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Home » Acceleration is defined as the change in velocity divided by the time taken: - ToelettAPP

Acceleration is defined as the change in velocity divided by the time taken: - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Evaluate \( g(x) \) at these critical points:

📌 At \( x = \frac{2}{\sqrt{3}} \):

📌 g\left(\frac{2}{\sqrt{3}}\right) = \left(\frac{8}{3\sqrt{3}}\right) - 4\left(\frac{2}{\sqrt{3}}\right) + 2 = \frac{8 - 24 + 6\sqrt{3}}{3\sqrt{3}} = \frac{-16 + 6\sqrt{3}}{3\sqrt{3}}

📌 This is negative, and at \( x = -\frac{2}{\sqrt{3}} \), it's positive. Since \( g(1) = -1 \) and \( g(2) = 2 \), there is a root in \( (1, 2) \), and by symmetry and behavior, another real root exists (confirm via intermediate value theorem or graphing).

📌 Alternatively, use cubic formula or numerical solvers:

📌 Using approximation or a calculator, the real roots are approximately:

📌 One root near \( x \approx 0.542 \)

📌 One root near \( x \approx 1.532 \)

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Suppose the question was:
What two-digit positive integer is three less than a multiple of 7 and...
Then $ x + 3 $ divisible by LCM(7,8)=56 → $ x = 56k - 3 $
Try $ k=1 $: $ x = 53 $ — two-digit!
$ k=2 $: $ 112 - 3 = 109 $ — too big.
is two-digit.
But not 9.
But if the original had and only for 7,8 — but says 7,8,9.
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