The monthly high temperature for Atlantic City. New Jersey, peaks at an average high of 86 ° in July and goes down to an average high of 64 ° in January. Assume that this pattern for monthly high temperatures continues indefinitely and behaves like a cosine wave. a. Write a function of the form H t = A cos B t − C + D to model the average high temperature. The value H t is the average high temperature for month t , with January as t = 0. b. Graph the function from part (a) on the interval 0 , 13 and plot the points 0 , 64 , 6 , 86 and 12 , 64 to check the accuracy of your model.
The monthly high temperature for Atlantic City. New Jersey, peaks at an average high of 86 ° in July and goes down to an average high of 64 ° in January. Assume that this pattern for monthly high temperatures continues indefinitely and behaves like a cosine wave. a. Write a function of the form H t = A cos B t − C + D to model the average high temperature. The value H t is the average high temperature for month t , with January as t = 0. b. Graph the function from part (a) on the interval 0 , 13 and plot the points 0 , 64 , 6 , 86 and 12 , 64 to check the accuracy of your model.
Solution Summary: The author explains how the monthly high temperature continues indefinitely and behaves like a cosine wave. The amplitude of the curve is half the distance between the highest value and lowest value.
The monthly high temperature for Atlantic City. New Jersey, peaks at an average high of
86
°
in July and goes down to an average high of
64
°
in January. Assume that this pattern for monthly high temperatures continues indefinitely and behaves like a cosine wave.
a. Write a function of the form
H
t
=
A
cos
B
t
−
C
+
D
to model the average high temperature. The value
H
t
is the average high temperature for month
t
, with January as
t
=
0.
b. Graph the function from part (a) on the interval
0
,
13
and plot the points
0
,
64
,
6
,
86
and
12
,
64
to check the accuracy of your model.
Problem 11 (a) A tank is discharging water through an orifice at a depth of T
meter below the surface of the water whose area is A m². The
following are the values of a for the corresponding values of A:
A 1.257 1.390
x 1.50 1.65
1.520 1.650 1.809 1.962 2.123 2.295 2.462|2.650
1.80 1.95 2.10 2.25 2.40 2.55 2.70
2.85
Using the formula
-3.0
(0.018)T =
dx.
calculate T, the time in seconds for the level of the water to drop
from 3.0 m to 1.5 m above the orifice.
(b) The velocity of a train which starts from rest is given by the fol-
lowing table, the time being reckoned in minutes from the start
and the speed in km/hour:
| † (minutes) |2|4 6 8 10 12
14 16 18 20
v (km/hr) 16 28.8 40 46.4 51.2 32.0 17.6 8 3.2 0
Estimate approximately the total distance ran in 20 minutes.
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY