The amount of water, A, in thousands of litres, available in a water tank located on a farm fluctuates in a yearly cycle and can be modelled by the function A(t) = a sin (kt) +b, where t is the elapsed time, in weeks, since the start of the year. The amount of water available in the tank on week 6 is 24 thousand litres and on week 31 is 9.2 thousand litres. (a) Find the value of k, in degrees, assuming there are 52 whole weeks in a year. (b) Set up a pair of equations to find the value of a and the value of b. Give your answers correct to the nearest integer. (c) Hence find the amount of water available in the tank in week 42. A(t) on the grid below, for one full year, indicating clearly (d) Draw the graph of the minimum and maximum points.

The amount of water, A, in thousands of litres, available in a water tank located on a farm fluctuates in a yearly cycle and can be modelled by the function A(t) = a sin (kt) +b, where t is the elapsed time, in weeks, since the start of the year. The amount of water available in the tank on week 6 is 24 thousand litres and on week 31 is 9.2 thousand litres. (a) Find the value of k, in degrees, assuming there are 52 whole weeks in a year. (b) Set up a pair of equations to find the value of a and the value of b. Give your answers correct to the nearest integer. (c) Hence find the amount of water available in the tank in week 42. A(t) on the grid below, for one full year, indicating clearly (d) Draw the graph of the minimum and maximum points.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: d) Using your equation, calculate the instantaneous rate of change at exactly 50 seconds. Use a…

Q: A Ferris wheel of diameter 18.5 m rotates at a rate of 0.2 rad/s. If passengers board the lowest car…

Q: The temperature, A, of a chemical reaction oscillates between a low of 30oC and high of 110oC. The…

Q: Suppose that Ashley's blood pressure can be modeled by the following function. p(t)=87-16 cos…

A: Given, Ashley's blood pressure can be modeled as- pt=87-16cos107πt The Time-Period of y=acosbt…

Q: The hours of daylight in Glasgow, Scotland, can be modeled by the function f given by f(d) =…

A: The function f which is modelling the hours of daylight in Glasgow, Scotland is given by :fd=5.3…

Q: Use cofunctions of complementary angles to find θ where cos(17deg) = sin(θ). Use logarithm…

Q: The doubling period of a certain bacteria is 6 hours. There is a 500 g sample of the bacteria. a)…

A: Given problem:- The doubling period of a certain bacteria is 6 hours. There is a 500 g sample of the…

Q: The inverse function of f(x) = 2 log3 (1-x) is اختراحد الخيارات A. 3 -1o B. 1+ 3 C. 3 D. 1-3

Q: Each person's blood pressure is different, but there is a range of blood pressure values that is…

A: A function Pt=-20cos5π3t+100 models the blood pressure P in millimeters in mercury. To Find: What…

Q: The value, v of a computer is modeled by the function V(t)=500(0.82)^t where t is the number of…

A: The value of computer is modeled by the function, V(t) = 500(0.82)t Where t is time in years

Q: The amount of daylight in a town can be modelled by the sinusoidal function d(t)= 4.37 cos 0.017t +…

A: Solution of given question is written in below steps.

Q: Is TSI (y) a function of years (x)? How do you know this?

A: Is TSI (y) a function of years (x), then by mathematically we can say that

Q: Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P…

Q: The number of acres of old growth forest in a park, N, initially 500 acres, is decreasing at a…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 3. A Ferris wheel of diameter 18.5 m rotates at a rate of 0.2 rad/s. If passengers board the lowest…

A: Given: Diameter of Ferris wheel=18.5 m, Rotation rate of wheel=0.2 radsTo find: The cosine function…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The amount of water, A, in thousands of litres, available in a water tank located on a farm
fluctuates in a yearly cycle and can be modelled by the function
A(t) = a sin (kt) + b,
%3D
where t is the elapsed time, in weeks, since the start of the year.
The amount of water available in the tank on week 6 is 24 thousand litres and on week 31 is
9.2 thousand litres.
(a) Find the value of k, in degrees, assuming there are 52 whole weeks in a year.
(b) Set up a pair of equations to find the value of a and the value of b. Give your answers
correct to the nearest integer.
(c)
) Hence find the amount of water available in the tank in week 42.
(d) Draw the graph of y = A(t) on the grid below, for one full year, indicating clearly
the minimunm and maximum points.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given information

VIEW

Step 2: Value of a and b

VIEW

Step 3: A(t=42)

VIEW

Step 4: The plot A(t)

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

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.

Similar questions

The San Francisco Bay tides vary between 1 foot and 7 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 8 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? A. Amplitude = 6 feet; period = 8 hours; midline: y = 4 B. Amplitude = 6 feet; period = 4 hours; midline: y = 3 C. Amplitude = 3 feet; period = 8 hours; midline: y = 4 D. Amplitude = 3 feet; period = 4 hours; midline: y = 3
The height of a buoy on a lake is changing during a storm. The height's rate of change can be modeled by r(t) = 0.5 cos(0.2t) feet per second where t is measured in seconds. Is the buoy's height increasing or decreasing at time t = 10 seconds? Why?
Suppose that Tammy's blood pressure can be modeled by the following function. p (t) = 91 + 24 cos (89 nt) 同 Tammy's blood pressure increases each time her heart beats, and it decreases as her heart rests in between beats. In this equation, p(t) is the blood pressure 00 in mmHg (millimeters of mercury), and t is the time in minutes. 民 Find the following. If necessary, round to the nearest hundredth. Amplitude of p : mmHg Number of heartbeats per minute: Period of p : minutes Save For Later Submit Assignment Check 2021 McGraw-Hili Ecucation. AlI Rights Reserved. Terms of Use Privacy Accessibility
The wind-chill index is modeled by the function W = 13.12 + 0.62157- 11.37v0.16 + 0.39657v0.16 where T is the temperature (°C) and v is the wind speed (in km/h). When T = -14°C and v= 35 km/h, by how much (in °C) would you expect the apparent temperature W to drop if the actual temperature decreases by 1°C? (Round your answers to two decimal places.) °C drop What if the wind speed increases by 1 km/h while the actual temperature stays constant at T = -14°C? °C drop