kukerules
Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

The area labeled B is 9 times the area labeled A. Express b in terms of a.
b=_____?

The Area Labeled B Is 9 Times The Area Labeled A Express B In Terms Of A B class=

Sagot :

leena

Hi there!

For the graph on the left, we know that the area A is equal to:
[tex]A = \int\limits^a_0 {e^x} \, dx[/tex]

Area 'B' is 9 times this area, so:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx[/tex]

We can evaluate the integral:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx \\\\B = 9 \cdot e^x \left \| a}} \atop {0}} \right. \\\\B = 9 (e^a - 1)[/tex]

We also know that:
[tex]B = \int\limits^b_0 {e^x} \, dx[/tex]

Evaluate:

[tex]B = e^x \left \| b}} \atop {0}} \right. = e^b - 1[/tex]

Set the two equations for 'B' equal:
[tex]e^b - 1 = 9(e^a - 1)\\\\e^b - 1 = 9e^a - 9 \\\\e^b = 9e^a - 8[/tex]

Take the natural log of both sides:
[tex]ln(e^b) = ln(9e^a - 8)\\\\\boxed{b = ln(9e^a - 8)}[/tex]

Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.