Changing the water levels of a lake

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Homework Help Overview

The discussion revolves around a problem related to the changing water levels of a lake, involving concepts of anti-derivatives and linear approximations. Participants are examining specific parts of the problem statement and their implications in the context of water depth and time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to interpret the meaning of specific mathematical expressions related to the problem, such as (w')^-1(1) and (w^{-1})'(1). There is also discussion on how to find the equation for a line using regression analysis.

Discussion Status

Some participants are seeking clarification on the problem statement and specific parts of the question. There is a focus on understanding the implications of certain mathematical terms in relation to the context of the lake and its water levels. Guidance has been offered regarding the interpretation of item iv, but no consensus has been reached on the overall problem.

Contextual Notes

There are indications of confusion regarding the problem statement due to the format of the attachment, which has led to requests for clearer information. Participants are also navigating the implications of the mathematical expressions in the context of the lake's water levels and related budgets.

Kingyou123
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Homework Statement


Attached problem

Homework Equations


Anti-derivatives, linear approx. F(a)=f(a)+F'(a)(x-a)

The Attempt at a Solution


I'm stuck on the first part, I think (w')^-1(1)= W which is 1. It seems too easy... and for part c I'm having trouble finding the equation for the line. I figured that if I graph it on my calculator and use a regression test to find the equation
 

Attachments

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Last edited:
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The attachment is way too zoomed out for me to read. Can you type the problem statement into the forum? That would help... :smile:
 
berkeman said:
The attachment is way too zoomed out for me to read. Can you type the problem statement into the forum? That would help... :smile:
updated it, sorry for that.
 
Is your question just the part that is checked: "(b) Explain what item iv means in terms of the city, lake, and IES budget"?

Item iv is "(w^{-1})'(1)". Since w(t) is the depth of water in the lake at time t, w^{-1}(x) is the time at which the level of the lake is x. Then (w^{-1})'(x) is the rate at which time for the water to decrease amount x is changing.
 
HallsofIvy said:
Is your question just the part that is checked: "(b) Explain what item iv means in terms of the city, lake, and IES budget"?

Item iv is "(w^{-1})'(1)". Since w(t) is the depth of water in the lake at time t, w^{-1}(x) is the time at which the level of the lake is x. Then (w^{-1})'(x) is the rate at which time for the water to decrease amount x is changing.
My question is on part a, I'm confused what(w')^-1(1) is. Thank you for help with part B :)
 
Last edited:

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