Solving Inequalities: h(t) > 25

In summary, the function h(t) = 30t - 5t^2 has an interval where it is greater than 25, which is between t = 1 and t = 5. This is because when solving for h(t) > 25, the inequality sign is reversed when multiplying by a negative number. Adding 5(t^2 - 6t + 5) to both sides can also help understand the solution.
  • #1
zeion
466
1

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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  • #2
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)
 
  • #3
oicic ty
 
  • #4
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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What does "h(t) > 25" mean?

"h(t) > 25" is an inequality statement which means that the value of h(t) is greater than 25. In other words, the quantity represented by h(t) is larger than 25.

How do you solve "h(t) > 25"?

To solve "h(t) > 25", you need to isolate the variable h(t) on one side of the inequality symbol and the constant value of 25 on the other side. This can be done by using algebraic operations such as addition, subtraction, multiplication, and division.

Can you graph "h(t) > 25"?

Yes, "h(t) > 25" can be graphed on a number line or a coordinate plane. The graph will show all the values of h(t) that are greater than 25 as a shaded region or line.

What is the solution set for "h(t) > 25"?

The solution set for "h(t) > 25" is all the possible values of h(t) that satisfy the inequality. This can be represented as an interval or a set of numbers, depending on the form of the solution.

Can the solution for "h(t) > 25" be a negative number?

Yes, the solution for "h(t) > 25" can include negative numbers. As long as the value of h(t) is greater than 25, it can be any real number, including negative numbers.

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