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Home » Stop Struggling – GoodMoodDotCom Teaches You How to Keep Your Mood Golden Forever! - Groen Casting

Stop Struggling – GoodMoodDotCom Teaches You How to Keep Your Mood Golden Forever! - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 First, express \( z(t) \) in terms of cosine and sine:

📌 z(t) = 4(\cos \omega t + i\sin \omega t) + 3(\cos \omega t - i\sin \omega t) = (4 + 3)\cos \omega t + i(4 - 3)\sin \omega t

📌 z(t) = 7\cos \omega t + i\sin \omega t

📌 Now compute the magnitude:

📌 |z(t)| = \sqrt{(7\cos \omega t)^2 + (\sin \omega t)^2} = \sqrt{49\cos^2 \omega t + \sin^2 \omega t}

📌 = \sqrt{48\cos^2 \omega t + (\cos^2 \omega t + \sin^2 \omega t)} = \sqrt{48\cos^2 \omega t + 1}

📌 The maximum occurs when \( \cos^2 \omega t = 1 \):

📌 |z(t)|_{\text{max}} = \sqrt{48 + 1} = \sqrt{49} = 7

🔥 Popular Posts

+ \sec^2 x + \csc^2 x = 5 + rac{1}{\cos^2 x} + rac{1}{\sin^2 x}
Write as:
+ rac{\sin^2 x + \cos^2 x}{\sin^2 x \cos^2 x} = 5 + rac{1}{\sin^2 x...
But \(\sin^2 x \cos^2 x = rac{1}{4} \sin^2 2x\), so:
= 5 + rac{4}{\sin^2 2x}
Minimum occurs when \(\sin^2 2x\) is maximized, i.e., \(\sin^2 2x = 1\...
Then value is \(5 + 4 = 9\)
oxed{9}
Question: Find the range of the function \(f(x) = rac{2\sin x + 3}{\s...
e -2\) (which is always true since \(\sin x \in [-1,1]\)).

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Probability all 15 fail: 0.9¹⁵ ≈ <<0.9^15=0.20589>>0.20589.
So, probability at least one succeeds: 1 – 0.20589 = <<1-0.20589=0.794...
#### 0.794
Alex determines that a suspect’s DNA is in 1 out of 2,000 individuals...
Expected matches: 15,000 × (1/2000) = <<15000/2000=7.5>>7.5.
For 350 targets: 350 × (1/2000) = <<350/2000=0.175>>0.175.
Since partial matches aren’t acceptable, but statistically expected va...
#### 0.175
Dr. Elena reviews a case where two DNA profiles match across 8 loci. I...
Probability of matching one locus: 1 – 0.05 = 0.95.

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