Consider the the following series. [infinity] 1 n3 n = 1 (a) use the sum of the first 10 terms to estimate the sum of the given series. (round the answer to six decimal places.) s10 = (b) improve this estimate using the following inequalities with n = 10. (round your answers to six decimal places.) sn + [infinity] f(x) dx n + 1 ≤ s ≤ sn + [infinity] f(x) dx n ≤ s ≤ (c) using the remainder estimate for the integral test, find a value of n that will ensure that the error in the approximation s ≈ sn is less than 0.0001.

Determine the volume of a cylinder bucket if the diameter is 8.5 in. and the height is 11.5 in.

Jace wrote a sentence as an equation. 56 is 14 more than a number. 14+ = 56 which statement best describes jace's work? jace is not correct. the phrase more than suggests using the symbol > and jace did not use that symbol. jace is not correct. he was correct to use addition, but the equation should be 56+ p = 14 jace is not correct. the first number in the sentence is 56, so the equation should start with 56. jace is correct. the phrase more than suggests addition, so jace showed that 14 plus a variable equals 56. o

In a two-digit number the units' digit is 7 more than the tens' digit. the number with digits reversed is three times as large as the sum of the original number and the two digits. find the number.