Posted by Jillian on Wednesday, August 22, 2012 at 4:34pm.
What would the values of A, B, and C be in this problem?
The tides in a particular bay can be modeled with an equation of the form d= A cos (Bt) + C, where t represents the number of hours since high-tide and d represents the depth of water in the bay. The maximum depth of water is 36 feet, the minimum depth is 22 feet and high-tide is hitting every 12 hours.
- Calculus - Reiny, Wednesday, August 22, 2012 at 4:46pm
max - min = 36-22 = 14
so the amplitude is 7
what do we have to add to 7 to get 36 ? ----- 29
period of cosine curve = 2π/k
12 = 2π/k
k = π/6
so d = 7 cos (πt/6) + 29
at t=0 , d = 7cos 0 + 29 = 36 ---> high tide
at t=3 , d = 7cos π/2 + 29 = 29 ---> makes sense
at t=6 , d = 7cos π + 29 = -7+29 = 22 ---> low tide
at t=9 , d = 7cos 3π/2 + 29 = 29 --->makes sense
at t=12, d = 7cos 2π + 29 = 7(1)+29 = 36 ---> back to high tide
- Calculus - Jillian, Wednesday, August 22, 2012 at 4:54pm
What will the graph look like for two full periods?
- Calculus - Reiny, Wednesday, August 22, 2012 at 5:06pm
mark off from 0 to 12, with marks at 0, 3, 6, 9, and 12
at 0 , d=36
at 3, d= 29
at 6, d = 22
at 9, d = 29
at 12, d = 36 --- end of first period, now repeat that
draw a smoth cosine curve .
(I am somewhat surprised you even asked that question)
Answer this Question
More Related Questions
- Calculus-HELP!!!! - Show that the function y=c_1 e^x cos(x)+ c_2 e^x sin(x) ...
- Math help - Help with any of these would be greatly appreciated! THANK YOU! 1. ...
- Science - what are spring tides and how do they occur? Spring tides are are ...
- Math - The tides at cape Capstan, New Brunswick, change the depth of the water ...
- Calculus - How would you begin this problem? On a standard summer day in upstate...
- calculus - Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x...
- Pre-calculus HELP PLASE ! - 1.Write the rectangular equation in polar form. (x...
- math - The table shows the depth (d metres) of water in a harbour at certain ...
- Trig/Precalc - So I have two questions that have been puzzling me for quite some...
- Pre-calculus - solve 4 sin^2x + 4 sqrt 2 cos x-6=0 for all real values of x. ...