Do as indicated. 1. A certain province widely cultivates maize crops during the dry season. The average weight (in tons) of the harvested crops is modelled by h(x, y, z)=240+y²ln(√27-2), where z is the average amount of rainfall, y is the amount of nitrogen in the soil, and z is the number of plants infected by several vector-borne viruses. a. What is the total average weight of the harvested maize crops at the end of the planting season if y=2.86, z = 32, and 8-e? b. Compute for h(0,0,0). Justify your result. c. Find the domain of the function h. In(4xy) 2. If w du - cos(2yz - 3), zlog(t), y4e and zsin(-1). Find dt 3. Use Lagrange multipliers to solve for the dimensions of a closed right circular cylindrical can with smallest surface area whose volume is 27 in". 4. Evaluate the double integral given by [f 5. Given the region R on the right, use vertical strip, SET UP the double integral that will solve its area. 1 -dydz I (1, 1) y = √z Z y=r³ THE

Find the intensities of earthquakes whose magnitudes are aR=6.0andbR=7.9.

The resistance of a copper wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. A copper wire with a diameter of 0.0126inch has a resistance of 64.9ohms per thousand feet. What length of 0.0201-inch-diameter copper wire will produce a resistance of 33.5ohms?

The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?

Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?

Solve each problem. w is directly proportional to z. If w=-6 when z=2, find w when z=-3.

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

Find the constant of proportionality. E varies jointly with I and R. If R=25 and I=5, then E=125.

All dimensions are in inches. Round the answers to 3 decimal places. a. If y = 2.145" find x. b If y = 2.265", find x.