Tsunamis A tsunami is an ocean wave often caused by earthquakes on the ocean floor; these waves typically have long wavelengths, ranging from 150 to 1000 km. Imagine a tsunami traveling across the Pacific Ocean, which is the deepest ocean in the world, with an average depth of about 4000 m. Explain why the shallow-water velocity equation (Exercise 75) applies to tsunamis even though the actual depth of the water is large. What does the shallow-water equation say about the speed of a tsunami in the Pacific Ocean (use d = 4000 m)?
Table of contents
- 0. Functions7h 55m
- Introduction to Functions18m
- Piecewise Functions10m
- Properties of Functions9m
- Common Functions1h 8m
- Transformations5m
- Combining Functions27m
- Exponent rules32m
- Exponential Functions28m
- Logarithmic Functions24m
- Properties of Logarithms36m
- Exponential & Logarithmic Equations35m
- Introduction to Trigonometric Functions38m
- Graphs of Trigonometric Functions44m
- Trigonometric Identities47m
- Inverse Trigonometric Functions48m
- 1. Limits and Continuity2h 2m
- 2. Intro to Derivatives1h 33m
- 3. Techniques of Differentiation3h 18m
- 4. Applications of Derivatives2h 38m
- 5. Graphical Applications of Derivatives6h 2m
- 6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
- 7. Antiderivatives & Indefinite Integrals1h 26m
- 8. Definite Integrals4h 44m
- 9. Graphical Applications of Integrals2h 27m
- 10. Physics Applications of Integrals 3h 16m
- 11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 31m
- 12. Techniques of Integration7h 41m
- 13. Intro to Differential Equations2h 55m
- 14. Sequences & Series5h 36m
- 15. Power Series2h 19m
- 16. Parametric Equations & Polar Coordinates7h 58m
0. Functions
Common Functions
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
In the graph shown, identify the y–intercept & slope. Write the equation of this line in Slope-Intercept form.

A
y=32x+1
B
y=−32x+1
C
y=−2x+1
D
y=x+2
Verified step by step guidance1
First, identify the y-intercept of the line on the graph. The y-intercept is the point where the line crosses the y-axis. In this graph, the line crosses the y-axis at y = 1.
Next, determine the slope of the line. The slope is calculated as the change in y divided by the change in x between two points on the line. Choose two points on the line, such as (0, 1) and (3, -1).
Calculate the slope using the formula: slope = (y2 - y1) / (x2 - x1). Substitute the chosen points into the formula: slope = (-1 - 1) / (3 - 0) = -2/3.
Now, write the equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Substitute the slope and y-intercept into the equation: y = -2/3x + 1.
Verify the equation by checking if other points on the line satisfy the equation. For example, check if the point (3, -1) satisfies the equation: y = -2/3(3) + 1 = -2 + 1 = -1, which is correct.
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Common Functions practice set

