1. Consider the data sets below, determine if it is reasonable to assume that y is proportional to x. If it is, approximate the constant of proportionality. If it is not, describe why this assumption is not reasonable. x 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Y 1 1.2 1.44 1.69 1.96 2.25 2.56 2.89
1. Consider the data sets below, determine if it is reasonable to assume that y is proportional
to x. If it is, approximate the constant of proportionality. If it is not, describe why this
assumption is not reasonable.
| x | 1 | 1.1 | 1.2 | 1.3 | 1.4 | 1.5 | 1.6 | 1.7 |
| Y | 1 | 1.2 | 1.44 | 1.69 | 1.96 | 2.25 | 2.56 | 2.89 |
2. If water bottles are geometrically similar, how much more water will a bottle that is 50 cm
tall hold than one that is 20 cm tall?
3. Use dimensional analysis to derive an expression for the volume flow rate, q, in terms of r
(the radius of the pipe), µ (the viscosity of the fluid) and dp
dz (the fall in pressure per unit length)
| q | r | µ | dp/dz |
| L 3T −1 |
L | ML−1T −1 |
ML−1T −2 |
4. Consider the below data set:
| X | 75 | 80 | 93 | 65 | 87 | 71 | 98 | 68 | 84 | 77 | |
| Y | 82 | 78 | 86 | 72 | 91 | 80 | 95 | 72 | 89 | 74 |
(a) Fit the straight line curve to the data
(b) Predict the value of y when x = 80
5. Find the solution of the differential equations that satisfies the given initial condition:
(a) (x^2 + 1)dy/dx + 3x(y − 1) = 0, y(0) = 2
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