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Think about the formulas formulas you know. What is their purpose? How are they better from written statements?
See solution.
We are asked to describe why formulas are important in math and science. First, note that that we learned and used many formulas at this point. Let's refresh our memory.
When we want to know the temperature in degrees Fahrenheit, we substitute the temperature in degrees Celsius and evaluate the expression on the right. See that the two temperatures are bonded
by this equation. If one temperature changes, so does the other.
Earlier we also learned about the Distance Formula. We use this formula when we calculate the distance d between two points on the coordinate plane, (x_1,y_1) and (x_2,y_2).
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
The coordinates of the points are everything we need to find the distance — there is no need to plot the points on the coordinate plane. This makes it easy to use.
In this chapter we also learned about the formula for the volume of a sphere.
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V = 4/3π r^3 |
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The volume of a sphere V with radius r is four-thirds the product of π and the radius cubed. |
See that the words used to describe the formula take a lot more space to write than the formula itself. This makes it very compact.
To summarize, formulas are important because they express information using mathematical symbols. What is more, they are more compact than word statements, they are ready to use, and they show relationships between variables.
