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2 years ago

Inverse Property

Mathematics

1 answer:

luda_lava [24]2 years ago

6 0

Answer:

Inverse Property

When adding the additive

inverse to the number, the sum

is zero.

Step-by-step explanation:

When multiplying a number by

its reciprocal, the product is multiplicative inverse.

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The domain of the function is 0 ≤ t ≤ 3 and the greatest concentration of the medication is 2mg/L

<h3>The domain of the function</h3>

The equation of the function is given as:

$C(t) = \frac{-18t^2 + 54t}{t^2 + 7t + 10}$

Time can be 0 or greater but cannot be negative.

So, the domain of the function includes t ≥ 0

Set the function to 0 to determine the maximum value of t.

$\frac{-18t^2 + 54t}{t^2 + 7t + 10} = 0$

Cross multiply

$-18t^2 + 54t = 0$

Factor out -18t

-18t(t - 3) = 0

Divide both sides by -18t

t - 3 = 0

Add 3 to both sides

t = 3

This means that the maximum value of t is 3

Hence, the domain of the function is 0 ≤ t ≤ 3

<h3>The greatest concentration of the medication</h3>

From the graph of the function (see attachment), we have the maximum value to be;

C(t) = 2

Hence, the greatest concentration of the medication is 2mg/L