darrel wants to see how much water is wasted by his leaky facet. he put a 4 gallon bucket under the fausey. after 24 hours the b
1 answer:
Answer:
The quantity of water filled in the bucket after 70 hours is 11.67 gallon .
Step-by-step explanation:
Given as :
The quantity of water filled in the bucket after 24 hours = 4 gallon
Let The quantity of water filled in the bucket after 70 hours = x gallon
So, According to question
<u>Applying unitary method</u>
∵In 24 hours, The quantity of water filled in bucket = 4 gallons
So,In 1 hour, The quantity of water filled in bucket = gallon
∴ In 70 hour, The quantity of water filled in bucket = × 70 gallon
I.e x = gallons
Or, x = 11.67 gallons
So,The quantity of water filled in the bucket after 70 hours = x = 11.67 gallon
Hence, The quantity of water filled in the bucket after 70 hours is 11.67 gallon . Answer
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Answer:
a) integral = 24.72
b) |Error| ≤ 0.4267
Step-by-step explanation:
a)
The integral:
can be approximated with the midpoint rule, as follows:
6.7*(0.8 - 0.0) + 8.9*(1.6 - 0.8) + 6.9*(2.4-1.6) + 8.4*(3.2 - 2.4) = 24.72
(that is, all the intervals are 0.8 units length and f(x) is evaluated in the midpoint of the interval)
b)The error bound for the midpoint rule with <em>n</em> points is:
|Error| ≤ K*(b - a)^3/(24*n^2)
where <em>b</em> and are the limits of integration of the integral and K = max |f''(x)|
Given that -5 ≤ f''(x) ≤ 1, then K = 5. Replacing into the equation:
|Error| ≤ 5*(3.2 - 0)^3/(24*4^2) = 0.4267