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Question about Quotient and remainder

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Use synthetic division to find the quotient q(x) and remainder r

(5 x 3 - 21 x 2 - 103) / (x - 5)

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This solution is comprised of a detailed explanation to use synthetic division to find the quotient q(x) and remainder r.

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SOLUTION

Ramp length 8ft
N

F
Mgsinθ 20 inches = 1.67ft

Mgcosθ
θ Mg

Let the mass of the keg be m1 and that of the beer be m2. Total mass M = m1+ m2.

Various forces acting on the beer keg are shown in the fig.. Total weight Mg is resolved into components Mgcosθ perpendicular to the ramp and Mgsinθ parallel to the ramp. Normal reaction N = Mgcosθ. F is the frictional force on the keg surface from the ramp.

Net linear force acting on the keg parallel to the ramp = Mgsinθ -F. Under this net force the keg starts to accelerate linearly down the ramp. In other words, this net force provides the keg with linear acceleration (and velocity) parallel to the ramp.

Linear acceleration of the keg down the ramp = a = (Mgsinθ ...

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  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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