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.

Q: The probability of precipitation in a California city varies from a peak of 0.38 (38%) in January to…

A:

Q: Sulphur dioxide is released into the atmosphere when coal is burnt . In a city the amount of sulphur…

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…

A:

Q: 7. The number of visible sun spots varies rhythmically from 10 to 110 per year over a period of…

A: Given: The sun spots varies from 10 to 110 per year over a period of 11 years. The 110 max last…

Q: 11. Martha Stewart is designing a box for her cat to sleep in. It has 4 sides and a bottom but no…

A: We will use the basic knowledge of the application of differentiation and the surface area and…

Q: The height above the ground of a rider on a Ferris wheel can be modelled by the sinusoidal function…

A: To find the maximum height of the rider above the ground based on the sinusoidal function, we need…

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: 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: On 31 January, 2009, during a heat wave in Mildura, Victoria, the maximum temperature recordedwas…

A: Given that the maximum temperature recorded was approximately 44°C and the minimum overnight…

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

A:

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.