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Home » After increasing each leg by 2 cm, the new legs are 10 cm and 17 cm. The new area is: - AMAZONAWS

After increasing each leg by 2 cm, the new legs are 10 cm and 17 cm. The new area is: - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 Since the number of cultures must be whole, we round to 259.

📌 A train travels at a constant speed of 80 km/h. It passes a station at 2:15 PM and reaches the next station 45 km away at 3:00 PM. How fast is the train actually going when it passes the second station?

📌 Time taken = 3:00 PM – 2:15 PM = 45 minutes = 0.75 hours.

📌 Distance covered = 45 km.

📌 Speed = distance ÷ time = \( 45 \div 0.75 = 60 \) km/h.

📌 So the speed at the second station is 60 km/h.

📌 In a right triangle, one leg is 6 cm longer than the other, and the hypotenuse is 15 cm. What is the length of the shorter leg?

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To find the cubic polynomial \( f(x) = ax^3 + bx^2 + cx + d \), we use...
\( f(1) = a(1)^3 + b(1)^2 + c(1) + d = 3 \), which simplifies to:
a + b + c + d = 3
\( f(2) = a(2)^3 + b(2)^2 + c(2) + d = -1 \), which simplifies to:
8a + 4b + 2c + d = -1
\( f(3) = a(3)^3 + b(3)^2 + c(3) + d = 2 \), which simplifies to:
27a + 9b + 3c + d = 2
\( f(4) = a(4)^3 + b(4)^2 + c(4) + d = 5 \), which simplifies to:
64a + 16b + 4c + d = 5
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Find the area of the region enclosed by the curves \( y = x^2 \) and \...
To find the area of the region enclosed by the curves \( y = x^2 \) an...
x^2 = 4x - x^2.
2x^2 - 4x = 0.
Factoring out \( 2x \):
2x(x - 2) = 0.
Thus, the points of intersection are \( x = 0 \) and \( x = 2 \).
The area \( A \) between the curves from \( x = 0 \) to \( x = 2 \) is...
A = \int_0^2 \left((4x - x^2) - x^2\right) \, dx = \int_0^2 (4x - 2x^2...
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