Thread: Application of calculus

Having trouble with two parts of this application.

Matthew is an escape artist who makes his living performing daring escapes from dangerous situations. He believes he has developed an escape trick that will prove he is the equal of the great escape artist Houdini.
In his escape his feet are chained to the top of a concrete block attached to the bottom of an enormous flask. He makes his esccape from the chains as water is pumped into the flask. The flask has a circular transverse cross section. Its longitudinal cross section takes the shape of the curve with equation y=a/x^2 +b, using the floor as the x axis and the vertical center of the flask as the y axis.(refer to url)


q1)
a) State the coordinates of the two points on the curve of the flask
b) Hence, find the values of a and b. (use fractions for exact values)

i found these successfully to be a) (-0.4,4) and (-1,1)
b) a=4/7 and b=3/7

q2)
a)find the exact volume of water, in m^3, that would be required to completely fill the tank.
b)find this volume in litres, giving your answer to the nearest ten litre
c) If h is the height of the water above the floor, write an expression, using integral notation, for the volume in the flask, at height h.

d) Express the volume of water(in litres) in the flask as a function of the height of the water above the floor.

For a) i got an answer of V=integral,from 4 to 1, of 4/7y-3 dy, which gave me a calculation of 3.29
b) 3.29x1000=3290 L
i wasn't sure how to do c or d. and i am not sure if my answers to a and b are correct.

If anyone could help that would be greatly appreciated, thanks.

Originally Posted by johnsy123

Having trouble with two parts of this application.

Matthew is an escape artist who makes his living performing daring escapes from dangerous situations. He believes he has developed an escape trick that will prove he is the equal of the great escape artist Houdini.
In his escape his feet are chained to the top of a concrete block attached to the bottom of an enormous flask. He makes his esccape from the chains as water is pumped into the flask. The flask has a circular transverse cross section. Its longitudinal cross section takes the shape of the curve with equation y=a/x^2 +b, using the floor as the x axis and the vertical center of the flask as the y axis.(refer to url)


q1)
a) State the coordinates of the two points on the curve of the flask
b) Hence, find the values of a and b. (use fractions for exact values)

i found these successfully to be a) (-0.4,4) and (-1,1)
b) a=4/7 and b=3/7

q2)
a)find the exact volume of water, in m^3, that would be required to completely fill the tank.
b)find this volume in litres, giving your answer to the nearest ten litre
c) If h is the height of the water above the floor, write an expression, using integral notation, for the volume in the flask, at height h.

d) Express the volume of water(in litres) in the flask as a function of the height of the water above the floor.

For a) i got an answer of V=integral,from 4 to 1, of 4/7y-3 dy, which gave me a calculation of 3.29
b) 3.29x1000=3290 L
i wasn't sure how to do c or d. and i am not sure if my answers to a and b are correct.

If anyone could help that would be greatly appreciated, thanks.

This looks like it has come from an assessment that counts towards your final grade. Please read rule #6: http://www.mathhelpforum.com/math-he...hp?do=vsarules.

Thread closed.