3. Show by substitution that p = −x − 2y is a solution of the pressure equation above and calculate the
corresponding velocity v assuming λ = 1.

 

10. Show by substitution that
 
is a solution of the transport equation with the velocity calculated in Q3. This would correspond to the spread of pollutant that was initially in a thin line along y = x. Hint: To reduce your writing, you may find it useful to write this as   with  

evaluate the expression $-x+4yz$ when $x=-2$, $y=-1$ show substitution and solve it

The kinetic energy KE of an object of mass m moving with a velocity v is defined as. If a forceacts on the object, moving it along the x-axis fromto, the Work-Energy Theorem states that the net work done is equal to the change in the kinetic energy: , whereis the velocity atand is the velocity at.

1. Letbe the position function of the object at time t and,the velocity and acceleration function. Prove the Work-Energy Theorem by first using substitution rule for Definite integrals (4.5.5) to show that

Then use Newton’s Second law of Motion () and the substitution to evaluate the integral.

2. How much work (in ft-lb) is required to hurl a 12-lb bowling ball at 20 mi/h (Note: Divide the weights in pounds by 32, the acceleration due to gravity, to find the mass, measured in slugs.)

The demand equation for a product is given by (p+10%(q +20) = 1000 (in dollars), and the supply equation is 4-4p+10 = 0 (in dollars). a) Verify, by substitution, that market equilibrium occurs when p = 10 and q = 30