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Explain the role of exponents in scientific notation for large and small numbers.
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Positive exponents represent large numbers (e.g., 10^9 for a billion), while negative exponents represent small numbers (e.g., 10^-9 for a billionth).
What is a direct relationship in the context of ultrasound physics variables?
A direct relationship means that two variables increase or decrease together.
Describe the relationship between frequency (F) and period (P) in ultrasound physics.
Frequency and period are inversely related; when frequency increases, the period decreases and vice versa.
What does the formula λ = C / F represent in ultrasound physics?
The formula represents the relationship between wavelength (λ), propagation speed (C), and frequency (F) in ultrasound.
What should be included in a practical formula sheet for ultrasound physics?
Formulas, definitions of each variable and units, relationships between variables, and rearrangements for solving different variables.
How does one convert between fractions and decimals using long division?
To convert, divide the numerator by the denominator using long division to get a decimal representation.
Why is understanding variable relationships within formulas important for ultrasound physics?
It is crucial for solving real-world problems, understanding how changing one variable affects others, and applying concepts in practical scenarios.
Given the formula A = B / C, what happens to A if B increases while C stays constant?
If B increases while C stays constant, A will increase.
What is the significance of the zero exponent in mathematics?
Any number raised to the power of zero equals one.
Given the formula A = B / C, what happens to A if C increases while B stays constant?
If C increases while B stays constant, A will decrease.
What type of relationship exists between power (P) and intensity (I) in ultrasound?
Power and intensity have a direct relationship; as power increases, intensity also increases.
Explain how to solve for B using the formula A = B / C when A = 10 and C = 2.
Multiply both sides by C: C * A = B. Therefore, B = 10 * 2 = 20.
What mathematical principle is used for simple formula manipulation in algebra?
The principle is to perform the same operation on both sides of the equation to isolate the desired variable.
Describe the use of the X-axis in graphing data.
The X-axis typically represents the horizontal line and is used to plot variables like time and distance.
Describe the use of the Y-axis in graphing data.
The Y-axis typically represents the vertical line and is used to plot variables like velocity and amplitude.
What is a reciprocal relationship in the context of variable multiplication?
A reciprocal relationship means that the product of the factors equals 1.
What is an inverse relationship in the context of ultrasound physics variables?
An inverse relationship means that when one variable increases, the other variable decreases.
How can you solve for propagation speed (C) using the formula λ = C / F?
You can rearrange the formula to C = λ * F.
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