Intergrate/differentiate?

Mar 2010
3
0
could someone explain too me the answer to this question?

water is emptied from a water tank using a tap at its base. The depth of the water in the tank, d cm, can be modelled by the function
\(\displaystyle
d(t) = (((t-150)^2)/1000)+1
\)

a) show it can be written as
d(t)=0.001t^2 - 0.3t + 23.5

b) find value of d'(80)

any help would be appreciated, im really stuck. even just an explination of how to go about this.
 
Apr 2010
384
153
Canada
could someone explain too me the answer to this question?

water is emptied from a water tank using a tap at its base. The depth of the water in the tank, d cm, can be modelled by the function
\(\displaystyle
d(t) = (((t-150)^2)/1000)+1
\)

a) show it can be written as
d(t)=0.001t^2 - 0.3t + 23.5

b) find value of d'(80)

any help would be appreciated, im really stuck. even just an explination of how to go about this.
Part A is asking you to expand,

\(\displaystyle
d(t) = \frac{ (t-150)^2)}{1000}+1 = \frac{ t^2 - 300t + 150^2 }{1000} + 1 = 0.001t^2 - 0.3t + 23.5
\)

Part B is asking for the derivative and to evaluate at 80.

\(\displaystyle d`(t) = 0.002t -.3 \)

\(\displaystyle d`(80) = 0.002(8) -. 3 \)
 
Apr 2010
384
153
Canada
could someone explain too me the answer to this question?

water is emptied from a water tank using a tap at its base. The depth of the water in the tank, d cm, can be modelled by the function
\(\displaystyle
d(t) = (((t-150)^2)/1000)+1
\)

a) show it can be written as
d(t)=0.001t^2 - 0.3t + 23.5

b) find value of d'(80)

any help would be appreciated, im really stuck. even just an explination of how to go about this.
Part A is asking you to expand,

\(\displaystyle
d(t) = \frac{ (t-150)^2)}{1000}+1 = \frac{ t^2 - 300t + 150^2 }{1000} + 1 = 0.001t^2 - 0.3t + 23.5
\)

Part B is asking for the derivative and to evaluate at 80.

\(\displaystyle d`(t) = 0.002t -.3 \)

\(\displaystyle d`(80) = 0.002(8) -. 3 \)
 
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