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Home » حيث \( (h, k) = (2, -3) \). - Ready Digital AB

حيث \( (h, k) = (2, -3) \). - Ready Digital AB

📅 March 7, 2026 👤 scraface

Mar 07, 2026

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📌 h(-1) = 4(-1)^5 - 3(-1)^4 + 2(-1)^3 - (-1) + 8

📌 = 4(-1) - 3(1) + 2(-1) + 1 + 8 = -4 - 3 - 2 + 1 + 8

📌 = (-4 - 3) = -7; \quad (-7 - 2) = -9; \quad (-9 + 1) = -8; \quad (-8 + 8) = 0

📌 Thus, \( h(-1) = \boxed{0} \).Question: An oceanographer measures the angle of elevation to the top of a lighthouse from a boat as $ 45^\circ $. If the boat is 100 meters from the base of the lighthouse, what is the height of the lighthouse?

📌 Solution: The angle of elevation is $ 45^\circ $, and the adjacent side (distance from the boat to the base) is 100 meters. Using $ \tan(45^\circ) = \frac{\text{opposite}}{\text{adjacent}} $, we have $ 1 = \frac{h}{100} $. Solving gives $ h = 100 $ meters. Thus, the height of the lighthouse is $\boxed{100}$ meters.

📌 Question: A spherical buoy used by an oceanographer has a radius of $ 2x $, while a hemisphere-shaped sensor has a radius of $ 3x $. What is the ratio of their volumes?

📌 Solution: The volume of the sphere is $ \frac{4}{3}\pi (2x)^3 = \frac{32}{3}\pi x^3 $. The volume of the hemisphere is $ \frac{2}{3}\pi (3x)^3 = 18\pi x^3 $. The ratio is $ \frac{32/3}{18} = \frac{32}{54} = \frac{16}{27} $. The ratio of their volumes is $\boxed{\dfrac{16}{27}}$.

📌 Question: A right triangle formed by ocean currents has sides of length 9 km, 12 km, and 15 km. What is the length of the shortest altitude?

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\binom{16}{5}
The number of favorable outcomes (3 red and 2 blue) is:
\binom{7}{3} \cdot \binom{9}{2}
Compute the values:
\binom{7}{3} = 35,\quad \binom{9}{2} = 36,\quad \binom{16}{5} = 4368
\frac{35 \cdot 36}{4368} = \frac{1260}{4368}
\frac{1260}{4368} = \frac{105}{364}
Thus, the probability is $\boxed{\frac{105}{364}}$.
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