![kimlyn58p0wyn0](/avatars/15642.jpg)
kimlyn58p0wyn0
20.12.2019 •
Mathematics
A. the figure at the right shows a long rectangular strip of paper, one corner of which has been folded over to meet the opposite edge, thereby creating a 30-degree angle. given the width of the strip is 12 inches, find the length of the crease.
b. instead of a 30-degree angle, suppose that the angle has an unspecified size t. use trigonometry to find the length of the crease, expressed in terms of t.
c. find the approximate value of t that makes the crease as short as it can be. restrict your attention to values of t that are less than 45 degrees. explain your method.
Solved
Show answers
More tips
- C Computers and Internet Where did torrents.ru move to?...
- B Business and Finance Understanding Cash Flow: What It Is and How It Works...
- C Computers and Internet What Are Peers and Seeds in Torrenting?...
- H Health and Medicine 10 Simple Techniques on How to Boost Your Mood...
- G Goods and services How to Choose the Right High Chair for Your Baby?...
- S Style and Beauty Learn how to tie a keffiyeh on your head like a pro...
- S Style and Beauty How to braid friendship bracelets?...
Answers on questions: Mathematics
- H History NEED AN ANSWER ASAP 1. Which disadvantages can happen in a sole proprietorship? Choose exactly two answers that are correct. An owner is personally liable for business debts....
- C Chemistry Facts about diane abbott...
- M Mathematics 2. Jarak titik S(-9, 3) terhadap sumbu X adalah ... satuan. a. -9 b. -3 C. 3 d. 9...
Ответ:
m∠CDF = m∠CAE = 2t
Putting these relationships together, we have
.. DF/CD = cos(2t) = (12-x*sin(t))/(x*sin(t))
Solving for x, we get
.. x*sin(t)*cos(2t) = 12 -x*sin(t)
.. x*sin(t)*(1 +cos(2t)) = 12
.. x = 12/(sin(t)*(1 +cos(2t))
.. x = 6/(sin(t)*cos(t)^2)
For t = 30°, x = 6/(3/8) = 16
For a 30° angle, the length of the crease in 16 inches.
B. From above,
.. crease length = (6 inches)/(sin(t)*cos(t)^2)
C. Using a graphing calculator, we can find the angle that makes the crease length a minimum. See the second figure. It is about 35.264°.
___
An exact solution using derivatives gives arcsin(1/√3) ≈ 35.264390°.
Ответ:
$6.75 per pound
Step-by-step explanation:
$54 ÷ 8lb = $6.75/lb
or a 1:6.75 ratio/rate