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Home » Find the number of integer solutions to the inequality \( |2x - 5| \leq 7 \). - Silent Sales Machine

Find the number of integer solutions to the inequality \( |2x - 5| \leq 7 \). - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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\sec \theta + \csc \theta = \frac{1}{\cos \theta} + \frac{1}{\sin \the...
The square is:
Using the identity \((\sin \theta + \cos \theta)^2 = 1 + \sin 2\theta\...
Let \(y = \sin 2\theta\), where \(y \in (0, 1]\). Define:
f(y) = \frac{4(1 + y)}{y^2}.
To find the maximum of \(f(y)\) on \( (0,1] \), take the derivative:
f'(y) = 4 \cdot \frac{(1)(y^2) - (1 + y)(2y)}{y^4} = 4 \cdot \frac{y^2...
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\frac{1}{R_{\text{total}}} = \frac{1}{12} + \frac{1}{6} + \frac{1}{4}
Find a common denominator (12):
\frac{1}{R_{\text{total}}} = \frac{1}{12} + \frac{2}{12} + \frac{3}{12...
Invert to solve:
R_{\text{total}} = 2 \, \Omega
Dr. Rivera, a science administrator, is reviewing a research grant pro...
Total grant: $1,200,000
Personnel: $600,000, Equipment: $300,000 → Remaining: $1,200,000 - $60...
Next year (year 2), equipment costs increase by 10%:
New equipment cost = $300,000 × 1.10 = $330,000

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