Velocity question and Riemann Sum question (1 Viewer)

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A particle is moving in a straight line and its displacement s from the initial position after t seconds is given by s= 36t-t^2. Find a) its velocity at time t and b) its initial velocity.

This is how I did it and I don't know if it is correct (most likely not)

a) dv/dt = 36-2t
b) when t=0
36 - 3(0)^2
therefore initial velocity = 36



Another question

Use a Riemann sum to approximate the area under y = e-x between x = 0 and x = 3 by

dividing the interval [0,3] into 3 equal subintervals and
calculating the height of the rectangles at the right hand end of each subinterval.
Enter your answer as a decimal correct to 2 decimal places in the box below.

 

[pLuvia]

a)v=ds/dt=36-2t
b)Initial velocity when t=0
v=36m/s

 

[Riviet]

Another question

Use a Riemann sum to approximate the area under y = e^-x between x = 0 and x = 3 by

dividing the interval [0,3] into 3 equal subintervals and
calculating the height of the rectangles at the right hand end of each subinterval.
Enter your answer as a decimal correct to 2 decimal places in the box below.

Width of each subinterval = 1 unit

Height at right side of first subinterval at x=1 is y=e^-1

Height at right side of second subinterval at x=2 is y=e^-2

Height at right side of third subinterval at x=3 is y=e^-3

.'. Area =:= 1(e^-1+e^-2+e^-3)
=0.55 units² (2dp)

 

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awesome! thanks guys

 

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riviet, your answer is incorrect

it's actually 0.55

do you know what you did wrong?

 

[Riviet]

All along until about 8pm, I thought it was the line y= e - x, please specify that it's an exponential function using either the notation e^-x or e[ sup]-x[/sup]. Correct solution edited above.