The polynomial function, w = 0.0071d3 – 0.09d2 + 0.48d, models the weight of the ideal round-cut diamond where w is the diamond’s weight (in carats) and d is the diameter (in millimeters). Based on the model, find the weight of the diamond with a diameter of 20 millimeters
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.
Direction: Answer the following question through evaluating each given polynomial
function.
1. The polynomial function, w = 0.0071d3 – 0.09d2 + 0.48d, models the weight of
the ideal round-cut diamond where w is the diamond’s weight (in carats) and d
is the diameter (in millimeters). Based on the model, find the weight of the
diamond with a diameter of 20 millimeters.
2. A drugstore that sells a certain brand of Vitamin C tablets predicts that their
profit P can be modeled by the polynomial function P(a) = -50a3 + 2400a2–2000, where a is the amount spent on advertising (in thousands of pesos).
What is its profit if a = 16?
3. Suppose that the total number attendance A (in thousands) at NCAA women’s
basketball games is modeled by the polynomial function
A = -1.95t3 + 70.1t2 – 188t + 2150, from 2000 to 2018, where t is the number of
years since 2000. Find the attendance for the year 2009.
4. The number of eggs, E(x), in a female butterfly is a function of her abdominal
width, x, in millimeters, modeled by E(x) = 14x3 – 17x2 – 16x + 34. How many
eggs can the butterfly carry if the width of her abdomen is 4 millimeters?
5. A pyramid can be formed using same sized balls. For example, 3 balls can be
arranged in a
The total number of balls used can be modeled by the polynomial function, P(n)= 1/6n(n+1)(n+2)
, where n is the number of balls on each side of the
bottom layer. What is the total number of balls used to form a pyramid if there
are 5 balls on each side of the bottom layer?
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