(a) Are D(t) and E(t) functions or not? Explain your answer. (b) Solve for a and b if the maximum value of f(t) on the interval [0, 48] is at the point (32; 24900).
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
a and b
![2. Unfortunately many people have died in South Africa due to the COVID-19 pandemic.
The black graph below shows the number of people over age 1 year who have died per
week (from all possible causes, not only COVID-19) in South Africa between 29 December
2019 and 12 June 2021. We will call this black graph D(t). The solid orange graph shows
how many people are normally expected to die per week, carrying on to the end of 2021.
We will call this graph E(t). (The dotted lines are just to show that the actual values may
be a little different to E(t).)
South Africa Weekly Deaths from All Causes 1+ years : 29 Dec 2019 - 12 June 2021
25,000
20,000
15,000
10,000
5,000
Week start date
- Weekly deaths
- Forecast
.. Lower Prediction Bound
.. Upper Prediction Bound
[Downloaded from https://www.samrc.ac.za on 16.06.2021.]
The functions f(t) and g(t) have similar shapes to D(t) and E(t) respectively. They are
sketched below on the interval [0, 48], measuring t in weeks and taking t = 0 on 1 June
2020.
23
3945
f(t)
8695
t² +7176t + b
256
16
64
g(t) = 2000 cos
30
+ 8500
(a) Are D(t) and E(t) functions or not? Explain your answer.
(b) Solve for a and b if the maximum value of f(t) on the interval [0, 48] is at the point
(32; 24900).
26-Jan-20
9 Feb-20
8 Mar 20
oz qo 4 ca
12-Dec21](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9360b24b-1524-427e-8abc-1f304465f396%2F719a9fe6-af4b-49a9-b170-a6b6f4c3dac4%2Fcba60cj_processed.jpeg&w=3840&q=75)
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