Question (1 point) Find the solution to the differential equation dy = 0.7(y – 150) - dt if y = 50 when t = 0. = y = 50/(105t+1)

Find the directional derivative of f at P in the direction of a vector making the counterclockwise angle 0 with the positive x-axis. f(x, y) = 5/æy; P(2,8); 0 = 3 NOTE: Enter the exact answer.

Which of the following is a true statement? Voltage is the energy per unit charge. Voltage is a force. Voltage is the product of current and time. Voltage is the same as power.

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.

Need help on this please 2) By direct integration, find the Laplace transforms of the following signals: sin : 1 1 1/e АД 1 TI 1 (a) (b) (c)

Ball Hits Wall 1 234567 A racquet ball with mass m 0.233 kg is moving toward the wall at v 18.5 m/s and at an angle of e 26 with respect to the horizontal. The ball makes a perfectly elastic collision with the solid, frictionless wall and rebounds at the same angle with respect to the horizontal. The ball is in contact with the wall for t 0.071 s.