function (e) on (0,e). Hint: Sketch lots of examples. 5. Use MATLAB to create and print a graph of f(e). (printed graph to be submitted separately to professor.) Awedge of pizza. (fam) That is it. Please choose from one of your options below Save Save your work for later. Save and Submt Save and submit for grading No more work allowed aR rinbte Powered hy e-Punde Convrsst 1oo0-2001

Answer 1

a). For $\theta=\frac{\pi}{6}$ , $r=f(\theta)=\frac{R}{2}cos(\frac{1}{2}(\frac{\pi}{6}))=2.414814565722671$

(b)

for $\theta=\pi,$  $r=f(\theta)=Rsin(\frac{1}{2}\pi)=5$

(c) The angle $\theta$ is defined only   $0\leq \theta \leqslant \pi$ in the question.

(e)

clc;clear all 1 2 m 0:0.01:pi 3 4 for i-1:length (m) if o<m (i) && m(i)<-pi/2 6 7 f(i) 2.5 cos (m (i)/2) 9 else 10 11 f(i) 5 sin (m (i) /2) end 12 end; 13 14 15 plot (m, f) st

4.5 4F 3.5 3 2.5 2 1.5 1 0.5 0 0.5 1.5 2 2.5 3 3.5 un