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Home » Divide the entire equation by 16 to get the standard form: - AMAZONAWS

Divide the entire equation by 16 to get the standard form: - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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f(x) = 1 + \frac{1}{\sin^2 x} + \frac{1}{\cos^2 x}
Let $ a = \sin^2 x $, $ b = \cos^2 x $, so $ a + b = 1 $, and $ a, b >...
f(x) = 1 + \frac{1}{a} + \frac{1}{b}
We now minimize $ \frac{1}{a} + \frac{1}{b} $ under the constraint $ a...
\frac{1}{a} + \frac{1}{b} \geq \frac{4}{a + b} = 4
Equality occurs when $ a = b = \frac{1}{2} $, i.e., when $ \sin^2 x =...
Substituting back:
f\left(\frac{\pi}{4}\right) = 1 + \frac{1}{\frac{1}{2}} + \frac{1}{\fr...
Thus, the minimum value of $ f(x) $ is:
Question: A science policy analyst is modeling the growth of renewable...

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t = rac{15 \pm \sqrt{15^2 - 4 imes 56}}{2} = rac{15 \pm \sqrt{225 -...
The solutions are \( t = 8 \) and \( t = 7 \).
#### 7, 8
A function \( f(x) = ax^2 + bx + c \) has a vertex at \( (2, -3) \) an...
The vertex form is \( f(x) = a(x-2)^2 - 3 \).
Substitute \( (1, 0) \): \( 0 = a(1-2)^2 - 3 \).
Simplifying, \( 0 = a(1) - 3 \), so \( a = 3 \).
Expand to standard form: \( f(x) = 3(x-2)^2 - 3 = 3(x^2 - 4x + 4) - 3...
Thus, \( f(x) = 3x^2 - 12x + 9 \), so \( a = 3 \), \( b = -12 \), \( c...
#### \( a = 3, b = -12, c = 9 \)

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