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A function is a rule that has exactly 1 output for each possible input.
In the function \(y=6x+4\), \(x\) is the input and \(y\) is the output. When \(x\) is 5, \(y\) has one value, 34.
\(\begin{align} y&=6x+4\\ y&=6(5)+4 \\ y&=34 \\ \end{align} \)
An independent variable represents the input of a function.
For example, suppose someone needs to buy 20 pieces of fruit and decides to buy some apples and bananas. If they select the number of apples first, the equation \(b=20-a\) shows the number of bananas they can buy. The number of apples is the independent variable because any number can be chosen for it.
A radius is a line segment that goes from the center of a circle to any point on the circle. The length of this segment is also called the radius. Every radius of a circle is the same length.
For example, \(r\) is the radius of this circle with center \(O\).
From an earlier course.
A sphere is a three-dimensional figure where any cross-section is a circle.
From an earlier course.
Volume is the number of cubic units that fill a three-dimensional region with no gaps or overlaps.
This rectangular prism has 3 layers that are each 20 units3. So, the volume of the prism is 60 units3.
From an earlier course.