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erastovalidia [21]
2 years ago
9

Use the change of base formula to compute log1/4 6. Round your answer to the nearest thousandth.

Mathematics
1 answer:
Arte-miy333 [17]2 years ago
8 0

Answer:

-1.292

Step-by-step explanation:

The change of base formula is log_b(a)=\frac{log(a)}{log(b)}, therefore:

log_{\frac{1}{4}}(6)=\frac{log(6)}{log(\frac{1}{4})}\approx-1.292

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Step-by-step explanation:

Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.

Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²

So, V = Ah = 2h = 2(10 - x)

The rate of change of volume is thus

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Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt

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And the height at this point when x = 8 inches = 8 in × 1 ft/12 in  = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft

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