Question FV, (due) - PMT i) Future Value, PV. (due)- PMT ii) Present Value, FV (due) PV (due) PMT (1 + i)" (1+1) iii) s(0-1)="]=> ] 11+(17) 10+1 (**-"]=> 1. Frank deposited $250 at the beginning of each month for four years into a savings account. For the next eight years he made no further deposits but left the money in the account. The savings account paid interest at 4.5% compounded monthly. i) What will the balance be after the first four years? ii) What will the balance be after 12 years? iii) How much in total he deposited? iv) How much interest will have been earned?

Write an iterated integral for SSA R bounded by y = √√x, y = 0, and x = 4 using a. vertical cross-sections, b. horizontal cross-sections. dA over the region R Write an iterated integral for SSA R bounded by y = √√x, y = 0, and x = 4 using a. vertical cross-sections, b. horizontal cross-sections. dA over the region R

3.[5 marks) Let D be the region in the first quadrant (x > 0, y > 0) of the xy-plane bounded by the curves y = VX, y = 2VX, x2 + y2 = 1 and x2 + y2 = 4. Using a change of variables, evaluate the double integral: 2.2? + y2 dA. S12 Hint: Use implicit differentiation to calculate the Jacobian.

Transcribed image text: = 3.[5 marks) Let D be the region in the first quadrant (x >0, y > 0) of the xy-plane bounded by the curves y = VT, y = 277, 2? + y2 = 1 and 2 + y2 = 4. Using a change of variables, evaluate the double integral: 2.x2 + y2 dA ту Hint: Use implicit differentiation to calculate the Jacobian. Sl.

What should be the minimum cross-sectional area of each conductor in a two-core cable 100 m long to limit the total voltage drop to 4% of the declared voltage of 250V when the conductors carry 60A ? The resistivity of the conductor is 2·845 µΩ cm. ANS IS [0·34 cm2]

Transcribed image text: A solar system is modelled by R3, with a sun at the origin. Let D be R3 with the origin removed. The gravitational force field exerted by the sun on an object of mass 1 at the point (x, y, z) in D is given by F(x, y, z) = 1 (502 + y2 + 2) 0 (a) [1 mark] Show that F is conservative on R3 - (0,0,0). (b) (1 mark] A meteor of mass 1 is travelling in the solar system. At any time time t, the position of the meteor is given by R(t) = (t, t, t2 - 3) Calculate the work done by the sun on the meteor when 0 <t<2. (e) [2 marks] This solar system is covered in dust particles, which causes the same meteor as in (b) to gain mass as it travels through the solar system. If m is the mass of the meteor and s is the distance travelled by the meteor, then the rate at which m changes with respect to s at the point (x,y,z) is given by dm ds Calculate the total change in the mass of the meteor between t = 0 and t = 2.

Gasoline-contaminated groundwater has flowed under a residentialdwelling from a nearby gasoline station. Two meters beneath the 100m2 dirt floor of the residential basement, theconcentration of hydrocarbon vapors in the soil air is 25 ppm on amass/mass basis. Estimate the flux density of gasoline vapor andthe daily rate of vapor transport into the basement by moleculardiffusion. Assume an approximate diffusion coefficient of10-2 cm2/sec for gasoline vapor inthe soil and, the basement is well ventilated, so that the gasolinevapor concentration in the basement is much less than 25 ppm. Airdensity is approximately 1.2 g/1000 cm3 at 1atm pressure and 20˚C.