212-5t+8 3. The value of a virtual currency (in $100) is given by V(t)= where t is the number " t²+4 of weeks since the virtual currency has been introduced. (a) Using the function given, determine the average rate of change of the virtual currency's value for (i) the first 2 weeks. (ii) from week 2 to week 4 (b) Find the instantaneous rate of change of the virtual currency's value at 2 weeks. (Round your answer to the nearest whole number) (c) What can you conclude from the results from (a) and (b)?

34) From a full 50-liter container of a 40% concentration of acid, x liters is removed and replaced with 100% acid. (a) Write the amount of acid in the final mixture as a function of x.

Boyle's Law expresses the relationship between the pressure, P, and the volume, V, of a gas under constant temperature. PVC where C is a constant Suppose the pressure and volume change with respect to time. (a) Write the equation that relates how fast the the pressure and volume are changing with respect to time. Use Leibniz notation for any derivatives, in addition to upper case letters for P and V. (b) Suppose the pressure is increasing by 20 atmospheres per minute when the volume is 600 cubic centimeters and the pressure is 150 atmospheres. How fast is the volume changing? dv dt -units-

y= 14x-2 6, *=4 Find the slope and the equation of the tangent line to the graph of the given function at the given value of x. 1 y= 14x +2x+6; x=4 + 2x +6; x= 4 The slope of the tangent line to the graph at the point x= 4 is. (Simplify your answer.)

Which of the following are one-to-one functions? OR = {(– 5,0), (2, 3), (6, 5), (8, 7), (11, 10), (15, 16)} ОМ - {(- 5, — 2), (3, 1), (3, 4), (5, 7), (9, — 6), (10, 13)} OS = {(– 2, – 3), ( – 5, 9), (2, 6), (5, 3), (6, – 4), (10, – 8)} OG = {(4, – 2), (1, 0), (3, – 1), ( – 1, – 1), (7, 1), (5, 2)} OF = {(– 5, – 1), (0, 0), (3, 1), (4, 6), (9, 7), (10, 14)}

Find derivative

IQ of a person is given by the formulaIQ =MA/CA × 100,where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.