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Home » But in math problems, sometimes they use values that work. - Midis

But in math problems, sometimes they use values that work. - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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🔥 Popular Posts

where $ t $ is time in years. Find the time $ t $ at which the rate of...
We are given the logistic growth function:
To find the time at which the rate of change is maximized, we compute...
Let’s denote the denominator as $ D(t) = 1 + 9e^{-0.5t} $, so:
P(t) = \frac{1000}{D(t)} \Rightarrow P'(t) = -1000 \cdot \frac{D'(t)}{...
Now compute $ D'(t) $:
D(t) = 1 + 9e^{-0.5t} \Rightarrow D'(t) = 9 \cdot (-0.5)e^{-0.5t} = -4...
P'(t) = -1000 \cdot \frac{-4.5e^{-0.5t}}{(1 + 9e^{-0.5t})^2} = \frac{4...
To find the maximum of $ P'(t) $, we define:
f(t) = \frac{e^{-0.5t}}{(1 + 9e^{-0.5t})^2}.

📝 Recent Posts

Solution: Given $ x + y = 4.5 $, multiplying by 5 yields $ 5x + 5y = 5...
Question: Rationalize the denominator of $ rac{\sqrt{7} + \sqrt{3}}{\...
Solution: Multiply numerator and denominator by $ \sqrt{7} + \sqrt{3}...
rac{(\sqrt{7} + \sqrt{3})^2}{(\sqrt{7})^2 - (\sqrt{3})^2} = rac{7 + 2...
The rationalized form is $ oxed{rac{5 + \sqrt{21}}{2}} $.
Solution: Recognize it as a difference of cubes: $ (2a)^3 - (3b)^3 = 8...
2a \cdot 4a^2 + 2a \cdot 6ab + 2a \cdot 9b^2 - 3b \cdot 4a^2 - 3b \cdo...
Combine like terms: $ 8a^3 - 27b^3 $. The expanded form is $ oxed{8a^...
Question: Two biotechnology strains grow according to $ y = 3x + 2 $ a...
Solution: Set $ 3x + 2 = -2x + 12 $. Solve: $ 5x = 10 $, so $ x = 2 $....

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