subject
Mathematics, 07.03.2020 02:24 katyym80

In the triangle pictured, let A, B, C be the angles at the three vertices, and let a, b,c be the sides opposite those angles.

According to the ``law of sines,'' you always have:
b/a=sinB/sinA

Suppose that a and b are pieces of metal which are hinged at C. At first the angle A is ?/4 radians=45o and the angle B is ?/3 radians = 60o. You then widen A to 46o, without changing the sides a and b. Our goal in this problem is to use the tangent line approximation to estimate the angle B.
(a) Notice that the angle B is a function of the angle A; i. e. B=f(A). Consequently, it makes sense to calculate the implicit derivative:
dB/dA
=(?3) / (?2)=
(b) Calculate
dB/dA
when A=?/4 and B=?/3; leave your answer in EXACT FORM:
(c) Write the linear approximation of f at A= ?/4:
(A ?/4) +
(d) Using (c), when A= 46o, B is approximately
degrees; either answer exactly or to three decimal places.

ansver
Answers: 2

Other questions on the subject: Mathematics

image
Mathematics, 21.06.2019 21:50, lucifer6669
What is the product? a-3/15a × 5/a-3
Answers: 1
image
Mathematics, 21.06.2019 23:30, drakkeo
Sam opened a money-market account that pays 3% simple interest. he started the account with $7,000 and made no further deposits. when he closed the account, he had earned $420 in interest. how long did he keep his account open?
Answers: 1
image
Mathematics, 22.06.2019 03:00, TheOriginalMeyah
The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?
Answers: 1
image
Mathematics, 22.06.2019 03:00, krlx
Which of the following statements must be true about this diagram? check all that apply. x°, y°, z°, & w°
Answers: 3
You know the right answer?
In the triangle pictured, let A, B, C be the angles at the three vertices, and let a, b,c be the sid...

Questions in other subjects:

Konu
Mathematics, 29.01.2020 16:06