Solving Inequalities: h(t) > 25

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Homework Help Overview

The problem involves the function h(t) = 30t - 5t² and seeks to determine the interval where h(t) is greater than 25. The context is centered around inequalities and their solutions.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to manipulate the inequality by rearranging and factoring, leading to a question about the implications of factoring out a negative. Other participants suggest alternative methods for handling the inequality.

Discussion Status

The discussion is ongoing, with participants providing guidance on the manipulation of the inequality and exploring different approaches. There is no explicit consensus yet, but the conversation is productive.

Contextual Notes

Participants are considering the effects of operations on inequalities, particularly the reversal of the inequality sign when multiplying by a negative number.

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Homework Statement



I have a function h(t) = 30t - 5t^2.
I need to find the interval for which h is > 25.

Homework Equations





The Attempt at a Solution



h(t) = 30t - 5t2 - 25 > 0
-5(t2 - 6t + 5) > 0
iff t2 - 6t + 5 > 0
Then the answer is t > 5 and t < 1.

But it is actually between those points.
Is it because I factored out a negative?
 
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In your last step, you get rid of the -5 by multiplying each side by -1/5.
This effectively reverses the inequality sign.

You may want to think of it another way...
You could add 5(t2 - 6t + 5) to both sides, which would give you
0 > 5(t2 - 6t + 5)
 
oicic ty
 
Not being a "texter," I'll assume that means "Oh, I see, I see. Thank you"

You're welcome!
(or, should I say, "yw"?)
 
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