1 / 11

Olympic National Park, Washington

Photo by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. 4.6: Related Rates. Olympic National Park, Washington. Photo by Vickie Kelly, 2007. Greg Kelly, Hanford High School, Richland, Washington. 4.6: Related Rates. Olympic National Park, Washington.

shenna
Télécharger la présentation

Olympic National Park, Washington

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Photo by Vickie Kelly, 2007 Greg Kelly, Hanford High School, Richland, Washington 4.6: Related Rates Olympic National Park, Washington

  2. Photo by Vickie Kelly, 2007 Greg Kelly, Hanford High School, Richland, Washington 4.6: Related Rates Olympic National Park, Washington

  3. Photo by Vickie Kelly, 2007 Greg Kelly, Hanford High School, Richland, Washington 4.6: Related Rates Olympic National Park, Washington

  4. Consider a sphere of radius 10cm. The volume would change by approximately . First, a review problem: If the radius changes 0.1cm (a very small amount) how much does the volume change?

  5. The sphere is growing at a rate of . Note: This is an exact answer, not an approximation like we got with the differential problems. Now, suppose that the radius is changing at an instantaneous rate of 0.1 cm/sec. (Possible if the sphere is a soap bubble or a balloon.)

  6. Find Water is draining from a cylindrical tank at 3 liters/second. How fast is the surface dropping? (We need a formula to relate V and h. ) (r is a constant.)

  7. Steps for Related Rates Problems: 1. Draw a picture (sketch). 2. Write down known information. 3. Write down what you are looking for. 4. Write an equation to relate the variables. 5. Differentiate both sides with respect to t. 6. Evaluate.

  8. Hot Air Balloon Problem: Given: How fast is the balloon rising? Find

  9. Hot Air Balloon Problem: Given: How fast is the balloon rising? Find

  10. Truck Problem: Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr. How fast is the distance between the trucks changing 6 minutes later? B A

  11. Truck Problem: Truck A travels east at 40 mi/hr. Truck B travels north at 30 mi/hr. How fast is the distance between the trucks changing 6 minutes later? B A p

More Related