Question 1: Find the dimensions of the rectangular corral producing the greatest enclosed area split into 3 pens of the same size given 500 feet of fencing. Question 2: Make a table to confirm the end behavior of the function. f (x) = x^2(1 − x)^2 Question 3: An oil slick is expanding as a circle. The radius of the circle is increasing at the rate of 20 meters per day. Express the area of the circle as a function of d, the number of days elapsed. Question 4: Make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote. f(x) = x/( x − 3) Question 5: For each year t, the population of a forest of trees is represented by the function A(t) = 115(1.025)^t. In a neighboring forest, the population of the same type of tree is represented by the function B(t) = 82(1.029)^t. Which forest had a greater number of trees initially? By how many? Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 100 years? By how many? Question 6: sketch a graph of the piecewise function. Write the domain in interval notation. f (x) ={x + 1 if x < −2 {−2x − 3 if x ≥ −2 Question 7: Meat consumption in the United States can be broken into three categories: red meat, poultry, and fish. If fish makes up 4% less than one-quarter of poultry consumption, and red meat consumption is 18.2% higher than poultry consumption, what are the percentages of meat consumption?
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
Question 1: Find the dimensions of the rectangular corral
producing the greatest enclosed area split into
3 pens of the same size given 500 feet of fencing.
Question 2: Make a table to confirm the end behavior of the function. f (x) = x^2(1 − x)^2
Question 3: An oil slick is expanding as a circle. The radius of
the circle is increasing at the rate of 20 meters per
day. Express the area of the circle as a function of d,
the number of days elapsed.
Question 4: Make tables to show the behavior of the function near the vertical asymptote and reflecting the horizontal asymptote. f(x) = x/( x − 3)
Question 5: For each year t, the population of a forest of trees is represented by the function A(t) = 115(1.025)^t. In a neighboring forest, the population of the same type of tree is represented
by the function B(t) = 82(1.029)^t. Which forest had a greater number of trees initially? By how many? Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 100 years? By how many?
Question 6: sketch a graph of the piecewise function. Write the domain in interval notation. f (x) ={x + 1 if x < −2
{−2x − 3 if x ≥ −2
Question 7: Meat consumption in the United States can be
broken into three categories: red meat, poultry, and
fish. If fish makes up 4% less than one-quarter of
poultry consumption, and red meat consumption is
18.2% higher than poultry consumption, what are
the percentages of meat consumption?
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