What is the Fuel Consumption of a Motor After 7 Minutes?

AI Thread Summary
The discussion revolves around a homework problem regarding the fuel consumption rate of an engine over time, defined by the equation R = 10 + 10/(2t + 1). Participants seek clarification on the equation's interpretation and how to approach various parts of the problem, including sketching the function, calculating the rate after 7 minutes, finding the limiting value as time increases, and determining total consumption in the first 7 minutes. One user indicates they can solve part of the problem but expresses uncertainty about the others. The conversation highlights the need for clear mathematical understanding and problem-solving strategies. Overall, the thread emphasizes collaborative learning in tackling complex mathematical concepts.
steve 99
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Homework Statement



I posted int he other section but not sure if that area was a bit high maths

I have this questions an answer to it would be great.
.Q.1 At t minutes after an engine starts, the rate of fuel consumption is Rkg per minute. it is given by R=10+ 10/2t+1.

a) Sketch R as a function of t

b) find the rate of consumption after 7 mins

c) find the limiting value of R as t becomes very large

d) calculate the total consumption in the 1st 7 mins

not sure how to do it
Thank You

Homework Equations





The Attempt at a Solution



I can do part 2
 
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You must show an attempt, although it may be something very basic.
 
steve 99 said:

Homework Statement



I posted int he other section but not sure if that area was a bit high maths

I have this questions an answer to it would be great.
.Q.1 At t minutes after an engine starts, the rate of fuel consumption is Rkg per minute. it is given by R=10+ 10/2t+1.
First, is this R= 10+ (10/2t)+ 1 or R= 10+ 10/(2t+ 1)

a) Sketch R as a function of t
Okay, have you done that? Just calculate some values and draw the graph.

b) find the rate of consumption after 7 mins

c) find the limiting value of R as t becomes very large

d) calculate the total consumption in the 1st 7 mins

not sure how to do it
Thank You

Homework Equations





The Attempt at a Solution



I can do part 2
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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