True or false
Some rational numbers are integers.
The radius of a circle and its circumference.
Direct or inverse
f(x) 0.08x^3 + 0.6x + 2.8
Rational function, another polynomial function
Quadratic function
True. Some rational numbers are integers. An integer is a rational number because it can be expressed as a ratio of two whole numbers. For example, the integer 5 can be written as 5/1, where both 5 and 1 are whole numbers.
The radius of a circle and its circumference have a direct relationship. The circumference of a circle is directly proportional to its radius. As the radius increases, the circumference also increases by a constant factor.
The function f(x) = 0.08x^3 + 0.6x + 2.8 is a polynomial function. It is not a rational function because a rational function is defined as the ratio of two polynomial functions.
A quadratic function is a special type of polynomial function where the highest power of x is 2. The function f(x) = 0.08x^3 + 0.6x + 2.8 is not a quadratic function because it has a term with an exponent greater than 2 (the x^3 term).
To determine whether the statement "Some rational numbers are integers" is true or false, we need to understand the definitions of rational numbers and integers.
Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. Integers, on the other hand, are positive or negative whole numbers (including zero) without any fractional or decimal parts.
Since integers can be expressed as the ratio of themselves and 1 (e.g., 3 = 3/1, -4 = -4/1), it is true that some rational numbers are integers. For example, the rational number 5 can be expressed as 5/1.
Regarding the question about the radius of a circle and its circumference, this refers to the relationship between these two properties.
The radius of a circle is the distance from the center of the circle to any point on its circumference. It is denoted by the symbol "r". The circumference, on the other hand, is the distance around the circle. It is denoted by the symbol "C".
The relationship between the radius and the circumference of a circle is an example of a direct proportion. This means that as the radius increases, the circumference also increases, and as the radius decreases, the circumference decreases proportionally. The formula to calculate the circumference of a circle is C = 2πr, where π (pi) is a mathematical constant approximately equal to 3.14159.
Now, moving on to the function f(x) = 0.08x^3 + 0.6x + 2.8. To determine the type of function, we can analyze the highest power of x in the equation.
In this case, the highest power of x is 3 (x^3 term), which means that the function is a cubic function or a polynomial function of degree 3. A polynomial function is a function that consists of terms involving non-negative integer powers of x. Therefore, f(x) = 0.08x^3 + 0.6x + 2.8 is both a rational function (since it is a ratio of polynomials) and a polynomial function (since it is a function of degree 3).
Lastly, a quadratic function is a polynomial function of degree 2. It can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a is not equal to zero. The provided function f(x) = 0.08x^3 + 0.6x + 2.8 is not a quadratic function since the highest power of x is 3, not 2.