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Home » Cry or Cease: Shut Down My Phone in Seconds with This Simple Hack! - Appcentric

Cry or Cease: Shut Down My Phone in Seconds with This Simple Hack! - Appcentric

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Thus, the number of such functions is equal to the number of real constants $ k $, which is uncountably infinite. But if we are to count **distinct functions**, and assuming only linear solutions are acceptable, the number is infinite.

📌 However, if the problem is interpreted as asking for the number of **continuous** solutions, then the only such functions are linear: $ f(x) = kx $, and there are infinitely many such functions (one for each real $ k $).

📌 Hence, the number of such functions is $ \boxed{\infty} $, assuming no further restrictions.

📌 Question: Let $ x, y, z $ be positive real numbers such that $ x + y + z = 3 $. Find the minimum value of

📌 \frac{x^2}{y + z} + \frac{y^2}{z + x} + \frac{z^2}{x + y}.

📌 Solution: We are to minimize

📌 under the constraint $ x + y + z = 3 $.

📌 Note that $ y + z = 3 - x $, $ z + x = 3 - y $, $ x + y = 3 - z $. So the expression becomes:

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Find intersection with \(y = 2x + 1\):
2x + 1 = -\frac{1}{2}x + \frac{11}{2}
Multiply both sides by 2:
4x + 2 = -x + 11
\Rightarrow 5x = 9 \Rightarrow x = \frac{9}{5}
y = 2 \cdot \frac{9}{5} + 1 = \frac{18}{5} + \frac{5}{5} = \frac{23}{5...
Thus, the closest point is \(\boxed{\left( \frac{9}{5}, \frac{23}{5} \...
Compute the maximum value of \((\sec x + \csc x)^2\) for \(0 < x < \fr...
Let \(f(x) = (\sec x + \csc x)^2 = \left(\frac{1}{\cos x} + \frac{1}{\...
Let \(u = \sin x + \cos x\). Then:

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For $ z = -15^\circ + 180^\circ k $:
$ k = 1 $: $ 165^\circ $
$ k = 2 $: $ 345^\circ $
$ k = 0 $: $ -15^\circ $ — invalid
$ k = 3 $: $ 525^\circ $ — too large
For $ z = 45^\circ + 180^\circ k $:
$ k = 0 $: $ 45^\circ $
$ k = 1 $: $ 225^\circ $
$ k = 2 $: $ 405^\circ $ — too large
Solutions: $ z = 45^\circ, 165^\circ, 225^\circ, 345^\circ $

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