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Home » Raven Titans Take Over: Why This Team Is Taking Over the Gaming Scene! - Abbey Badges

Raven Titans Take Over: Why This Team Is Taking Over the Gaming Scene! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Thus, the smallest three-digit number divisible by both 9 and 12 is \(\boxed{108}\).A venture capitalist invests $500,000 in a clean technology startup that promises a 12% annual return compounded quarterly. If all returns are reinvested, how much will the investment be worth after 3 years?

📌 The quarterly interest rate is 12% / 4 = 0.03.

📌 The number of compounding periods is 3 years × 4 = 12.

📌 Using the compound interest formula: A = P(1 + r)^n = 500,000 × (1 + 0.03)^12.

📌 A ≈ 500,000 × 1.42576 = 712,880.

📌 The investment will be worth approximately $712,880 after 3 years.

📌 #### 712880

📌 A mining engineer is designing a cylindrical shaft with a diameter of 6 meters and a depth of 120 meters. If the rock density is 2.8 metric tons per cubic meter, how many metric tons of rock must be removed to create the shaft?

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Original area = 30m * 20m = 600 square meters
New dimensions: length = \( 30 + 2x \), width = \( 20 + 2x \)
New area = (30 + 2x)(20 + 2x) = 1,056 square meters
Expanding: \( 600 + 60x + 40x + 4x^2 = 1,056 \)
Simplifying: \( 4x^2 + 100x + 600 = 1,056 \)
\( 4x^2 + 100x - 456 = 0 \)
Dividing by 4: \( x^2 + 25x - 114 = 0 \)
Solving quadratic equation using the quadratic formula:
\( x = \frac{-25 \pm \sqrt{25^2 + 4 \times 114}}{2} \)
\( x = \frac{-25 \pm \sqrt{625 + 456}}{2} \)

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