) A metal component is subjected to heat-treatment called normalisation. The component is eated to a temperature T, (which is above the critical phase transformation temperatures) nd cooled in air. The elementary change dT(t) of temperature T(t) of a heated component s determined from the heath energy balance equation cmdT(t)=-hA(T(1)– Tuir)dt vhere cmdT(t) is the energy which is lost due to cooling; hA(T(t)– Tuir )dt is the total heat lux from the component to the air during an infinitesimally small time interval dt. The onstant c [J/(kg K)] is the specific heath capacity, m is the mass of the component in kg, h W/(m² K)] is the heat transfer coefficient and A is the surface area in m?. Derive an eguation which gives the temperature T7) as a function of the cooling time t.

11. INSTRUCTIONS: Two cars start moving from the same point. One travels south at 60 miles per hour. The other car travels west at 25 miles per hour. At what rate is the distance between the cars increasing 2 hours later? 12. 5 pu of: INSTRUCTIONS: State L(x) (the linearization) at a = ㅠ 6 f(x) = sin(x)

Active oxygen and free radicals are believed to be exacerbating factors in causing cell injury and aging in living tissue . Researchers are therefore interested in understanding the protective role of natural antioxidants. In the study of one such antioxidant (Hsian-tsao leaf gum), the antioxidation activity of the substance has been found to depend on concentration in the following way:   dA(c)\dc=k[L−A(c)],   A(0)=0.dA(c)dc=k[L−A(c)],   A(0)=0. In this equation, the dependent variable AA is a quantitative measure of antioxidant activity at concentration cc. The constant LL represents a limiting or equilibrium value of this activity, and kk a positive rate constant.   Let B(c)=A(c)−L and reformulate the given initial value problem in terms of this new dependent variable, B.dB(c)/dc=  B(0)= Solve the new initial value problem for B(c)and then determine the quantity A(c).A(c)= Does the activity A(c) ever exceed the value L?  ? yes no  Determine the concentration at which 95% of the…

Activity 2.5.4. Use known derivative rules, including the chain rule, as needed to answer each of the following questions. a. Find an equation for the tangent line to the curve y = ve* +3 at the point where x = 0. b. If s(t) = 1 represents the position function of a particle moving horizontally along an axis at time t (t2 + 1)3 (where s is measured in inches and t in seconds), find the particle's instantaneous velocity at t = 1. Is the particle moving to the left or right at that instant? c. At sea level, air pressure is 30 inches of mercury. At an altitude of h feet above sea level, the air pressure, P, in inches of mercury, is given by the function P = 30e-0.0000323h. Compute dP/dh and explain what this derivative function tells you about air pressure, including a discussion of the units on dP/dh. In addition, determine how fast the air pressure is changing for a pilot of a small plane passing through an altitude of 1000 feet. d. Suppose that f(x) and g(x) are differentiable…