The answer is 12. This is the step by step
Find when f(x) = 0. By factorizing, we have
-x² + 8x - 7 = - (x - 7) (x - 1) = 0
so either x - 7 = 0 or x - 1 = 0, or simply x = 1 or x = 7.
Split the domain into three intervals, and check the sign of f(x) over each interval at some test point in the interval. The sign will tell you when the icicle is dripping (positive) or not (negative).
• [0, 1) : at x = 0, we have f(0) = -7 < 0
• (1, 7) : at x = 2, we have f(2) = 5 > 0
• (7, 10] : at x = 8, we have f(8) = -7 < 0
This tells us that the icicle is not dripping when 0 ≤ x < 1, begins to drip when x = 1, drips for the duration of 1 < x < 7, stops dripping when x = 7, and keeps on not dripping when 7 < x ≤ 10.
The mass in kg is 106.27 if the mass of a cube, M (kg), is proportional to the cube of the length of its edge, L(m).
<h3>What is a proportional relationship?</h3>
It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
We have:
The mass of a cube, M (kg), is proportional to the cube of the length of its edge, L(m).
M ∝ L³
After removing proportional sign
M = cL³
Plug M = 50 kg and L = 70 cm = 0.7 m
50 = c(0.7)³
c = 145.77 kg/m³
If L = 0.9 m, then M
M = (145.77 kg/m³)(0.9 m)³
M = 106.266 ≈ 106.27 kg
Thus, the mass in kg is 106.27 if the mass of a cube, M (kg), is proportional to the cube of the length of its edge, L(m).
Learn more about the proportional here:
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