[填空题]
Lohan receives an antique vaseg4ogvj2;zcs9jbmj 2m3 9 smk 1 as a gift from her grandparents. S6drhe szw67r25f nsx+ he decides to model the shape of the vase to calculate its volums+62w rxdnezf6hs r57 e.
She places the vase horizontally on a piece of paper and uses a pencil to mark five representative points (0,5),(7.5,10),(17,7.5),(25,3) and (35,7.5) , as shown below. These points are connected to form a symmetrical cross-section about the x -axis. All units are in centimetres.
Lohan initially uses a straight line to model the section from (25,3) to (35,7.5) .
1. Determine the equation of the line that passes through these two points.
Lohan thinks that a quadratic curve might be a good model for the section from (0,5) to (25,3) . She carries out a least squares regression using this model for the points she has recorded.y =ax+b a = b =
2. 1. Determine the equation of the least squares regression quadratic curve found by Lohan.y≈ $ax^b+cx+d$ a = b = c = d =
2. By considering the gradient of the curve at the point where x=10 , determine whether the quadratic regression curve is a good model or not.
Lohan decides that a cubic curve for the entire section from (0,5) to (35,7.5) would be a better fit.
3. Find the equation of the cubic model.
Using this model, Lohan estimates the volume of the vase by calculating the volume of revolution about the x -axis.y≈ $ax^b+cx^d+ex+f$ a = b = c = d = e = f =
4. Find the volume of the vase estimated by Lohan.
Lohan subsequently fills the vase with water and discovers that the true volume is 5500 $cm^3$ . ≈ $cm^3$
5. Calculate the percentage error in Lohan's estimate of the volume. %
