Monday, May 2, 2016
Monday, March 21, 2016
This Blog be Spinnin'
3.18 Blog Post
- Identify the difference between rotating around a vertical line and a horizontal line.
- When rotating around the x-axis, the important variable is y because it becomes the radius of the figure being formed. When rotating around the y-axis, the important variable is x because it becomes the radius of the former figure.
- What is the difference between creating a washer and a disk?
- When a washer is created, the two radii must be subtracted from each other in order to find the volume of the the existing figure. When a disk is created, there is only one radius for the whole figure so it is not necessary to subtract.
- Identify two examples that use rotating about a vertical line and a horizontal line.
Example #1:
Example #2:
Thursday, February 25, 2016
Tuesday, January 12, 2016
Blog Post 7: Get Optimized
1. What is Optimization?
Optimization involves using the first derivative to find a maximum or minimum. Several optimization problems are word problems, so there are multiple equations involved. In order to find what you are looking for you will have to pick a variable to solve for, then plug the equation into one of the other equations. After getting all the variables to be the same and in one equation, you can then find the first derivative and solve for the missing variable, then plug that value in to find the variable you solved for first.
2. Find the point on the line y = 2x + 3 that is closest to the origin.
In this optimization problem, there are two equations involved. the original equation of y = 2x +3 and the distance formula. Since y is already solved for, you plug it into the distance formula. This is so the only variable in the formula now is x. This allows you to solve for x. To solve for x you must square everything in order to eliminate the radical. Once the radical is eliminated you can find the first derivative using the chain rule and the power rule. Once you've found the first derivative you need to set it equal to zero then solve for x. this gives you the x - coordinate for the point you are looking for. Then, in order to find the y- coordinate you simply plug the x value you just found into y = 2x + 3. This will give you your y - coordinate and then you have found the point on y = 2x + 3 that is closest to the origin.
3.
Optimization involves using the first derivative to find a maximum or minimum. Several optimization problems are word problems, so there are multiple equations involved. In order to find what you are looking for you will have to pick a variable to solve for, then plug the equation into one of the other equations. After getting all the variables to be the same and in one equation, you can then find the first derivative and solve for the missing variable, then plug that value in to find the variable you solved for first.
2. Find the point on the line y = 2x + 3 that is closest to the origin.
In this optimization problem, there are two equations involved. the original equation of y = 2x +3 and the distance formula. Since y is already solved for, you plug it into the distance formula. This is so the only variable in the formula now is x. This allows you to solve for x. To solve for x you must square everything in order to eliminate the radical. Once the radical is eliminated you can find the first derivative using the chain rule and the power rule. Once you've found the first derivative you need to set it equal to zero then solve for x. this gives you the x - coordinate for the point you are looking for. Then, in order to find the y- coordinate you simply plug the x value you just found into y = 2x + 3. This will give you your y - coordinate and then you have found the point on y = 2x + 3 that is closest to the origin.
3.
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