WEEK 2: Think of a personal or professional situation where you would need to (or want to) use algebra. In your post, state the situation and create an equation to help you solve it. Also, include the solution. You can use the example provided in the video to guide you, but you need to create an original situation, equation and solution.
The projectile motion equation is s(t)=-16t^2+vt+h where s(t) represents the distance or height of an object at time t, v represents the initial speed of the object in ft/s, and h is the initial height of the object, measured in feet.
If an object is starting at rest, then v=0 (such as for a penny being dropped from a building). If the object is starting from the ground, h=0. The baseball or cannonball situations, each have an initial velocity. For example, the initial velocity of the baseball is based on the speed at which the ball comes at you (the speed of the pitch).
Come up with a situation that you can model with this equation. Describe the situation, and tell us what v and h are. Fill in the values so that you have a quadratic equation. If you do research to find initial velocities, include the links to the websites where you found that information. If you would like to make up your own numbers as well, you can (be creative)!
Once you have your equation, find the maximum height as well as the time it takes to reach that maximum. Then use your equation to find when the object hits the ground (i.e. the x-intercepts).
Finally, use those three points as well as the initial height to sketch a graph. You can take a photo of it and include the image, or use an online graphing calculator and take a screenshot if that is easier.
A cab company charges a flat fee boarding rate in addition to a per mile rate. Using your own experience or some Internet research:
Write a function that represents a cab company’s rate taking into account the initial flat boarding rate and the per mile rate.
Based on the function you created, how much would it cost to go from your home to nearest grocery store in this cab?
Would you suspect that this function could be modeled by a linear, a quadratic function, or another type of function?
In order for a film camera with a fixed focal length F to focus on anobject located a distance x from the lens, the lens must be a distance yfrom the film. F, y, and x are related as follows:
Now suppose a camera has a lens with focal length F = 65.
- Explain what happens to the distance between the lens and the film as the object moves far away from the lens. When an object far away (x is near infinity), what is the internal distance from the lens and film?
- Consider the opposite. Explain what happens to the distance between the lens and the film as the object moves closer and closer to the lens. Is there a distance from the lens at which you can no longer focus?
- In general, why is it not possible to cross a vertical asymptote?
What is focal length, and how does it work?
In photography, fixed focal length means that the focal length is not adjustable. Focal length determines the magnification and angle of the view of your scene. A longer focal length increases the magnification and decreases the angle of view, while a shorter focal length does the opposite.
With a fixed focal length, photographers are unable to zoom in and out on a particular subject. In order to zoom they would either have to change their distance to the object or change the lens. Not being able to easily zoom in on a subject might seem like a huge disadvantage, but such lenses are credited with being able to produce much higher quality pictures in controlled settings.
While the photographer cannot zoom while using a fixed focal length lens,he can still adjust the focus on the object. When the photographer twists the focusing ring, the location of the lens inside the camera adjusts.This change in distance from the lens to the film inside the camera is governed by a rational equation.
Hint: These websites may help with your understanding of this concept
Next, do some research on important numbers in mathematics. Choose one that is interesting to you (it can be on e or pi or a different number)
In your post, share with us what you have found out about the number, for example, its history, some trivial facts about the number, and/or how it is applied.
To get you started in your research, below are some sources you can use.
answer the following questions based on your experiences within the course:
- Did this course meet your expectations?
- How do you feel about your progress in the course?
- What skills do you think this course has helped you to develop, and do you see those skills being beneficial in other courses, your daily life or in your career?
- What topic did you find most interesting and why?
- What advice would you give to a student starting the class next term?