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Home » Future value = 1000(1 + 0.05)³ = 1000(1.157625) ≈ 1157.63. - Get link 4share

Future value = 1000(1 + 0.05)³ = 1000(1.157625) ≈ 1157.63. - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Start by isolating \(x\) in the equation \(3x - 7 = 2x + 5\).

📌 Subtract \(2x\) from both sides:

📌 Thus, the value of \(x\) is:

📌 \]Question: Find the vertex of the parabola modeling the growth rate of a climate-dependent species, given by $ y = -2x^2 + 8x - 5 $.

📌 Solution: The vertex form of a parabola $ y = ax^2 + bx + c $ has its vertex at $ x = -\frac{b}{2a} $. Here, $ a = -2 $, $ b = 8 $, so $ x = -\frac{8}{2(-2)} = 2 $. Substituting $ x = 2 $ into the equation: $ y = -2(2)^2 + 8(2) - 5 = -8 + 16 - 5 = 3 $. Thus, the vertex is at $ (2, 3) $. \boxed{(2, 3)}

📌 Question: Solve for $ v $ in the equation $ \frac{1}{2}mv^2 = \frac{3}{4}kT $, where $ m $ is mass, $ k $ is Boltzmann’s constant, and $ T $ is temperature, to express $ v $ in terms of $ k $, $ T $, and $ m $.

📌 Solution: Multiply both sides by 2: $ mv^2 = \frac{3}{2}kT $. Divide by $ m $: $ v^2 = \frac{3kT}{2m} $. Take the square root: $ v = \sqrt{\frac{3kT}{2m}} $. \boxed{v = \sqrt{\dfrac{3kT}{2m}}}

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