The table gives the gross world product, G, which measures global output of goods and services. If t is in years since 1950, the regression line for these data is $G=3.543+0.734 t$.

$$\begin{array}{|c|ccccccc|} \hline \text { Year } & {1950} & {1960} & {1970} & {1980} & {1990} & {2000} \\ \hline G & {6.4} & {10.0} & {16.3} & {23.6} & {31.9} & {43.2} \\ \hline \end{array}$$

Interpret the slope of the line in terms of gross world product.

Evaluate the iterated integral. $\int_{0}^{1} \int_{0}^{y}\left(6 x+5 y^{3}\right) d x d y$

Consider the system of equations $y^{\prime}=2 x+z, \ z^{\prime}=3 x y+x^{2} z,$ with initial conditions y = 2 and z = 0 when x = 0. Start with the initial guesses Y,(x) = 2, Z,,(x) = 0, use the method of successive approximations, and determine Y,(x) and $Z_3(x)$.

Consider the initial-value problem $y^{\prime \prime}=x^{2} y^{\prime}+x^{4} y,$ with $y=5$ and $y^{\prime}=1$ when x = 0. Change this problem to an equivalent problem involving a system of two equations for two unknown functions y = Y(x) and z = Z(x), where z = y’. Then use the method of successive approximations, starting with initial guesses $Y,(x) = 5$ and $Z_0(x) = 1$, and determine $Y_3(x)$ and $Z,(x).$

The total drag coefficient for an airplane wing is, where CD0 is the form drag coefficient, CL is the lift coefficient and is the aspect ratio of the wing. The power is given by P = FDV = 1/2 CD p V3S. For level flight the lift is equal to the weight, so W/S p 1/2pCLV2, where W/S is called the “wing loading.” Find an expression for V for which the power is a minimum in terms of VMinPower = f (p, $\delta$, W/S,CD0), and find the V for minimum power when p = 1 kg/m3, $\delta$= 10, W/S = 600 N/m2, and CD = 0.02.

A 0.900-V potential difference is maintained across a 1.50-m length of tungsten wire that has a cross-sectional area of 0.600 mm2. What is the current in the wire?

A right circular cone of height h=16 meters and radius r=6 meters is constructed, and in the process, errors of $\Delta r$ and $\Delta h$ are made in the radius and height, respectively. Let S be the lateral surface area of the cone. Complete the table above to show the relationship between $\Delta S$ and dS for the indicated errors.

ee 8. A silicon chip is 14 nanometers thick. A nanometer is equal to 0.000000001 meter. Express the thickness of the chip using scientific notation. @ $1.4 \times 10 ^ { - 9 } m$ 8) $1.4 \times 10 ^ { - 8 } m$

$$1.4 \times 10 ^ { 8 } m$$

) $1.2 \times 10 ^ { 9 } m$

A stream of incompressible liquid moving at low speed leaves a nozzle pointed directly downward. Assume the speed at any cross section is uniform and neglect viscous effects. The speed and area of the jet at the nozzle exit are $V_{0}$ and $A_{0}$, respectively. Apply conservation of mass and the momentum equation to a differential control volume of length dz in the flow direction. Derive expressions for the variations of jet speed and area as functions of z. Evaluate the distance at which the jet area is half its original value. (Take the origin of coordinates at the nozzle exit.)

A common commercial hydrometer for measuring the amount of antifreeze in the coolant system of an automobile engine consists of a chamber with differently colored balls. The system is calibrated to give the range of specific gravity by distinguishing between the balls that sink and those that float. The specific gravity of an ethylene glycol-water mixture varies from 1.012 to 1.065 for 10% to 50% by weight of ethylene glycol. Assume there are six balls, 1 cm in diameter each, in the chamber. What should the weight of each ball be to provide a range of specific gravities between 1.01 and 1.06 with 0.01 intervals?

The velocity of oil (S=0.8) through the 5-cm smooth pipe is 1.2 m/s. Here L=12 m, z1=1 m, z2=2 m, and the manometer deflection is 10 cm. Determine the flow direction, the resistance coefficient f, whether the flow is laminar or turbulent, and the viscosity of the oil.

Find the inverse function $f^{-1}$ of the function f. Then, using a graphing utility, graph both f and $f^{-1}$ in the same viewing window. $f(x)=x^{3 / 5}-2$

Find the values of $d$

$$13= d \div 6$$

Find the radius of (a) a nucleus of and (b) a nucleus of $^{238} _{92} U$ $^4 _2 He$