Directions: Read and understand each situation. Then, give the required mathematical
model.
1. The sum of two numbers is 25. Represent their product as a function of one of them.
2. Monique sells disposable protective face masks made of local textiles for P 12.00 each. Define a
function C(n) to represent the cost of buying n pieces.
3. The length of a rectangular lot is twice its width. Express its perimeter as a function of its width.
4. Working at a constant rate, AJ can finish painting a wall in three hours. Give an appropriate mathematical model for the part of the job she finishes after working for hours?
5. The Mathematics Club in your school raises fund by selling palitaw in tubs. Each tub costs P 35.00, but if you will buy at least three tubs, you can get each at P 30.00. Use a piecewise function to represent the cost of buying tubs of palitaw.
no ideas on any of these?
Is this just a homework dump?
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1. The sum of two numbers is 25. Represent their product as a function of one of them.
Let's assume the two numbers are x and y. The problem states that their sum is 25, so we can write an equation as:
x + y = 25
To represent their product as a function of one of them, let's express the second number (y) in terms of the first number (x):
y = 25 - x
Now we can define the product of the two numbers as a function of x:
f(x) = x * (25 - x)
2. Monique sells disposable protective face masks made of local textiles for P 12.00 each. Define a function C(n) to represent the cost of buying n pieces.
The cost of buying n pieces of disposable face masks can be represented as a function C(n), where n represents the number of masks bought. Since each mask costs P 12.00, the function C(n) can be defined as:
C(n) = 12 * n
3. The length of a rectangular lot is twice its width. Express its perimeter as a function of its width.
Let's assume the width of the rectangular lot is w. According to the problem, the length is twice the width, so the length can be expressed as:
l = 2w
The perimeter of a rectangle is given by the formula: perimeter = 2(length + width). Substitute the values of length and width in terms of w:
perimeter = 2(2w + w) = 2(3w) = 6w
Therefore, the perimeter of the rectangular lot can be represented as a function of its width (w):
P(w) = 6w
4. Working at a constant rate, AJ can finish painting a wall in three hours. Give an appropriate mathematical model for the part of the job she finishes after working for hours.
If AJ can finish painting the wall in three hours, it means she completes 1/3 of the job in one hour because 1 hour is 1/3 of three hours.
Let J represent the whole job. Then, the part of the job AJ finishes after working for x hours can be represented by the function:
f(x) = (1/3) * x
5. The Mathematics Club in your school raises funds by selling palitaw in tubs. Each tub costs P 35.00, but if you will buy at least three tubs, you can get each at P 30.00. Use a piecewise function to represent the cost of buying tubs of palitaw.
Let's define the piecewise function C(n) to represent the cost of buying n tubs of palitaw.
C(n) =
P 35.00 if n < 3
(P 30.00) * n if n >= 3
This represents that if the number of tubs purchased is less than 3, the cost per tub is P 35.00. But if the number of tubs purchased is 3 or more, the cost per tub is P 30.00 and is multiplied by the number of tubs bought.