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Home » Use the Pythagorean theorem to compute the diagonal \(d\) of the rectangle: - Silent Sales Machine

Use the Pythagorean theorem to compute the diagonal \(d\) of the rectangle: - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 So, $ A = 40(1.15)^5 $.

📌 Calculating: $ 1.15^5 \approx 2.011357 $, so $ A \approx 40 \times 2.011357 = 80.45428 $.

📌 Rounding to two decimal places, the amplitude is approximately 80.45 units.

📌 #### 80.45

📌 A theoretical physicist explains that a certain virtual particle fluctuates in energy according to the function $ E(t) = 3\sin(2\pi t) + 4 $, where $ t $ is in nanoseconds. What is the average energy of the particle over one full cycle?

📌 The function $ E(t) = 3\sin(2\pi t) + 4 $ has a sinusoidal component with period $ \frac{2\pi}{2\pi} = 1 $ nanosecond.

📌 The average value of $ \sin(2\pi t) $ over one full cycle is 0, so the average of $ 3\sin(2\pi t) $ is 0.

📌 Thus, the average energy is $ 0 + 4 = 4 $.

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The \( n \)-th term is given by \( a_n = a + (n-1)d \).
Use \( n = 15 \): \( a_{15} = 3 + (15-1) \times 4 \).
Simplify: \( a_{15} = 3 + 14 \times 4 = 3 + 56 = 59 \).
Therefore, the 15th term is 59.
#### 59
The ratio of the number of apples to oranges in a basket is 5:3. If th...
Let the number of oranges be \( x \). The ratio equation is \( \frac{4...
Cross-multiply: \( 5x = 3 \times 40 \).
Solve for \( x \): \( 5x = 120 \).
Divide by 5: \( x = 24 \).

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